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<loc>https://alphabetamath.cc/algebraic-geometry/etale-covers-and-the-etale-fundamental-group-examples</loc>
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<url>
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<loc>https://alphabetamath.cc/algebraic-geometry/projective-git-from-linearized-line-bundles-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/complex-topological-k-theory-and-bott-periodicity-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/cup-cap-cross-products-and-cohomology-rings-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/cup-cap-cross-products-and-cohomology-rings</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/cw-complexes-and-cellular-homology-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/cw-complexes-and-cellular-homology</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/fibrations-fiber-bundles-and-homotopy-exact-sequences-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/generalized-cohomology-and-the-atiyah-hirzebruch-spectral-sequence-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/generalized-cohomology-and-the-atiyah-hirzebruch-spectral-sequence</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/higher-homotopy-groups-and-cofiber-sequences-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/higher-homotopy-groups-and-cofiber-sequences</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/homology-axioms-degree-and-classical-applications-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/homology-axioms-degree-and-classical-applications</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/hurewicz-whitehead-freudenthal-and-cw-approximation-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/hurewicz-whitehead-freudenthal-and-cw-approximation</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/leray-hirsch-thom-isomorphism-and-gysin-sequences-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/leray-hirsch-thom-isomorphism-and-gysin-sequences</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/local-coefficients-twisted-homology-and-duality-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/local-coefficients-twisted-homology-and-duality</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/obstruction-theory-postnikov-towers-and-classifying-spaces-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/obstruction-theory-postnikov-towers-and-classifying-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/orientations-poincare-lefschetz-and-alexander-duality-examples</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<loc>https://alphabetamath.cc/algebraic-topology/orientations-poincare-lefschetz-and-alexander-duality</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/real-clifford-modules-ko-and-abs-orientations-examples</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/real-clifford-modules-ko-and-abs-orientations</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/relative-homology-excision-and-mayer-vietoris-examples</loc>
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<loc>https://alphabetamath.cc/algebraic-topology/relative-homology-excision-and-mayer-vietoris</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/simple-homotopy-whitehead-groups-and-torsion-examples</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/simple-homotopy-whitehead-groups-and-torsion</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/simplicial-complexes-and-simplicial-homology-examples</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/simplicial-complexes-and-simplicial-homology</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/simplicial-subdivision-and-simplicial-approximation-examples</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/simplicial-subdivision-and-simplicial-approximation</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/singular-chains-and-singular-homology-examples</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/singular-chains-and-singular-homology</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/singular-cohomology-and-coefficient-theorems-examples</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/singular-cohomology-and-coefficient-theorems</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/spectra-and-stable-homotopy-groups-examples</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/spectra-and-stable-homotopy-groups</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/stiefel-whitney-and-euler-classes-by-universal-constructions-examples</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/stiefel-whitney-and-euler-classes-by-universal-constructions</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/the-serre-spectral-sequence-and-applications-examples</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/the-serre-spectral-sequence-and-applications</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/thom-spectra-and-unoriented-bordism-detection-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/thom-spectra-and-unoriented-bordism-detection</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/topological-vector-bundles-and-grassmannian-classification-examples</loc>
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<url>
<loc>https://alphabetamath.cc/algebraic-topology/topological-vector-bundles-and-grassmannian-classification</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/abc-mcmc-and-sequential-abc-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/abc-mcmc-and-sequential-abc</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/adaptive-empirical-bayes-credible-set-calibration-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/adaptive-empirical-bayes-credible-set-calibration</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/adaptive-mcmc-convergence-and-limitations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/adaptive-mcmc-convergence-and-limitations</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/approximate-bayesian-computation-and-simulation-based-inference-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/approximate-bayesian-computation-and-simulation-based-inference</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/asymptotically-robust-permutation-tests-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/asymptotically-robust-permutation-tests</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/bayesian-models-priors-and-posterior-laws-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/bayesian-models-priors-and-posterior-laws</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/block-bootstrap-for-dependent-data-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/block-bootstrap-for-dependent-data</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/bootstrap-failure-and-subsampling-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/bootstrap-failure-and-subsampling</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/conjugate-families-and-posterior-prediction-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/conjugate-families-and-posterior-prediction</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/cross-validation-risk-and-model-comparison-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/cross-validation-risk-and-model-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/data-assimilation-variational-and-ensemble-methods-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/data-assimilation-variational-and-ensemble-methods</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/dirichlet-normal-mixture-contraction-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/dirichlet-normal-mixture-contraction</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/dirichlet-process-priors-and-finite-partition-updates-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/dirichlet-process-priors-and-finite-partition-updates</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/em-algorithm-and-latent-variable-likelihood-ascent-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/em-algorithm-and-latent-variable-likelihood-ascent</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/feynman-kac-particle-filters-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/feynman-kac-particle-filters</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/finite-group-permutation-inference-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/finite-group-permutation-inference</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/functional-bayesian-limits-and-credible-set-calibration-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/functional-bayesian-limits-and-credible-set-calibration</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/gaussian-process-posterior-contraction-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/gaussian-process-posterior-contraction</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/gaussian-process-priors-and-posterior-laws-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/gaussian-process-priors-and-posterior-laws</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/gaussian-process-support-and-concentration-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/gaussian-process-support-and-concentration</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/general-state-mcmc-kernels-and-reversibility-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/general-state-mcmc-kernels-and-reversibility</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/generalized-bayes-loss-updates-and-temperature-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/generalized-bayes-loss-updates-and-temperature</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/gibbs-sampling-and-scan-schemes-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/gibbs-sampling-and-scan-schemes</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/hamiltonian-monte-carlo-and-leapfrog-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/hamiltonian-monte-carlo-and-leapfrog</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/hierarchical-bayesian-models-and-partial-pooling-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/hierarchical-bayesian-models-and-partial-pooling</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/identifiability-and-approximation-bias-in-computational-inference-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/identifiability-and-approximation-bias-in-computational-inference</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/iid-bootstrap-and-jackknife-validity-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/iid-bootstrap-and-jackknife-validity</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/iid-monte-carlo-integration-and-error-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/iid-monte-carlo-integration-and-error</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/iid-posterior-contraction-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/iid-posterior-contraction</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/importance-sampling-and-weight-diagnostics-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/importance-sampling-and-weight-diagnostics</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/kalman-filtering-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/kalman-filtering</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/kalman-smoothing-and-rts-recursion-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/kalman-smoothing-and-rts-recursion</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/langevin-monte-carlo-mala-and-ula-examples</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/langevin-monte-carlo-mala-and-ula</loc>
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<loc>https://alphabetamath.cc/bayesian-computational-statistics/laplace-approximation-and-marginal-integration-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/laplace-approximation-and-marginal-integration</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/marginal-likelihoods-bayes-factors-and-empirical-bayes-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/marginal-likelihoods-bayes-factors-and-empirical-bayes</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/mcmc-clt-and-monte-carlo-standard-error-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/mcmc-clt-and-monte-carlo-standard-error</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/mcmc-diagnostics-and-finite-run-limitations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/mcmc-diagnostics-and-finite-run-limitations</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/mcmc-ergodicity-and-mixing-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/mcmc-ergodicity-and-mixing</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/metropolis-hastings-algorithm-and-invariance-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/metropolis-hastings-algorithm-and-invariance</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/misspecified-posterior-consistency-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/misspecified-posterior-consistency</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/multilevel-monte-carlo-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/multilevel-monte-carlo</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/numerical-optimization-for-statistical-computation-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/numerical-optimization-for-statistical-computation</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/parametric-bernstein-von-mises-and-misspecification-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/parametric-bernstein-von-mises-and-misspecification</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/particle-mcmc-pmmh-and-particle-gibbs-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/particle-mcmc-pmmh-and-particle-gibbs</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/particle-smoothing-backward-simulation-and-rbpf-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/particle-smoothing-backward-simulation-and-rbpf</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/posterior-consistency-and-tests-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/posterior-consistency-and-tests</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/posterior-prediction-and-bayesian-decision-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/posterior-prediction-and-bayesian-decision</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/posterior-propriety-and-dominated-bayes-formula-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/posterior-propriety-and-dominated-bayes-formula</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/quasi-monte-carlo-discrepancy-and-rules-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/quasi-monte-carlo-discrepancy-and-rules</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/randomized-quasi-monte-carlo-and-replicates-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/randomized-quasi-monte-carlo-and-replicates</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/rejection-sampling-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/rejection-sampling</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/resampling-algorithms-and-sampling-units-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/resampling-algorithms-and-sampling-units</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/smc-clts-error-and-degeneracy-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/smc-clts-error-and-degeneracy</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/state-space-filtering-and-predictive-laws-examples</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/state-space-filtering-and-predictive-laws</loc>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/statistical-and-computational-error-accounting-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/statistical-and-computational-error-accounting</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/synthetic-likelihood-and-indirect-inference-examples</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/synthetic-likelihood-and-indirect-inference</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/variance-reduction-and-randomized-integration-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/variance-reduction-and-randomized-integration</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/variational-inference-and-evidence-lower-bound-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/variational-inference-and-evidence-lower-bound</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/weak-nonparametric-bernstein-von-mises-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/bayesian-computational-statistics/weak-nonparametric-bernstein-von-mises</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/artin-presentation-completeness-and-braid-combing-examples</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/braid-groups/artin-presentation-completeness-and-braid-combing</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/braids-as-fundamental-groups-of-configuration-spaces-examples</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/braid-groups/braids-as-fundamental-groups-of-configuration-spaces</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/categorical-braid-actions-and-decategorification-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/braid-groups/categorical-braid-actions-and-decategorification</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/garside-structure-normal-forms-and-the-center-examples</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/braid-groups/garside-structure-normal-forms-and-the-center</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/geometric-braids-and-artin-generators-examples</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/geometric-braids-and-artin-generators</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/graded-quiver-algebras-and-derived-tensor-functors-examples</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/graded-quiver-algebras-and-derived-tensor-functors</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/hecke-markov-traces-and-polynomial-link-invariants-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/hecke-markov-traces-and-polynomial-link-invariants</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/hochschild-homology-and-triply-graded-link-homology-examples</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/hochschild-homology-and-triply-graded-link-homology</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/lawrence-krammer-bigelow-and-linearity-examples</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/lawrence-krammer-bigelow-and-linearity</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/matrix-factorizations-and-khovanov-rozansky-link-homology-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/braid-groups/matrix-factorizations-and-khovanov-rozansky-link-homology</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/ordered-and-unordered-configuration-spaces-examples</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/ordered-and-unordered-configuration-spaces</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/oriented-links-braid-closures-and-markov-equivalence-examples</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/oriented-links-braid-closures-and-markov-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/punctured-disks-mapping-classes-and-point-pushing-examples</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/braid-groups/punctured-disks-mapping-classes-and-point-pushing</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/pure-braids-fadell-neuwirth-and-asphericity-examples</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/pure-braids-fadell-neuwirth-and-asphericity</loc>
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<url>
<loc>https://alphabetamath.cc/braid-groups/rouquier-complexes-and-categorical-braid-relations-examples</loc>
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<loc>https://alphabetamath.cc/combinatorics/erdos-hajnal-for-the-e-graph-and-bird-examples</loc>
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<loc>https://alphabetamath.cc/combinatorics/finite-counting-and-binomial-coefficients</loc>
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<loc>https://alphabetamath.cc/combinatorics/finite-probability-and-the-probabilistic-method</loc>
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<loc>https://alphabetamath.cc/combinatorics/finite-probability-spaces-and-random-variables-examples</loc>
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<loc>https://alphabetamath.cc/combinatorics/finite-probability-spaces-and-random-variables</loc>
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<loc>https://alphabetamath.cc/combinatorics/formal-power-series-examples</loc>
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<loc>https://alphabetamath.cc/combinatorics/formal-power-series</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/from-generalized-niceness-to-erdos-hajnal-examples</loc>
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<loc>https://alphabetamath.cc/combinatorics/from-generalized-niceness-to-erdos-hajnal</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/generalized-niceness-and-reduction-outcomes-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/generalized-niceness-and-reduction-outcomes</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/graph-colouring-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/graph-colouring</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/graphs-walks-and-connectivity-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/graphs-walks-and-connectivity</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/incidence-algebras-and-mobius-inversion-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/incidence-algebras-and-mobius-inversion</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/inclusion-exclusion-and-the-pigeonhole-principle-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/inclusion-exclusion-and-the-pigeonhole-principle</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/induced-subgraphs-and-hereditary-graph-classes-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/induced-subgraphs-and-hereditary-graph-classes</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/integer-partitions-and-the-twelvefold-way-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/integer-partitions-and-the-twelvefold-way</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/iterative-restriction-and-comb-extraction-lemmas-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/iterative-restriction-and-comb-extraction-lemmas</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/iterative-sparsification-and-the-five-vertex-path-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/iterative-sparsification-and-the-five-vertex-path</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/lattice-paths-and-catalan-numbers-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/lattice-paths-and-catalan-numbers</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/leaf-reducibility-and-wonderful-families-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/leaf-reducibility-and-wonderful-families</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/linear-algebra-methods-in-combinatorics-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/linear-algebra-methods-in-combinatorics</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/linear-recurrences-and-rational-generating-functions-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/linear-recurrences-and-rational-generating-functions</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/matchings-covers-menger-and-network-flows-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/matchings-covers-menger-and-network-flows</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/modules-substitution-and-prime-graphs-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/modules-substitution-and-prime-graphs</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/plane-graphs-euler-and-the-five-colour-theorem-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/combinatorics/plane-graphs-euler-and-the-five-colour-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/polynomial-rodl-and-viral-equivalence-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/polynomial-rodl-and-viral-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/property-star-and-comb-outcomes-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/property-star-and-comb-outcomes</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/pure-pairs-forests-and-path-antipath-classes-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/pure-pairs-forests-and-path-antipath-classes</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/quantitative-induced-density-and-the-loglog-step-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/quantitative-induced-density-and-the-loglog-step</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/quotient-blockades-and-mixing-relations-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/combinatorics/quotient-blockades-and-mixing-relations</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/ramsey-theory-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/ramsey-theory</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/regular-pairs-and-induced-counting-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/combinatorics/regular-pairs-and-induced-counting</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/combinatorics/set-partitions-stirling-numbers-and-exponential-generating-functions-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/set-partitions-stirling-numbers-and-exponential-generating-functions</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/small-graph-erdos-hajnal-consequences-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/small-graph-erdos-hajnal-consequences</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/sparse-restricted-subgraphs-and-rodl-nikiforov-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/sparse-restricted-subgraphs-and-rodl-nikiforov</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/star-expansions-and-erdos-hajnal-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/star-expansions-and-erdos-hajnal</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/the-five-cycle-and-erdos-hajnal-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/the-five-cycle-and-erdos-hajnal</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/the-structural-criterion-for-property-star-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/the-structural-criterion-for-property-star</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/trees-forests-and-spanning-trees-examples</loc>
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<url>
<loc>https://alphabetamath.cc/combinatorics/trees-forests-and-spanning-trees</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/algebraic-zariski-main-for-quasi-finite-morphisms-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/algebraic-zariski-main-for-quasi-finite-morphisms</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/artinian-rings-and-length-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/artinian-rings-and-length</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/associated-primes-and-primary-decomposition-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/associated-primes-and-primary-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/dedekind-domains-and-ideal-classes-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/dedekind-domains-and-ideal-classes</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/depth-and-cohen-macaulay-modules-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/depth-and-cohen-macaulay-modules</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/flatness-and-faithful-flatness-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/flatness-and-faithful-flatness</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/henselian-rings-and-equicharacteristic-cohen-structure-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/henselian-rings-and-equicharacteristic-cohen-structure</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/homogeneous-resultants-and-projective-intersection-length-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/homogeneous-resultants-and-projective-intersection-length</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/integral-extensions-and-going-up-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/integral-extensions-and-going-up</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/inverse-limits-and-noetherian-completion-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/inverse-limits-and-noetherian-completion</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/koszul-complexes-and-regular-sequences-examples</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/koszul-complexes-and-regular-sequences</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/koszul-euler-characteristics-and-hilbert-samuel-multiplicity-examples</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/koszul-euler-characteristics-and-hilbert-samuel-multiplicity</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/krull-dimension-and-height-theorems</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/localisation-of-modules-and-support-examples</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/localisation-of-modules-and-support</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/noether-normalisation-and-nullstellensatz</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/noetherian-rings-and-hilbert-basis-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/noetherian-rings-and-hilbert-basis</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/normalization-finiteness-for-affine-domains-examples</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/normalization-finiteness-for-affine-domains</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/prime-spectra-and-radicals-examples</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/prime-spectra-and-radicals</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/rees-modules-artin-rees-and-hilbert-samuel-theory-examples</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/rees-modules-artin-rees-and-hilbert-samuel-theory</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/regular-local-rings-and-homological-dimension-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/regular-local-rings-and-homological-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/valuation-rings-and-discrete-valuation-rings-examples</loc>
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<loc>https://alphabetamath.cc/commutative-algebra/valuation-rings-and-discrete-valuation-rings</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/zariski-topology-on-prime-spectra-examples</loc>
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<url>
<loc>https://alphabetamath.cc/commutative-algebra/zariski-topology-on-prime-spectra</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/analytic-continuation-and-monodromy-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/analytic-continuation-and-monodromy</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/analytic-hardy-spaces-and-canonical-factorisation-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/analytic-hardy-spaces-and-canonical-factorisation</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/analytic-hypersurfaces-and-local-parametrisation-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/analytic-hypersurfaces-and-local-parametrisation</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/analyticity-liouville-and-morera-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/analyticity-liouville-and-morera</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/beltrami-equation-and-measurable-riemann-mapping-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/beltrami-equation-and-measurable-riemann-mapping</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/bergman-and-szego-kernels-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/bergman-and-szego-kernels</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/bloch-schottky-and-picard-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/bloch-schottky-and-picard</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/compact-kahler-hodge-foundations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/compact-kahler-hodge-foundations</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/complex-coordinate-and-path-transport-examples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/complex-coordinate-and-path-transport</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/complex-differentiability-and-cauchy-riemann-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/complex-differentiability-and-cauchy-riemann</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/complex-power-series-and-analytic-functions-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/complex-power-series-and-analytic-functions</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/conformal-mapping-branches-and-the-schwarz-lemma-examples</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/conformal-mapping-branches-and-the-schwarz-lemma</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/contour-integration-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/contour-integration</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/divisors-riemann-roch-and-duality-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/divisors-riemann-roch-and-duality</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/domains-of-holomorphy-and-pseudoconvexity-examples</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/domains-of-holomorphy-and-pseudoconvexity</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/elliptic-functions-and-complex-tori-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/elliptic-functions-and-complex-tori</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/extremal-length-and-planar-quasiconformality-examples</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/extremal-length-and-planar-quasiconformality</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/goursat-and-cauchys-theorem-in-a-convex-domain-examples</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/goursat-and-cauchys-theorem-in-a-convex-domain</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/green-functions-harmonic-measure-and-conformal-invariance-examples</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/green-functions-harmonic-measure-and-conformal-invariance</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/harmonic-functions-and-the-poisson-integral-examples</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/harmonic-functions-and-the-poisson-integral</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/harmonic-hardy-classes-and-fatou-boundary-limits-examples</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/harmonic-hardy-classes-and-fatou-boundary-limits</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/hodge-theory-on-compact-riemann-surfaces-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/hodge-theory-on-compact-riemann-surfaces</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/holomorphic-functions-of-several-variables-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/holomorphic-functions-of-several-variables</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/holomorphic-inverse-and-weierstrass-preparation-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/holomorphic-inverse-and-weierstrass-preparation</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/hormander-estimates-and-the-levi-problem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/hormander-estimates-and-the-levi-problem</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/hyperbolic-riemann-surfaces-and-uniformization-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/hyperbolic-riemann-surfaces-and-uniformization</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/infinite-products-and-weierstrass-factorisation-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/complex-analysis/infinite-products-and-weierstrass-factorisation</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/isolated-singularities-and-laurent-series-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/isolated-singularities-and-laurent-series</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/jensen-theory-and-nevanlinnas-first-main-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/jensen-theory-and-nevanlinnas-first-main-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/level-one-modular-forms-and-the-j-invariant-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/level-one-modular-forms-and-the-j-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/logarithmic-potential-capacity-and-riesz-decomposition-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/logarithmic-potential-capacity-and-riesz-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/mittag-leffler-and-runges-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/mittag-leffler-and-runges-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/nevanlinna-second-main-theorem-and-defects-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/nevanlinna-second-main-theorem-and-defects</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/normal-families-and-montels-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/normal-families-and-montels-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/periods-jacobians-and-abel-jacobi-theory-examples</loc>
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<loc>https://alphabetamath.cc/complex-analysis/periods-jacobians-and-abel-jacobi-theory</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/projective-hodge-polarization-foundations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/projective-hodge-polarization-foundations</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/quasisymmetry-welding-and-conformal-removability-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/quasisymmetry-welding-and-conformal-removability</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/riemann-surfaces-branched-maps-and-differentials-examples</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/riemann-surfaces-branched-maps-and-differentials</loc>
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<url>
<loc>https://alphabetamath.cc/complex-analysis/simply-connected-plane-domains-examples</loc>
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<loc>https://alphabetamath.cc/complex-analysis/simply-connected-plane-domains</loc>
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<loc>https://alphabetamath.cc/complex-analysis/the-winding-number-and-the-global-cauchy-theorem-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/alphabet-reduction-and-the-pcp-theorem-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/alphabet-reduction-and-the-pcp-theorem</loc>
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<loc>https://alphabetamath.cc/computability-theory/arithmetization-and-the-sum-check-protocol-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/arithmetization-and-the-sum-check-protocol</loc>
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<loc>https://alphabetamath.cc/computability-theory/boolean-circuits-and-nonuniform-complexity-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/boolean-circuits-and-nonuniform-complexity</loc>
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<loc>https://alphabetamath.cc/computability-theory/classical-np-completeness-reductions-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/classical-np-completeness-reductions</loc>
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<loc>https://alphabetamath.cc/computability-theory/computable-reductions-and-rices-theorem-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/computable-reductions-and-rices-theorem</loc>
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<loc>https://alphabetamath.cc/computability-theory/context-free-grammars-and-normal-forms-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/context-free-grammars-and-normal-forms</loc>
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<loc>https://alphabetamath.cc/computability-theory/context-free-pumping-ogden-and-parsing-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/context-free-pumping-ogden-and-parsing</loc>
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<loc>https://alphabetamath.cc/computability-theory/counting-complexity-and-sharpp-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/counting-complexity-and-sharpp</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/decidable-recognizable-and-enumerable-languages-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/decidable-recognizable-and-enumerable-languages</loc>
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<loc>https://alphabetamath.cc/computability-theory/deterministic-finite-automata-and-regular-languages-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/diagonalization-and-the-halting-problem-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/diagonalization-and-the-halting-problem</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/effective-numberings-reductions-resources-and-randomness-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/expander-graphs-and-constraint-graphs-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/expander-graphs-and-constraint-graphs</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/finite-automata-transition-and-determinisation-interfaces-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/finite-automata-transition-and-determinisation-interfaces</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/formal-languages-encodings-and-decision-problems-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/formal-languages-encodings-and-decision-problems</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/gap-amplification-and-assignment-testing-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/gap-amplification-and-assignment-testing</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/interactive-proof-systems-and-public-coins-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/interactive-proof-systems-and-public-coins</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/kolmogorov-complexity-and-algorithmic-randomness-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/kolmogorov-complexity-and-algorithmic-randomness</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/logarithmic-space-nl-and-reachability-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/logarithmic-space-nl-and-reachability</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/myhill-nerode-theory-and-dfa-minimization-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/myhill-nerode-theory-and-dfa-minimization</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/nondeterministic-finite-automata-and-subset-construction-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/nondeterministic-finite-automata-and-subset-construction</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/nondeterministic-recursive-padding-and-time-separation-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/nondeterministic-recursive-padding-and-time-separation</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/one-tape-simulation-normal-forms-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/one-tape-simulation-normal-forms</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/oracle-computability-the-jump-and-turing-degrees-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/oracle-computability-the-jump-and-turing-degrees</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/p-np-conp-and-polynomial-reductions-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/p-np-conp-and-polynomial-reductions</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/post-correspondence-and-language-undecidability-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/post-correspondence-and-language-undecidability</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/primitive-recursive-and-partial-computable-functions-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/primitive-recursive-and-partial-computable-functions</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/pushdown-automata-and-context-free-languages-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/pushdown-automata-and-context-free-languages</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/randomized-complexity-and-amplification-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/randomized-complexity-and-amplification</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/regular-expressions-and-kleenes-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/regular-expressions-and-kleenes-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/resource-bounds-and-machine-invariance-examples</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/resource-bounds-and-machine-invariance</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/robust-machine-models-and-universal-computation-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/robust-machine-models-and-universal-computation</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/sat-tableaux-and-quantified-space-completeness-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/sat-tableaux-and-quantified-space-completeness</loc>
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<loc>https://alphabetamath.cc/computability-theory/space-complexity-savitch-and-tqbf-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/space-complexity-savitch-and-tqbf</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/the-arithmetical-hierarchy-and-posts-theorem-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/the-arithmetical-hierarchy-and-posts-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/the-cook-levin-theorem-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/the-cook-levin-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/computability-theory/the-ip-equals-pspace-theorem-examples</loc>
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<loc>https://alphabetamath.cc/computability-theory/the-ip-equals-pspace-theorem</loc>
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<loc>https://alphabetamath.cc/differential-geometry/measurable-densities-and-radon-volume-on-manifolds-examples</loc>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/measurable-densities-and-radon-volume-on-manifolds</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/moment-maps-and-symplectic-reduction-examples</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/moment-maps-and-symplectic-reduction</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/poisson-algebras-and-hamiltonian-representations-examples</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/poisson-algebras-and-hamiltonian-representations</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.7</priority>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/rank-theorems-and-embedded-submanifolds-examples</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/rank-theorems-and-embedded-submanifolds</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/riemann-curvature-and-riemannian-submanifolds-examples</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/riemann-curvature-and-riemannian-submanifolds</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/riemannian-comparison-theorems-examples</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/riemannian-comparison-theorems</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/riemannian-metrics-length-distance-and-volume-examples</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/riemannian-metrics-length-distance-and-volume</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.7</priority>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/sard-theorem-and-transversality-examples</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/sard-theorem-and-transversality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.7</priority>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/singular-cochains-mayer-vietoris-and-smooth-singular-comparison-examples</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.7</priority>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/singular-cochains-mayer-vietoris-and-smooth-singular-comparison</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.7</priority>
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<url>
<loc>https://alphabetamath.cc/differential-geometry/smooth-manifolds-and-smooth-maps-examples</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/smooth-manifolds-and-smooth-maps</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/smooth-partitions-of-unity-and-exhaustions-examples</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/smooth-partitions-of-unity-and-exhaustions</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/smooth-vector-bundles-and-sections-examples</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/smooth-vector-bundles-and-sections</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/spin-geometry-dirac-and-index-theory-examples</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/spin-geometry-dirac-and-index-theory</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/symplectic-manifolds-moser-stability-and-darboux-weinstein-theory-examples</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/symplectic-manifolds-moser-stability-and-darboux-weinstein-theory</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/tangent-cotangent-and-the-differential-examples</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/tangent-cotangent-and-the-differential</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/tensor-fields-exterior-algebra-and-differential-forms-examples</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/tensor-fields-exterior-algebra-and-differential-forms</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/the-de-rham-complex-homotopy-and-mayer-vietoris-examples</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/the-de-rham-complex-homotopy-and-mayer-vietoris</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/the-de-rham-theorem-and-degree-examples</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/the-de-rham-theorem-and-degree</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/the-exterior-derivative-and-cartan-calculus-examples</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/the-exterior-derivative-and-cartan-calculus</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/the-gauss-bonnet-theorem-for-riemannian-surfaces-examples</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/the-gauss-bonnet-theorem-for-riemannian-surfaces</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/vector-fields-flows-and-lie-derivatives-examples</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/vector-fields-flows-and-lie-derivatives</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/whitney-embedding-tubular-neighbourhoods-and-approximation-examples</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-geometry/whitney-embedding-tubular-neighbourhoods-and-approximation</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/characteristic-class-obstructions-to-immersions-and-embeddings-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/characteristic-class-obstructions-to-immersions-and-embeddings</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/characteristic-numbers-and-cobordism-obstructions-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/characteristic-numbers-and-cobordism-obstructions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/codimension-one-foliations-and-secondary-classes-examples</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/codimension-one-foliations-and-secondary-classes</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/exotic-smooth-structures-and-milnor-spheres-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/exotic-smooth-structures-and-milnor-spheres</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/fixed-point-index-and-the-lefschetz-theorem-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/fixed-point-index-and-the-lefschetz-theorem</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/foliation-holonomy-and-the-holonomy-groupoid-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/foliation-holonomy-and-the-holonomy-groupoid</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/formal-immersions-and-the-smale-hirsch-theorem-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/formal-immersions-and-the-smale-hirsch-theorem</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/gradient-like-vector-fields-and-morse-trajectories-examples</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/gradient-like-vector-fields-and-morse-trajectories</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/handle-cancellation-slides-and-elementary-moves-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/handle-cancellation-slides-and-elementary-moves</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/handle-decompositions-duality-and-rearrangement-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/handle-decompositions-duality-and-rearrangement</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/intersection-pairings-self-intersection-and-euler-classes-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/intersection-pairings-self-intersection-and-euler-classes</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/isotopy-extension-and-embedding-theory-beyond-whitney-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/isotopy-extension-and-embedding-theory-beyond-whitney</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-critical-points-hessians-and-indices-examples</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-critical-points-hessians-and-indices</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-functions-critical-values-and-genericity-examples</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-functions-critical-values-and-genericity</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-homology-continuation-and-comparison-examples</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-homology-continuation-and-comparison</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-inequalities-and-the-handle-chain-complex-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-inequalities-and-the-handle-chain-complex</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-trajectory-moduli-spaces-and-the-morse-differential-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/morse-trajectory-moduli-spaces-and-the-morse-differential</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/oriented-and-mod-two-intersection-numbers-examples</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/oriented-and-mod-two-intersection-numbers</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/pontryagin-thom-and-framed-cobordism-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/pontryagin-thom-and-framed-cobordism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/reeb-stability-and-global-foliation-constructions-examples</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/reeb-stability-and-global-foliation-constructions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/regular-homotopy-and-sphere-eversion-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/regular-homotopy-and-sphere-eversion</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/relative-smooth-triangulation-and-bundle-fitting-examples</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/relative-smooth-triangulation-and-bundle-fitting</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/smooth-cobordism-relations-groups-and-rings-examples</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/smooth-cobordism-relations-groups-and-rings</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/smooth-surgery-traces-and-handle-trading-examples</loc>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/smooth-surgery-traces-and-handle-trading</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/stable-unstable-manifolds-and-morse-smale-transversality-examples</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/stable-unstable-manifolds-and-morse-smale-transversality</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/sublevel-deformation-and-the-handle-attachment-theorem-examples</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/sublevel-deformation-and-the-handle-attachment-theorem</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/the-hirzebruch-signature-theorem-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/the-hirzebruch-signature-theorem</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/differential-topology/the-hopf-degree-theorem-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
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<loc>https://alphabetamath.cc/fourier-analysis/carleson-hunt-time-frequency-theorem-examples</loc>
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<loc>https://alphabetamath.cc/fourier-analysis/fourier-multipliers-and-sobolev-characterisations-examples</loc>
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<loc>https://alphabetamath.cc/fourier-analysis/fourier-restriction-and-the-stein-tomas-theorem-examples</loc>
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<loc>https://alphabetamath.cc/fourier-analysis/hilbert-and-riesz-transforms-examples</loc>
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<url>
<loc>https://alphabetamath.cc/fourier-analysis/muckenhoupt-weights-and-weighted-estimates-examples</loc>
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<url>
<loc>https://alphabetamath.cc/fourier-analysis/muckenhoupt-weights-and-weighted-estimates</loc>
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<loc>https://alphabetamath.cc/fourier-analysis/poisson-summation-sampling-and-lattice-duality-examples</loc>
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<loc>https://alphabetamath.cc/fourier-analysis/pontryagin-duality-for-locally-compact-abelian-groups-examples</loc>
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<loc>https://alphabetamath.cc/fourier-analysis/real-hardy-spaces-maximal-functions-and-atoms-examples</loc>
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<url>
<loc>https://alphabetamath.cc/fourier-analysis/real-hardy-spaces-maximal-functions-and-atoms</loc>
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<loc>https://alphabetamath.cc/fourier-analysis/uncertainty-principles-for-fourier-analysis-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/banach-alaoglu-goldstine-and-krein-milman-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/banach-alaoglu-goldstine-and-krein-milman</loc>
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<loc>https://alphabetamath.cc/functional-analysis/banach-algebras-spectrum-and-holomorphic-functional-calculus-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/banach-algebras-spectrum-and-holomorphic-functional-calculus</loc>
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<loc>https://alphabetamath.cc/functional-analysis/banach-space-differential-calculus-and-banach-manifolds-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/banach-valued-integration-and-the-radon-nikodym-property-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/banach-valued-integration-and-the-radon-nikodym-property</loc>
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<loc>https://alphabetamath.cc/functional-analysis/bounded-linear-operators-and-quotient-spaces</loc>
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<loc>https://alphabetamath.cc/functional-analysis/norming-and-separation-under-hahn-banach-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/schauder-bases-approximation-and-banach-space-pathologies-examples</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/sequential-uniform-boundedness-with-countable-choice</loc>
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<loc>https://alphabetamath.cc/functional-analysis/spectral-measures-and-borel-functional-calculus-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/spectral-measures-and-borel-functional-calculus</loc>
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<loc>https://alphabetamath.cc/functional-analysis/square-integrable-kernels-and-hilbert-schmidt-compactness-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/square-integrable-kernels-and-hilbert-schmidt-compactness</loc>
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<loc>https://alphabetamath.cc/functional-analysis/tempered-distributions-and-the-fourier-transform-examples</loc>
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<loc>https://alphabetamath.cc/functional-analysis/tempered-distributions-and-the-fourier-transform</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/the-analytic-hahn-banach-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/the-analytic-hahn-banach-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/the-baire-principles-of-functional-analysis-examples</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/the-baire-principles-of-functional-analysis</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/unbounded-self-adjoint-operators-and-stones-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/unbounded-self-adjoint-operators-and-stones-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/weak-and-weak-star-topologies-examples</loc>
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<url>
<loc>https://alphabetamath.cc/functional-analysis/weak-and-weak-star-topologies</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/a-projective-line-simple-group-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/a-projective-line-simple-group</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/amenable-groups-and-folner-criteria-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/amenable-groups-and-folner-criteria</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/asymptotic-cones-and-the-sublinear-triangle-criterion-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/asymptotic-cones-and-the-sublinear-triangle-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/blocks-primitivity-and-multiple-transitivity-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/blocks-primitivity-and-multiple-transitivity</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/boone-machine-simulation-and-fixed-presentation-undecidability-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/boone-machine-simulation-and-fixed-presentation-undecidability</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/group-theory/brauer-characters-and-decomposition-matrices-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/brauer-characters-and-decomposition-matrices</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/cayley-graphs-word-metrics-and-quasi-isometry-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/cayley-graphs-word-metrics-and-quasi-isometry</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/crossed-homomorphisms-complements-and-first-cohomology-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/crossed-homomorphisms-complements-and-first-cohomology</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/decision-problems-for-finitely-presented-groups-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/decision-problems-for-finitely-presented-groups</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/extraspecial-p-groups-and-central-products-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/extraspecial-p-groups-and-central-products</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/frattini-subgroups-and-the-burnside-basis-theorem-examples</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/group-theory/frattini-subgroups-and-the-burnside-basis-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/geometric-actions-svarc-milnor-and-growth-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/geometric-actions-svarc-milnor-and-growth</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/graphs-of-groups-and-bass-serre-theory-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/graphs-of-groups-and-bass-serre-theory</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/group-extensions-complements-and-schur-zassenhaus-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/group-extensions-complements-and-schur-zassenhaus</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/group-homology-transfer-and-low-degree-exact-sequences-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/group-homology-transfer-and-low-degree-exact-sequences</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/group-theory/hall-malcev-coordinates-and-bass-guivarch-growth-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/hall-malcev-coordinates-and-bass-guivarch-growth</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/hnn-extensions-and-brittons-lemma-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/group-theory/hnn-extensions-and-brittons-lemma</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/hyperbolic-spaces-and-hyperbolic-groups-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/group-theory/hyperbolic-spaces-and-hyperbolic-groups</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/inverse-systems-profinite-groups-and-completion-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/group-theory/inverse-systems-profinite-groups-and-completion</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/modular-representations-and-projective-covers-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/group-theory/modular-representations-and-projective-covers</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/modular-traces-and-brauer-character-independence-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/modular-traces-and-brauer-character-independence</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/pro-p-groups-and-the-p-adic-integers-examples</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/group-theory/pro-p-groups-and-the-p-adic-integers</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/quantitative-hyperbolic-geometry-toolkit-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/quantitative-hyperbolic-geometry-toolkit</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/schur-multipliers-and-universal-central-extensions-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/schur-multipliers-and-universal-central-extensions</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/second-cohomology-and-abelian-kernel-extensions-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/second-cohomology-and-abelian-kernel-extensions</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/simplicial-trees-and-group-actions-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/simplicial-trees-and-group-actions</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/small-cancellation-and-dehn-algorithms-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/small-cancellation-and-dehn-algorithms</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/small-cancellation-disc-diagrams-and-torsion-toolkit-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/small-cancellation-disc-diagrams-and-torsion-toolkit</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/socles-and-the-onan-scott-landscape-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/socles-and-the-onan-scott-landscape</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/subgroups-of-free-groups-and-schreier-rewriting-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/subgroups-of-free-groups-and-schreier-rewriting</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/the-finite-simple-group-classification-landscape-examples</loc>
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<url>
<loc>https://alphabetamath.cc/group-theory/the-finite-simple-group-classification-landscape</loc>
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<url>
<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/cohomological-hall-algebras-and-quiver-correspondences-examples</loc>
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<url>
<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/cohomological-hall-algebras-and-quiver-correspondences</loc>
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<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/derived-hall-algebras-examples</loc>
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<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/derived-hall-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/finitary-ringel-hall-algebras-examples</loc>
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<url>
<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/finitary-ringel-hall-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/frobenius-algebras-and-two-dimensional-sewing-examples</loc>
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<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/frobenius-algebras-and-two-dimensional-sewing</loc>
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<url>
<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/green-hall-bialgebras-and-quantum-group-realizations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/hall-algebras-and-tensor-categories/green-hall-bialgebras-and-quantum-group-realizations</loc>
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<loc>https://alphabetamath.cc/homological-algebra/finite-abelian-categories-and-eilenberg-watts</loc>
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<url>
<loc>https://alphabetamath.cc/homological-algebra/graded-bimodules-and-tensor-functors</loc>
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<loc>https://alphabetamath.cc/homological-algebra/graded-eilenberg-watts-and-shift-coherence</loc>
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<loc>https://alphabetamath.cc/homological-algebra/grothendieck-groups-and-graded-cartan-pairings-examples</loc>
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<loc>https://alphabetamath.cc/homological-algebra/grothendieck-spectral-sequences-and-computations</loc>
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<loc>https://alphabetamath.cc/homological-algebra/mapping-cones-cylinders-and-chain-triangles</loc>
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<url>
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<loc>https://alphabetamath.cc/homological-algebra/morita-bicategories-and-projective-generators</loc>
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<url>
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<loc>https://alphabetamath.cc/homological-algebra/perfect-complexes-and-triangulated-grothendieck-groups</loc>
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<loc>https://alphabetamath.cc/homological-algebra/projective-and-injective-resolutions-examples</loc>
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<loc>https://alphabetamath.cc/homological-algebra/projective-and-injective-resolutions</loc>
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<loc>https://alphabetamath.cc/homological-algebra/spectral-sequences-examples</loc>
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<loc>https://alphabetamath.cc/homological-algebra/spectral-sequences</loc>
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<url>
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<loc>https://alphabetamath.cc/homological-algebra/tor-flatness-and-global-dimension</loc>
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<loc>https://alphabetamath.cc/homological-algebra/triangulated-categories-examples</loc>
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<loc>https://alphabetamath.cc/homological-algebra/triangulated-categories</loc>
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<url>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/coalgebras-counits-and-the-fundamental-coalgebra-theorem-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/comodules-matrix-coefficients-and-coalgebra-duality-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/cyclotomic-hecke-quotients-and-ariki-koike-pbw-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/cyclotomic-hecke-quotients-and-ariki-koike-pbw</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/drinfeld-doubles-and-yetter-drinfeld-module-constructions-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/finite-hopf-integrals-frobenius-duality-and-maschke-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/finite-hopf-integrals-frobenius-duality-and-maschke</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/generic-coxeter-hecke-algebras-and-the-standard-basis-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hecke-base-change-semisimplicity-and-deformation-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hecke-base-change-semisimplicity-and-deformation</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hecke-parabolic-induction-and-symmetrizing-traces-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hecke-symmetries-and-generic-quantum-schur-weyl-duality-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hopf-hecke-and-quantum-symmetry-interfaces-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hopf-hecke-and-quantum-symmetry-interfaces</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hopf-ideals-finite-duals-and-basic-constructions</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hopf-module-tensor-products-and-rigid-duality</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/hopf-modules-coinvariants-and-the-fundamental-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/hopf-hecke-algebras/hopf-modules-coinvariants-and-the-fundamental-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/hopf-hecke-algebras/quasi-hopf-weak-hopf-and-relative-tensor-products-examples</loc>
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<url>
<loc>https://alphabetamath.cc/hopf-hecke-algebras/quasitriangular-hopf-algebras-and-braided-module-categories</loc>
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<url>
<loc>https://alphabetamath.cc/hopf-hecke-algebras/tensor-coherence-and-algebraic-descent-examples</loc>
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<loc>https://alphabetamath.cc/hopf-hecke-algebras/tensor-coherence-and-algebraic-descent</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/cost-constrained-gaussian-and-feedback-channels</loc>
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<loc>https://alphabetamath.cc/information-theory/discrete-memoryless-channel-capacity-examples</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/discrete-memoryless-channel-capacity</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/distributed-source-coding-examples</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/distributed-source-coding</loc>
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<loc>https://alphabetamath.cc/information-theory/f-divergences-renyi-and-hypothesis-testing-examples</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/f-divergences-renyi-and-hypothesis-testing</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/finite-alphabet-entropy-and-divergence-examples</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/finite-alphabet-entropy-and-divergence</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/finite-blocklength-and-reliability-examples</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/finite-blocklength-and-reliability</loc>
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<url>
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<loc>https://alphabetamath.cc/information-theory/finite-quantization-lloyd-and-compact-companders</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/information-theory/measure-theoretic-information-and-conditioning</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/information-theory/multiuser-channel-networks</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/information-theory/prefix-codes-and-finite-lossless-coding</loc>
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<url>
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</url>
<url>
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<url>
<loc>https://alphabetamath.cc/information-theory/quantum-key-distribution-and-composable-secrecy</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/information-theory/relay-and-interference-channel-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/information-theory/secrecy-and-information-privacy</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/information-theory/stationary-ergodic-sources-and-universal-coding</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/lie-theory/borel-weil-and-borel-weil-bott</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/lie-theory/cartan-subalgebras-and-root-space-decompositions</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/lie-theory/category-o-finiteness-duality-and-blocks</loc>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/lie-theory/integrable-highest-weight-kac-moody-modules-examples</loc>
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<loc>https://alphabetamath.cc/lie-theory/integrable-highest-weight-kac-moody-modules</loc>
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<loc>https://alphabetamath.cc/lie-theory/kac-moody-algebras-from-generalized-cartan-matrices-examples</loc>
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<loc>https://alphabetamath.cc/lie-theory/kac-moody-algebras-from-generalized-cartan-matrices</loc>
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<loc>https://alphabetamath.cc/lie-theory/lie-algebra-cohomology-and-kostants-nilradical-theorem-examples</loc>
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<loc>https://alphabetamath.cc/lie-theory/lie-algebra-cohomology-and-kostants-nilradical-theorem</loc>
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<loc>https://alphabetamath.cc/lie-theory/lie-algebra-representations-enveloping-algebras-and-pbw-examples</loc>
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<loc>https://alphabetamath.cc/lie-theory/lie-algebra-representations-enveloping-algebras-and-pbw</loc>
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<loc>https://alphabetamath.cc/lie-theory/lie-groups-invariant-fields-and-the-exponential-map-examples</loc>
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<loc>https://alphabetamath.cc/lie-theory/lie-groups-invariant-fields-and-the-exponential-map</loc>
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<loc>https://alphabetamath.cc/lie-theory/lie-subgroups-actions-and-homogeneous-spaces-examples</loc>
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<loc>https://alphabetamath.cc/lie-theory/lie-subgroups-actions-and-homogeneous-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/lie-superalgebras-and-super-representation-theory-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/lie-superalgebras-and-super-representation-theory</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/primitive-ideals-and-duflo-theorem-examples</loc>
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<loc>https://alphabetamath.cc/lie-theory/primitive-ideals-and-duflo-theorem</loc>
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<loc>https://alphabetamath.cc/lie-theory/projectives-standard-filtrations-and-bgg-reciprocity-examples</loc>
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<loc>https://alphabetamath.cc/lie-theory/projectives-standard-filtrations-and-bgg-reciprocity</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/real-forms-and-real-semisimple-lie-algebras-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/real-forms-and-real-semisimple-lie-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/root-systems-dynkin-diagrams-and-cartan-killing-classification-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/root-systems-dynkin-diagrams-and-cartan-killing-classification</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/semisimple-lie-algebras-cohomology-and-levi-theory-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/semisimple-lie-algebras-cohomology-and-levi-theory</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/solvable-and-nilpotent-lie-algebras-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/solvable-and-nilpotent-lie-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/tensor-product-multiplicities-and-littlewood-richardson-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/tensor-product-multiplicities-and-littlewood-richardson</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/the-bgg-resolution-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/the-bgg-resolution</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/the-weyl-kac-character-formula-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/the-weyl-kac-character-formula</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/verma-modules-and-shapovalov-forms-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/verma-modules-and-shapovalov-forms</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/weyl-character-and-multiplicity-formulas-examples</loc>
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<url>
<loc>https://alphabetamath.cc/lie-theory/weyl-character-and-multiplicity-formulas</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/complexification-realification-and-real-structures-examples</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/complexification-realification-and-real-structures</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/conjugate-gradients-minres-and-preconditioning-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/conjugate-gradients-minres-and-preconditioning</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/determinants-of-matrices-over-a-commutative-ring-examples</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/determinants-of-matrices-over-a-commutative-ring</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/diagonalisation-and-the-minimal-polynomial-examples</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/diagonalisation-and-the-minimal-polynomial</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/direct-matrix-factorisations-lu-cholesky-and-qr-examples</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/direct-matrix-factorisations-lu-cholesky-and-qr</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/dual-spaces-bilinear-forms-and-inertia-examples</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/dual-spaces-bilinear-forms-and-inertia</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/eigenvalue-iterations-and-the-qr-algorithm-examples</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/eigenvalue-iterations-and-the-qr-algorithm</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/eigenvalues-eigenvectors-and-the-characteristic-polynomial-examples</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/eigenvalues-eigenvectors-and-the-characteristic-polynomial</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/exterior-powers-orientation-and-hodge-duality-examples</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/exterior-powers-orientation-and-hodge-duality</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/gaussian-elimination-and-row-reduction-examples</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/gaussian-elimination-and-row-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/inner-product-spaces-and-orthogonality-examples</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/inner-product-spaces-and-orthogonality</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/krylov-subspaces-arnoldi-and-gmres-examples</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/krylov-subspaces-arnoldi-and-gmres</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/linear-independence-bases-and-dimension-examples</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/linear-independence-bases-and-dimension</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/linear-maps-rank-nullity-and-quotient-spaces-examples</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/linear-maps-rank-nullity-and-quotient-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/matrices-and-the-matrix-of-a-linear-map-examples</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/matrices-and-the-matrix-of-a-linear-map</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/matrix-differentiation-and-first-order-spectral-perturbation-examples</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/matrix-differentiation-and-first-order-spectral-perturbation</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/matrix-norms-condition-numbers-and-numerical-stability-examples</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/matrix-norms-condition-numbers-and-numerical-stability</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/the-determinant-of-a-linear-operator-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/the-determinant-of-a-linear-operator</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/the-moore-penrose-pseudoinverse-and-regularised-least-squares-examples</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/the-moore-penrose-pseudoinverse-and-regularised-least-squares</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/the-spectral-theorem-and-singular-value-decomposition-examples</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/the-spectral-theorem-and-singular-value-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/triangularisation-and-jordan-canonical-form-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/linear-algebra/triangularisation-and-jordan-canonical-form</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/vector-spaces-and-subspaces-examples</loc>
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<url>
<loc>https://alphabetamath.cc/linear-algebra/vector-spaces-and-subspaces</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/mathematical-statistics/asymptotic-convergence-consistency-and-identification-examples</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/asymptotic-convergence-consistency-and-identification</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/mathematical-statistics/boundary-and-misspecified-asymptotics-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/mathematical-statistics/boundary-and-misspecified-asymptotics</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/mathematical-statistics/chaining-uniform-laws-and-empirical-process-limits-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/mathematical-statistics/chaining-uniform-laws-and-empirical-process-limits</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/mathematical-statistics/complete-sufficiency-exponential-families-and-basu-examples</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/complete-sufficiency-exponential-families-and-basu</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/concentration-inequalities-and-tail-bounds-examples</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/concentration-inequalities-and-tail-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/conditional-and-finite-group-exact-inference-examples</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/conditional-and-finite-group-exact-inference</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/confidence-sets-pivots-and-test-inversion-examples</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/confidence-sets-pivots-and-test-inversion</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/conformal-prediction-and-exchangeable-ranks-examples</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/conformal-prediction-and-exchangeable-ranks</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/contamination-models-and-robust-risk-examples</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/contamination-models-and-robust-risk</loc>
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<url>
<loc>https://alphabetamath.cc/mathematical-statistics/decision-theoretic-upper-bounds-and-oracle-risk-examples</loc>
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<loc>https://alphabetamath.cc/measure-theory/complex-riesz-thorin-endpoint-interpolation-examples</loc>
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<loc>https://alphabetamath.cc/measure-theory/hausdorff-measure-and-hausdorff-dimension-examples</loc>
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<loc>https://alphabetamath.cc/measure-theory/modes-of-convergence-egorov-and-lusin-examples</loc>
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<loc>https://alphabetamath.cc/measure-theory/the-ergodic-theorems-of-von-neumann-and-birkhoff-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/average-orders-divisor-sums-and-representation-counts-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/chebyshev-bounds-and-mertens-theorems-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/chebyshev-bounds-and-mertens-theorems</loc>
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<loc>https://alphabetamath.cc/number-theory/classical-zero-free-region-and-the-prime-number-theorem-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/classical-zero-free-region-and-the-prime-number-theorem</loc>
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<loc>https://alphabetamath.cc/number-theory/congruences-and-the-chinese-remainder-theorem-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/congruences-and-the-chinese-remainder-theorem</loc>
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<loc>https://alphabetamath.cc/number-theory/cyclotomic-arithmetic-and-reciprocity-via-frobenius-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/cyclotomic-arithmetic-and-reciprocity-via-frobenius</loc>
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<loc>https://alphabetamath.cc/number-theory/decomposition-inertia-and-frobenius</loc>
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<loc>https://alphabetamath.cc/number-theory/dirichlet-characters-l-functions-and-primes-in-progressions-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/dirichlet-characters-l-functions-and-primes-in-progressions</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/dirichlet-series-and-euler-products-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/dirichlet-series-and-euler-products</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/dirichlets-unit-theorem-regulators-and-s-units-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/dirichlets-unit-theorem-regulators-and-s-units</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/divisibility-gcd-and-bezout-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/divisibility-gcd-and-bezout</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/hilbert-symbols-and-the-quadratic-local-global-principle-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/hilbert-symbols-and-the-quadratic-local-global-principle</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/lagrange-four-square-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/lagrange-four-square-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/minkowski-theory-and-number-field-class-groups-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/minkowski-theory-and-number-field-class-groups</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/number-fields-rings-of-integers-and-discriminants-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/number-fields-rings-of-integers-and-discriminants</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/pell-equations-and-generalized-pell-orbits-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/pell-equations-and-generalized-pell-orbits</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/perron-inversion-and-the-explicit-formula-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/perron-inversion-and-the-explicit-formula</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/positive-definite-binary-quadratic-forms-and-reduction-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/positive-definite-binary-quadratic-forms-and-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/prime-ideal-decomposition-ramification-and-the-different-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/prime-ideal-decomposition-ramification-and-the-different</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/primes-and-the-fundamental-theorem-of-arithmetic-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/primes-and-the-fundamental-theorem-of-arithmetic</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/primitive-dirichlet-l-functions-and-functional-equations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/primitive-dirichlet-l-functions-and-functional-equations</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/primitive-roots-and-unit-groups-modulo-n-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/primitive-roots-and-unit-groups-modulo-n</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/quadratic-reciprocity-and-the-jacobi-symbol-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/quadratic-reciprocity-and-the-jacobi-symbol</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/quadratic-residues-and-the-legendre-symbol-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/quadratic-residues-and-the-legendre-symbol</loc>
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<loc>https://alphabetamath.cc/number-theory/regular-continued-fractions-and-diophantine-approximation-examples</loc>
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<loc>https://alphabetamath.cc/number-theory/regular-continued-fractions-and-diophantine-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/sums-of-two-squares-examples</loc>
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<url>
<loc>https://alphabetamath.cc/number-theory/sums-of-two-squares</loc>
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<url>
<loc>https://alphabetamath.cc/numerical-analysis/euler-maruyama-convergence-examples</loc>
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<url>
<loc>https://alphabetamath.cc/numerical-analysis/euler-maruyama-convergence</loc>
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<loc>https://alphabetamath.cc/numerical-analysis/euler-maruyama-scheme-and-conditions-examples</loc>
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<url>
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<url>
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<loc>https://alphabetamath.cc/numerical-differential-equations-and-stochastic-dynamics/deferred-correction-and-collocation-iterations-examples</loc>
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<loc>https://alphabetamath.cc/numerical-differential-equations-and-stochastic-dynamics/delay-differential-equations-and-history-discretization-examples</loc>
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<loc>https://alphabetamath.cc/pde/quasilinear-characteristics-and-cauchy-kovalevskaya-examples</loc>
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<loc>https://alphabetamath.cc/pde/rellich-kondrachov-and-sobolev-compactness-examples</loc>
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<loc>https://alphabetamath.cc/pde/scalar-conservation-laws-and-entropy-solutions-examples</loc>
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<loc>https://alphabetamath.cc/pde/schauder-and-lp-elliptic-estimates-examples</loc>
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<loc>https://alphabetamath.cc/pde/sobolev-poincare-and-morrey-inequalities-examples</loc>
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<loc>https://alphabetamath.cc/pde/strongly-continuous-semigroups-and-hille-yosida-examples</loc>
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<loc>https://alphabetamath.cc/pde/the-direct-method-and-euler-lagrange-equations-examples</loc>
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<loc>https://alphabetamath.cc/pde/the-direct-method-and-euler-lagrange-equations</loc>
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<loc>https://alphabetamath.cc/pde/the-heat-kernel-and-the-cauchy-problem-examples</loc>
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<loc>https://alphabetamath.cc/pde/the-heat-kernel-and-the-cauchy-problem</loc>
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<loc>https://alphabetamath.cc/pde/wave-energy-finite-propagation-and-huygens-examples</loc>
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<loc>https://alphabetamath.cc/pde/wave-energy-finite-propagation-and-huygens</loc>
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<url>
<loc>https://alphabetamath.cc/pde/wave-equation-representation-formulas-examples</loc>
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<loc>https://alphabetamath.cc/pde/wave-equation-representation-formulas</loc>
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<loc>https://alphabetamath.cc/pde/weak-derivatives-and-sobolev-spaces-examples</loc>
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<loc>https://alphabetamath.cc/pde/weak-derivatives-and-sobolev-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/pde/weak-elliptic-maximum-principles-and-holder-regularity-examples</loc>
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<loc>https://alphabetamath.cc/pde/weak-elliptic-maximum-principles-and-holder-regularity</loc>
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<loc>https://alphabetamath.cc/probability/brownian-motion-construction-and-continuity-examples</loc>
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<loc>https://alphabetamath.cc/probability/brownian-motion-construction-and-continuity</loc>
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<url>
<loc>https://alphabetamath.cc/probability/brownian-motion-markov-properties-and-hitting-times-examples</loc>
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<loc>https://alphabetamath.cc/probability/brownian-motion-markov-properties-and-hitting-times</loc>
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<url>
<loc>https://alphabetamath.cc/probability/brownian-path-properties-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/brownian-path-properties</loc>
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<url>
<loc>https://alphabetamath.cc/probability/central-limit-theorems-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/central-limit-theorems</loc>
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<url>
<loc>https://alphabetamath.cc/probability/characteristic-functions-inversion-and-continuity-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/characteristic-functions-inversion-and-continuity</loc>
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<url>
<loc>https://alphabetamath.cc/probability/conditional-distributions-and-regular-conditional-probability-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/conditional-distributions-and-regular-conditional-probability</loc>
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<url>
<loc>https://alphabetamath.cc/probability/conditional-expectation-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/conditional-expectation</loc>
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<url>
<loc>https://alphabetamath.cc/probability/discrete-time-martingales-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/discrete-time-martingales</loc>
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<url>
<loc>https://alphabetamath.cc/probability/forward-ito-sde-well-posedness-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/forward-ito-sde-well-posedness</loc>
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<url>
<loc>https://alphabetamath.cc/probability/independence-borel-cantelli-and-zero-one-laws-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/independence-borel-cantelli-and-zero-one-laws</loc>
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<url>
<loc>https://alphabetamath.cc/probability/infinite-product-measures-and-kolmogorov-extension-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/infinite-product-measures-and-kolmogorov-extension</loc>
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<url>
<loc>https://alphabetamath.cc/probability/itos-formula-and-brownian-martingales-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/itos-formula-and-brownian-martingales</loc>
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<url>
<loc>https://alphabetamath.cc/probability/markov-kernels-and-markov-chains-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/markov-kernels-and-markov-chains</loc>
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<url>
<loc>https://alphabetamath.cc/probability/martingale-inequalities-and-convergence-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/martingale-inequalities-and-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/probability/modes-of-convergence-for-random-variables-examples</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/probability/modes-of-convergence-for-random-variables</loc>
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<url>
<loc>https://alphabetamath.cc/probability/probability-spaces-random-variables-and-expectation-examples</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/probability/probability-spaces-random-variables-and-expectation</loc>
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<url>
<loc>https://alphabetamath.cc/probability/recurrence-transience-and-hitting-times-for-markov-chains-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/recurrence-transience-and-hitting-times-for-markov-chains</loc>
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<url>
<loc>https://alphabetamath.cc/probability/standard-borel-real-codings-and-determining-classes-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/standard-borel-real-codings-and-determining-classes</loc>
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<url>
<loc>https://alphabetamath.cc/probability/stationary-markov-chains-and-ergodic-limits-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/stationary-markov-chains-and-ergodic-limits</loc>
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<url>
<loc>https://alphabetamath.cc/probability/stopping-times-and-optional-stopping-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/stopping-times-and-optional-stopping</loc>
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<url>
<loc>https://alphabetamath.cc/probability/strong-laws-of-large-numbers-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/strong-laws-of-large-numbers</loc>
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<url>
<loc>https://alphabetamath.cc/probability/the-ito-integral-with-respect-to-brownian-motion-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/the-ito-integral-with-respect-to-brownian-motion</loc>
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<url>
<loc>https://alphabetamath.cc/probability/weak-convergence-tightness-and-representation-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/weak-convergence-tightness-and-representation</loc>
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<url>
<loc>https://alphabetamath.cc/probability/weak-laws-and-series-of-independent-random-variables-examples</loc>
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<url>
<loc>https://alphabetamath.cc/probability/weak-laws-and-series-of-independent-random-variables</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/affine-current-algebras-virasoro-and-sugawara-examples</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/affine-current-algebras-virasoro-and-sugawara</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/brauer-bmw-and-partition-diagram-algebras-examples</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/brauer-bmw-and-partition-diagram-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/car-algebras-majorana-generators-and-clifford-comparison-examples</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/car-algebras-majorana-generators-and-clifford-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/clifford-universal-algebras-and-pbw-examples</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/clifford-universal-algebras-and-pbw</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/pin-spin-and-clifford-module-representations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/pin-spin-and-clifford-module-representations</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/real-complex-clifford-classification-and-graded-products-examples</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/real-complex-clifford-classification-and-graded-products</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-cellularity-and-representation-theory-examples</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-cellularity-and-representation-theory</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-diagram-algebra-and-catalan-basis-examples</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-diagram-algebra-and-catalan-basis</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-jones-wenzl-traces-and-quotients-examples</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-jones-wenzl-traces-and-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-root-of-unity-and-modular-representation-theory-examples</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-root-of-unity-and-modular-representation-theory</loc>
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<loc>https://alphabetamath.cc/quantum-algebra-and-representation-theory/temperley-lieb-semisimplicity-and-generic-structure-examples</loc>
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<loc>https://alphabetamath.cc/real-analysis/the-gauge-integral-and-cousins-lemma-examples</loc>
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<loc>https://alphabetamath.cc/real-analysis/the-gauge-integral-and-cousins-lemma</loc>
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<loc>https://alphabetamath.cc/real-analysis/the-integral-logarithm-and-its-characterisations-examples</loc>
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<loc>https://alphabetamath.cc/real-analysis/the-inverse-function-theorem-completed</loc>
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<loc>https://alphabetamath.cc/real-analysis/the-logarithm-and-general-powers</loc>
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<loc>https://alphabetamath.cc/real-analysis/the-real-gamma-and-beta-functions-examples</loc>
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<loc>https://alphabetamath.cc/real-analysis/the-riemann-integral-examples</loc>
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<loc>https://alphabetamath.cc/real-analysis/the-total-derivative-examples</loc>
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<loc>https://alphabetamath.cc/real-analysis/topology-of-r-examples</loc>
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<loc>https://alphabetamath.cc/real-analysis/uniform-convergence-of-functions-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/amenability-reiter-nets-and-folner-conditions-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/artin-induction-and-rational-characters-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/blocks-defect-groups-and-the-brauer-homomorphism-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/brauer-induction-and-elementary-subgroups</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/brauers-first-main-theorem-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/equivariant-constructible-perverse-foundations-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/galois-orbits-and-descent-of-simple-finite-group-modules-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/quiver-full-flag-projective-semisimplicity</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/regular-weyl-representations-and-stone-von-neumann-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/regular-weyl-representations-and-stone-von-neumann</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/schur-indices-and-fields-of-definition-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/schur-indices-and-fields-of-definition</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/signed-quiver-flag-convolution-and-klr-ext-realization-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/signed-quiver-flag-convolution-and-klr-ext-realization</loc>
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<loc>https://alphabetamath.cc/representation-theory/sl2-r-discrete-series-and-unitary-dual-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/sl2-r-discrete-series-and-unitary-dual</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/sl2-r-principal-and-complementary-series-examples</loc>
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<loc>https://alphabetamath.cc/representation-theory/sl2-r-principal-and-complementary-series</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/the-modular-function-and-l1-group-algebras-examples</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/the-modular-function-and-l1-group-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/unitary-poincare-representations-and-little-groups-examples</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/unitary-poincare-representations-and-little-groups</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/unitary-representations-positive-type-and-gns-examples</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/unitary-representations-positive-type-and-gns</loc>
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<url>
<loc>https://alphabetamath.cc/representation-theory/vertices-sources-and-the-green-correspondence-examples</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<loc>https://alphabetamath.cc/representation-theory/vertices-sources-and-the-green-correspondence</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/affine-group-schemes-hopf-algebras-and-rational-representations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/affine-group-schemes-hopf-algebras-and-rational-representations</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/affine-schemes-and-the-structure-sheaf-examples</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/affine-schemes-and-the-structure-sheaf</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/algebraic-group-actions-orbits-stabilizers-and-controlled-quotients-examples</loc>
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<loc>https://alphabetamath.cc/scheme-theory/algebraic-group-actions-orbits-stabilizers-and-controlled-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/algebraic-spaces-stacks-and-derived-algebraic-geometry-foundations-examples</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/algebraic-spaces-stacks-and-derived-algebraic-geometry-foundations</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/analytic-derived-six-operations-and-duality-examples</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/analytic-derived-six-operations-and-duality</loc>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/blowups-exceptional-divisors-and-strict-transforms-examples</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/blowups-exceptional-divisors-and-strict-transforms</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/cartier-and-weil-divisors-line-bundles-and-picard-groups-examples</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/cartier-and-weil-divisors-line-bundles-and-picard-groups</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/cohomology-of-quasi-coherent-sheaves-on-affine-and-projective-schemes-examples</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/cohomology-of-quasi-coherent-sheaves-on-affine-and-projective-schemes</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/compact-support-sheaf-calculus-examples</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.7</priority>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/compact-support-sheaf-calculus</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/deformation-theory-of-schemes-and-obstruction-spaces-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/deformation-theory-of-schemes-and-obstruction-spaces</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/diagonals-separated-morphisms-and-valuative-uniqueness-examples</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/diagonals-separated-morphisms-and-valuative-uniqueness</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/fibre-products-base-change-and-scheme-theoretic-fibres-examples</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/fibre-products-base-change-and-scheme-theoretic-fibres</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/scheme-theory/finite-proper-and-projective-morphisms-examples</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/finite-proper-and-projective-morphisms</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/flat-smooth-and-etale-morphisms-examples</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/flat-smooth-and-etale-morphisms</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/group-schemes-of-finite-type-over-a-field-examples</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/group-schemes-of-finite-type-over-a-field</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/hilbert-functors-and-projective-hilbert-schemes-examples</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/hilbert-functors-and-projective-hilbert-schemes</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/kahler-differentials-conormal-sequences-and-infinitesimal-lifting-examples</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/kahler-differentials-conormal-sequences-and-infinitesimal-lifting</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/lie-algebras-and-infinitesimal-group-schemes-examples</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/lie-algebras-and-infinitesimal-group-schemes</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/presheaves-sheaves-stalks-and-sheafification-examples</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/presheaves-sheaves-stalks-and-sheafification</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/proj-projective-schemes-twisting-sheaves-and-ampleness-examples</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/proj-projective-schemes-twisting-sheaves-and-ampleness</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/quasi-coherent-and-coherent-sheaves-and-vector-bundles-examples</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/quasi-coherent-and-coherent-sheaves-and-vector-bundles</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/residues-serre-duality-for-curves-and-the-full-riemann-roch-theorem-examples</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/residues-serre-duality-for-curves-and-the-full-riemann-roch-theorem</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/riemann-roch-for-curves-via-euler-characteristics-examples</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/riemann-roch-for-curves-via-euler-characteristics</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/schemes-subschemes-and-morphisms-locally-of-finite-type-examples</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/schemes-subschemes-and-morphisms-locally-of-finite-type</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/sheaf-cohomology-cech-cohomology-and-comparison-examples</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/sheaf-cohomology-cech-cohomology-and-comparison</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/sheaf-operations-exactness-ringed-spaces-and-module-pullback-examples</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/sheaf-operations-exactness-ringed-spaces-and-module-pullback</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/smooth-proper-curves-divisors-genus-and-ramification-examples</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/scheme-theory/smooth-proper-curves-divisors-genus-and-ramification</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/set-theory/arithmetization-incompleteness-and-relative-consistency-examples</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/set-theory/arithmetization-incompleteness-and-relative-consistency</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.7</priority>
</url>
<url>
<loc>https://alphabetamath.cc/set-theory/boolean-algebras-stone-duality-and-the-prime-ideal-theorem-examples</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/boolean-algebras-stone-duality-and-the-prime-ideal-theorem</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/boolean-prime-ideal-theorem-in-the-basic-cohen-model-examples</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/set-theory/boolean-prime-ideal-theorem-in-the-basic-cohen-model</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/set-theory/borel-analytic-sets-perfect-sets-and-determinacy-examples</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/set-theory/borel-analytic-sets-perfect-sets-and-determinacy</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/cardinal-arithmetic-and-cofinality-examples</loc>
<lastmod>2026-08-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/cardinal-arithmetic-and-cofinality</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/choice-strength-in-baire-urysohn-stone-and-tychonoff-examples</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/set-theory/choice-strength-in-baire-urysohn-stone-and-tychonoff</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/club-stationary-sets-and-pressing-down-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/club-stationary-sets-and-pressing-down</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/condensation-gch-and-diamond-in-l-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/condensation-gch-and-diamond-in-l</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/construction-of-the-natural-numbers</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/deduction-soundness-completeness-and-compactness-examples</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/deduction-soundness-completeness-and-compactness</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/dependent-choice-and-the-complete-metric-baire-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/dependent-choice-and-the-complete-metric-baire-theorem</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/set-theory/eastons-theorem-and-cardinal-invariants-of-the-continuum-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/eastons-theorem-and-cardinal-invariants-of-the-continuum</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/filters-and-ultrafilters-examples</loc>
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</url>
<url>
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<loc>https://alphabetamath.cc/set-theory/ordinals-and-transfinite-recursion-examples</loc>
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<loc>https://alphabetamath.cc/set-theory/ordinals-and-transfinite-recursion</loc>
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<loc>https://alphabetamath.cc/set-theory/pcf-scales-and-zfc-dowker-spaces-examples</loc>
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<loc>https://alphabetamath.cc/set-theory/pcf-scales-and-zfc-dowker-spaces</loc>
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<loc>https://alphabetamath.cc/set-theory/permutation-models-and-transfer-to-zf-examples</loc>
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<loc>https://alphabetamath.cc/set-theory/permutation-models-and-transfer-to-zf</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/preservation-cohen-forcing-and-the-continuum-examples</loc>
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<loc>https://alphabetamath.cc/set-theory/preservation-cohen-forcing-and-the-continuum</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/prikry-forcing-and-gitiks-singular-cardinal-model-examples</loc>
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<loc>https://alphabetamath.cc/set-theory/prikry-forcing-and-gitiks-singular-cardinal-model</loc>
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<loc>https://alphabetamath.cc/set-theory/proper-forcing-countable-support-iterations-and-pfa-examples</loc>
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<loc>https://alphabetamath.cc/set-theory/proper-forcing-countable-support-iterations-and-pfa</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/reflection-absoluteness-and-elementary-submodels-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/reflection-absoluteness-and-elementary-submodels</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/relations-functions-and-quotients-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/relations-functions-and-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/set-theoretic-trees-delta-systems-and-diamond-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/set-theoretic-trees-delta-systems-and-diamond</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/shelahs-baire-property-model-and-inner-model-lower-bounds-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/shelahs-baire-property-model-and-inner-model-lower-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/solovays-model-and-regularity-of-all-sets-of-reals-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/solovays-model-and-regularity-of-all-sets-of-reals</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/suslin-trees-lines-algebras-and-independence-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/suslin-trees-lines-algebras-and-independence</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/symmetric-collapse-and-ultrafilter-free-models-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/symmetric-collapse-and-ultrafilter-free-models</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/symmetric-extensions-and-basic-choice-failure-models-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/symmetric-extensions-and-basic-choice-failure-models</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/the-constructible-hierarchy-and-inner-models-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/the-constructible-hierarchy-and-inner-models</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/the-forcing-theorem-and-formal-consistency-transfer-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/the-forcing-theorem-and-formal-consistency-transfer</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/the-zfc-axioms-and-basic-set-constructions-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/the-zfc-axioms-and-basic-set-constructions</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/weak-choice-principles-and-sierpinskis-theorem-examples</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/weak-choice-principles-and-sierpinskis-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/set-theory/well-founded-relations-rank-and-the-cumulative-hierarchy-examples</loc>
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<loc>https://alphabetamath.cc/set-theory/well-founded-relations-rank-and-the-cumulative-hierarchy</loc>
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<url>
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</url>
<url>
<loc>https://alphabetamath.cc/statistical-models-and-experiments/arma-causality-invertibility-and-spectra</loc>
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<url>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/benjamini-hochberg-independent-fdr-control</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/statistical-models-and-experiments/biological-and-technical-replication</loc>
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<url>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/blocking-and-paired-designs</loc>
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<url>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/competing-risks-and-cumulative-incidence</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/counting-process-compensators-and-integrals-examples</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/counting-process-compensators-and-integrals</loc>
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<url>
<loc>https://alphabetamath.cc/statistical-models-and-experiments/cox-ph-and-partial-likelihood-examples</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/cox-ph-and-partial-likelihood</loc>
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<url>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/detection-and-quantification-limits</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/discrete-sequential-test-validity-and-ville</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/event-time-censoring-and-truncation</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/exact-gaussian-linear-regression-inference</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/fdr-control-under-dependence</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/finite-window-spatial-point-process-likelihoods</loc>
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<loc>https://alphabetamath.cc/statistical-models-and-experiments/full-factorial-contrasts-and-interactions-examples</loc>
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<url>
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<url>
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<url>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-bijective-smooth-map-with-nonsmooth-inverse</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-bivector-in-r-four-need-not-be-decomposable</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-boundary-spur-when-free-reduction-is-omitted</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-bounded-continuous-function-need-not-have-positive-type</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-bounded-harmonic-boundary-value-problem-can-be-nonunique-without-almost-sure-boundary-hitting</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-braiding-alone-does-not-define-a-link-trace</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-bundle-map-with-rank-drop-is-not-a-formal-immersion</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-c-one-bijection-of-the-line-that-is-not-a-diffeomorphism</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-c1-map-whose-critical-values-have-positive-measure</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-category-that-is-not-well-powered</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-category-with-enough-injectives-but-not-enough-projectives</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-category-with-products-and-a-diagram-without-a-limit</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-cauchy-sequence-in-calligraphic-l-p-can-converge-to-two-distinct-functions</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-cell-decomposition-without-the-weak-topology-need-not-be-a-cw-complex</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-character-modulus-need-not-be-its-conductor</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-characteristic-analytic-surface-does-not-determine-the-normal-jet</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-chart-dependent-coordinate-vector-is-not-an-intrinsic-tangent-vector</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-closed-graph-without-continuity</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-closed-manifold-with-formally-plausible-rank-data-needs-positive-codimension</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-closed-subspace-need-not-have-a-best-approximation</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-closed-uncomplemented-subspace-is-not-a-split-banach-submanifold</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-coequalizer-not-preserved-by-a-forgetful-functor</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-coercive-functional-need-not-attain-without-weak-lower-semicontinuity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-comb-can-have-an-edge-between-two-blocks</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-comb-fails-when-a-tooth-sees-a-foreign-block</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-compact-leaf-with-infinite-fundamental-group-can-still-have-trivial-holonomy</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-compact-operator-can-have-nondense-range</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-compatible-almost-complex-structure-that-is-not-integrable</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-complement-in-a-semidirect-product-need-not-be-normal</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-complete-category-whose-coseparating-sets-are-never-small</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-complete-graph-has-no-large-sparse-set</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-complete-manifold-with-zero-global-injectivity-radius</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-complex-linear-map-can-fail-to-preserve-a-chosen-real-form</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-componentwise-family-that-is-not-a-unit</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-composition-of-integrable-functions-that-is-not-integrable</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-conjugate-point-at-which-there-are-many-geodesics</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-conservative-functor-that-is-not-monadic</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-continuous-function-of-modulus-at-most-one-need-not-be-positive-definite</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-continuous-function-on-a-non-closed-subspace-with-no-extension</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-continuous-image-of-a-locally-compact-space</loc>
<lastmod>2026-08-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-continuous-map-need-not-be-simplicial-before-subdivision</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-continuous-nowhere-differentiable-singular-one-simplex</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-continuous-preimage-can-break-lebesgue-measurability</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-corner-is-not-covered-by-the-single-c-one-chart-theorem</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-count-that-double-counts</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-covariant-hom-functor-on-an-additive-category-need-not-preserve-cokernels</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-critical-point-free-noncompact-band-need-not-be-a-global-product</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-crossing-diagram-without-height-monotonicity-does-not-define-a-configuration-loop</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-curl-free-c1-field-on-an-open-subset-of-r3-that-is-not-conservative</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-cut-point-that-is-not-conjugate-because-two-minimizers-arrive</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-cycle-graph-fails-finite-type-positive-definiteness</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-defective-jordan-block-has-ill-conditioned-eigenvectors</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-defective-jordan-block-produces-square-root-eigenvalue-splitting</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-degenerate-isolated-critical-point</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-degenerate-nonisolated-critical-set</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-degenerate-pullback-metric-under-a-constant-map</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-degree-one-derivation-need-not-square-to-zero</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-degreewise-split-cone-sequence-with-no-chain-splitting</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-deligne-kernel-need-not-be-one-external-tensor-factor</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-dfa-transition-diagram-may-omit-a-sink-without-changing-totality</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-difference-of-nested-modules-need-not-be-a-module</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-disconnected-base-allows-variable-sheet-number</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-disconnected-compact-group-element-outside-every-identity-component-torus</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-disconnected-rim-set-is-not-a-border-strip</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-distribution-function-need-not-have-a-density</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-domain-of-holomorphy-need-not-be-convex</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-family-of-components-need-not-be-natural</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-fibration-need-not-be-a-locally-trivial-bundle</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-finitely-additive-finite-valued-set-function-can-have-infinite-total-variation</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-four-dimensional-boundary-case-is-outside-the-smooth-h-cobordism-theorem</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-full-subcategory-limit-can-differ-from-ambient-limit</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-function-can-have-measurable-level-sets-without-being-measurable</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-function-with-a-primitive-that-is-not-integrable</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-functor-preserving-monomorphisms-but-not-pullbacks</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-galois-stable-character-need-not-have-schur-index-one</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-general-member-of-an-abelian-group-need-not-come-from-an-element</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-global-product-threshold-is-not-a-per-triple-sharpness-claim</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-harmonic-function-can-vanish-on-a-line-without-vanishing-identically</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-hecke-action-alone-does-not-imply-double-centralizer</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-homology-cobordism-need-not-be-an-h-cobordism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-homology-equivalence-need-not-be-a-homotopy-equivalence-without-simple-connectivity</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-homotopy-through-maps-with-a-rank-drop-is-not-a-regular-homotopy</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-jump-across-a-hypersurface-is-not-in-w-one-p</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-kac-moody-verma-module-is-not-integrable-in-general</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-kan-extension-that-is-not-pointwise</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-language-is-a-set-of-symbols</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-large-adverse-zero-order-term-destroys-dirichlet-coercivity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-last-exit-time-need-not-be-a-stopping-time</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-laurent-series-on-a-punctured-disc-can-have-infinitely-many-negative-terms</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-limit-of-discrete-series-is-not-square-integrable</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-linear-representation-need-not-be-faithful</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-list-of-length-mn-with-no-long-monotone-sublist</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-map-between-two-catalan-families-that-is-not-injective</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-map-with-two-preimages-but-degree-zero</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-matrix-with-one-zero-off-diagonal-is-not-a-gcm</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-maximal-abelian-subalgebra-that-is-not-a-cartan-subalgebra-in-a-nonsemisimple-algebra</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-maximal-antichain-that-is-not-maximum</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-meromorphic-function-on-the-plane-can-omit-two-sphere-values</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-mild-heat-solution-need-not-be-classical-at-initial-time</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-mild-solution-need-not-be-classical</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-minimising-sequence-need-not-converge-strongly</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-modular-specht-module-need-not-be-simple-or-have-nonzero-form-head</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-monoidal-category-need-not-be-closed</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-monomorphism-need-not-split</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-multiple-traversal-has-the-same-circle-trace-but-greater-length</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-naive-signed-count-without-the-quotient-orientation-can-fail-d-squared-zero</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nearest-point-projection-is-not-unique-outside-the-tubular-radius</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nilpotent-by-nilpotent-extension-that-is-not-nilpotent</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-no-proper-power-presentation-with-torsion-outside-small-cancellation</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-non-dini-continuous-poisson-source-can-destroy-continuity-of-second-derivatives</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-non-disjoint-union-does-not-satisfy-the-sum-rule</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-non-locally-finite-poset</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-non-locally-finite-sum-can-be-discontinuous</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-non-split-short-exact-sequence-of-abelian-groups</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonadapted-step-integrand-breaks-the-ito-isometry</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-noncommutative-handedness-error-in-tor</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-noncompact-codimension-one-foliation-need-not-satisfy-novikov-compactness-conclusions</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-noncompactly-supported-form-with-divergent-chart-integral</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-noncoprime-residue-class-has-no-dirichlet-conclusion</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-noncylinder-path-functional-may-fail-measurability</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nondegenerate-nonclosed-two-form-in-dimension-at-least-four</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nondominant-integral-verma-quotient-that-is-infinite-dimensional</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-noninvariant-quadratic-pbw-element-is-not-central</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonnatural-choice-of-connecting-maps-does-not-form-a-delta-functor</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonnatural-choice-of-uct-splitting</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonorientable-manifold-has-no-ordinary-integral-fundamental-class</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonproper-noncompact-morse-function-can-lose-continuation-trajectories-at-infinity</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonproper-pullback-destroys-compact-support</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nontight-sequence-with-no-probability-law-subsequence-limit</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nontransitive-system-is-not-classified-by-one-stabilizer</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nontrivial-whitney-circle-in-the-fundamental-group-blocks-cancellation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonunit-differential-entry-cannot-be-gaussian-cancelled</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonzero-function-on-a-null-set-has-zero-l-p-seminorm</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonzero-polynomial-vanishing-on-a-grid-of-exactly-its-degree</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-nonzero-stable-schur-function-can-vanish-in-too-few-variables</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-norm-closed-nonconvex-set-need-not-be-weakly-closed</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-norm-need-not-satisfy-the-parallelogram-law</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-normal-operator-need-not-have-any-eigenvectors</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-normalised-cube-indicator-is-not-a-hone-atom</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-null-recurrent-chain-has-no-stationary-probability</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-null-set-that-is-no-functions-discontinuity-set</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-partition-that-is-not-self-conjugate</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-partition-with-too-many-rows-vanishes-at-fixed-rank</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-path-connected-space-that-is-not-locally-connected</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-pointwise-finite-smooth-family-whose-sum-is-not-continuous</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-preconditioner-can-worsen-the-preconditioned-condition-number</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-process-with-the-right-transition-probabilities-relative-to-its-natural-filtration-may-fail-for-a-larger-filtration</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-product-without-unique-factorisation-does-not-satisfy-the-product-rule</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-projective-generator-need-not-be-small</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-projective-verma-flag-need-not-split</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-proper-action-with-stabilizers-whose-quotient-is-not-a-principal-bundle</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-proper-endpoint-homotopy-that-is-not-a-proper-combined-map</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-proper-subgroup-of-r-can-be-nonmeasurable</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-quasi-bialgebra-need-not-be-quasi-hopf</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-quasi-isometry-need-not-be-continuous-injective-or-surjective</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-quasi-isomorphism-that-is-not-an-isomorphism-of-complexes</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-quasi-isomorphism-with-no-homotopy-inverse</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-quasinilpotent-operator-need-not-be-zero</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-random-variable-need-not-have-a-finite-expectation</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-rank-drop-at-a-point-need-not-persist-locally</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-rank-jumping-kernel-is-not-a-vector-subbundle</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-rational-recurrence-may-need-a-proper-splitting-field</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-real-invertible-matrix-with-no-real-logarithm</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-reeb-component-has-a-compact-boundary-leaf-with-infinite-holonomy-behaviour</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-reflective-inclusion-need-not-preserve-colimits</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-reflexive-pair-whose-coequalizer-is-not-preserved</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-root-field-need-not-be-a-splitting-field</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-round-annulus-is-connected-but-not-simply-connected</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-schwartz-function-need-not-have-compact-support</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-semistandard-skew-tableau-with-nonlattice-word-is-not-lr</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-set-of-ordinals-that-is-not-transitive</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-set-theoretic-section-of-c-four-onto-c-two-need-not-be-homomorphic</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-sieve-computation-that-omits-a-term</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-singular-cochain-is-not-a-finite-singular-chain</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-singular-common-level-need-not-be-a-torus</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-smooth-approximation-without-relative-control-destroys-prescribed-values</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-smooth-density-can-have-infinite-total-mass</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-smooth-integrable-function-need-not-be-schwartz</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-snake-configuration-whose-kernel-row-is-not-short-exact</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-solution-of-yang-baxter-without-invertibility-does-not-represent-the-braid-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-special-p-group-that-is-not-extraspecial</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-stable-letter-word-that-is-not-britton-reduced</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-start-vector-orthogonal-to-the-dominant-left-eigendirection-can-defeat-power-iteration</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-stationary-chain-need-not-be-ergodic</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-step-set-for-which-the-reflection-argument-fails</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-subgraph-copy-need-not-be-induced</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-subgroup-of-an-abelian-group-need-not-be-characteristic</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-submanifold-meeting-the-ambient-boundary-nonneatly</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-a-submartingale-need-not-have-increasing-sample-paths</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-subobject-lattice-need-not-be-distributive</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-subspace-stable-under-one-generator-but-not-a-subrepresentation</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-surjective-image-of-n-need-not-be-equinumerous-with-n</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-surjective-local-homeomorphism-need-not-be-a-covering-map</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-surjective-map-need-not-be-a-fibration</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-symmetric-design-need-not-be-a-projective-plane</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-symmetric-transitive-relation-that-is-not-reflexive</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-tangent-intersection-whose-set-theoretic-intersection-is-not-of-the-expected-dimension</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-three-term-zero-composite-diagram-that-is-not-distinguished</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-time-discontinuous-forcing-can-block-classical-regularity-at-its-jump</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-tiny-residual-does-not-force-a-small-forward-error</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-torsion-free-connection-that-is-not-metric-compatible</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-transient-chain-can-return-with-positive-probability</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-transitive-action-need-not-be-frobenius</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-tree-cayley-graph-need-not-come-from-a-free-generating-set</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-two-dimensional-irreducible-real-representation-of-an-abelian-lie-algebra</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-union-of-two-disjoint-modules-need-not-be-a-module</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-variable-rank-involutive-family-outside-regular-frobenius</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-vector-field-with-no-pullback-under-a-noninjective-map</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-verma-module-need-not-be-projective-in-the-whole-block</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-version-can-fail-a-pointwise-identity-on-a-null-set</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-vertex-map-need-not-be-simplicial</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-vitali-set</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-weakly-convergent-net-need-not-be-eventually-norm-bounded</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-weight-module-with-unbounded-upward-support-is-not-in-o</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-wild-arc-drawing-is-not-a-plane-graph</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-a-zero-kernel-does-not-force-monicity-in-a-merely-semiadditive-category</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-abc-zero-tolerance-limit-fails-without-integrable-envelope</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-abel-summability-does-not-imply-ordinary-convergence</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-abel-test-needs-monotonicity</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-abelian-groups-do-not-satisfy-ab5-star</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-abelian-variety-does-not-have-good-model-over-every-base</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-absolute-value-integrable-without-the-function</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-absolute-value-is-not-differentiable-at-zero</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-abstract-group-action-is-not-algebraic-action</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-acyclic-disconnected-graph</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-adam-periodic-linear-losses-force-divergence</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-additive-rationals-show-finiteness-is-essential</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-adjacent-index-handles-with-zero-intersection-do-not-cancel</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ae-equality-can-fail-on-an-incomplete-space</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ae-zero-derivative-does-not-determine-endpoint-change</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-affine-bezout-misses-points-at-infinity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-affine-intersection-bound-singular-ambient</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-affine-line-not-proper</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-affine-vanishing-fails-non-qc-sheaf</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ag-differentials-arbitrary-map-is-not-base-change</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ag-regular-factors-product-not-regular</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-algebraic-intersection-one-with-three-geometric-points</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-almost-sure-convergence-does-not-imply-convergence-of-expectations</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-almost-sure-convergence-need-not-imply-lp-convergence</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-almost-sure-martingale-convergence-need-not-preserve-expectation</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-almost-surely-finite-stopping-does-not-imply-integrable-stopping</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-alpha-p-mu-p-rational-points-do-not-detect-scheme</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-am-gm-needs-nonnegative-terms</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-amenability-does-not-imply-subexponential-growth</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-a-zero-lattice-without-a-crystal-basis</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-abelian-category-with-no-nonzero-projective-object</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-abscissa-need-not-be-a-line-of-convergence</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-absolutely-continuous-finite-measure-can-have-an-unbounded-radon-nikodym-derivative</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-abstractly-dense-proper-subgroup-of-zp</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-acyclic-noncontractible-complex-from-a-nonsplit-extension</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-acyclic-noncontractible-cone</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-adapted-process-need-not-be-a-martingale</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-adjunction-whose-triangle-identities-fail-for-a-wrong-counit</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-alexander-horned-sphere-has-complementary-components-that-need-not-be-balls</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-algebra-that-is-not-free</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-algebraic-complement-need-not-be-topological</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-algebraic-extension-need-not-be-finite</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-ambiguous-cfg-need-not-generate-an-inherently-ambiguous-language</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-analytic-semigroup-need-not-be-norm-continuous-at-zero</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-annihilating-polynomial-need-not-be-minimal</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-arbitrary-subspace-inclusion-need-not-be-a-cofibration</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-arbitrary-transversal-does-not-give-the-reduced-schreier-basis</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-averaging-bound-that-is-not-attained</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-effective-encoding-need-not-be-prefix-free</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-eigenvector-branch-cannot-stay-differentiable-through-a-symmetric-crossing</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-embedded-sphere-with-nontrivial-normal-bundle-is-not-valid-framed-surgery-data</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-everywhere-defined-closed-operator-on-a-banach-space-cannot-be-unbounded</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-exact-functor-need-not-be-faithful</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-excellent-approximation-at-the-legendre-boundary</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-exhaustive-nonseparated-filtration-with-the-wrong-naive-abutment</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-hone-atom-need-not-be-smooth</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-immersed-whitney-disk-in-a-four-manifold-does-not-give-the-smooth-trick</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-incidence-function-with-nonunit-diagonal</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-incomplete-gradient-flow-on-a-noncompact-manifold</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-incomplete-subspace-need-not-be-closed</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-indefinite-nondegenerate-form-need-not-split-off-orthogonal-complements</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-index-one-moduli-space-can-be-infinite-without-compactness</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-infinite-coproduct-need-not-agree-with-the-infinite-product</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-infinite-dimensional-vector-space-has-no-dual-object</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-infinite-direct-sum-of-verma-modules-is-not-in-category-o</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-infinite-generating-set-destroys-the-comparison-of-word-metrics</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-infinite-level-is-not-a-combinatorial-class</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-inner-product-space-need-not-be-complete</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<loc>https://alphabetamath.cc/item/cex-an-integrable-function-with-no-primitive</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-intersection-of-cyclotomic-extensions-larger-than-the-gcd-case</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-intersection-of-two-primitive-ideals-need-not-be-primitive</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-interval-has-nonzero-euler-characteristic-despite-being-odd-dimensional</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-invariant-line-need-not-have-an-invariant-complement-over-a-laurent-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-inward-pointing-field-with-no-negative-time-flow-in-the-half-line</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-inward-radial-field-violates-the-outward-boundary-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-irrational-real-action-on-the-torus-that-is-free-but-not-proper</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-lone-function-with-nonzero-integral-is-not-in-real-hone</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-nfa-accepts-only-if-every-branch-accepts</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-odd-three-mod-four-valuation-obstructs-two-squares</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-oracle-machine-reads-the-infinite-oracle-at-once</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-ordered-eigenvector-branch-need-not-be-differentiable-through-a-crossing</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-ordinary-irreducible-with-reducible-mod-p-reduction</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-overlap-at-exactly-one-sixth-under-the-strict-convention</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-an-unbounded-complex-of-projectives-that-is-not-k-projective</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-unbounded-harmonic-function-need-not-extend-across-a-puncture</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-unbounded-predictable-transform-may-lose-integrability</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-unbounded-stopped-exponential-local-martingale-needs-uniform-integrability</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-uncountable-disjoint-union-of-points-is-not-second-countable</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-uncountable-supremum-of-indicators-need-not-be-measurable</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-unnormalized-hecke-trace-is-not-markov-invariant</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-unordered-infinite-zero-sum-is-not-a-formula</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-unoriented-real-bundle-has-no-integral-thom-class</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-an-unstable-homotopy-class-need-not-yet-be-stable</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-analytic-elliptic-cauchy-solutions-lack-smooth-continuous-dependence</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-analytic-heat-data-can-have-divergent-time-taylor-series</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-annulus-is-connected-but-not-homologically-simply-connected</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-annulus-needs-a-pole-in-each-bounded-complementary-component</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-antidiagonal-of-the-sorgenfrey-plane</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-antipodal-points-on-a-round-sphere-have-many-minimizing-geodesics</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-antisymmetric-need-not-be-alternating-in-characteristic-two</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-approximate-jacobian-breaks-stiff-damping</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-arbitrary-dominator-factorization-fails</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-arbitrary-link-isotopy-need-not-be-braid-isotopy</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-arbitrary-ltwo-boundary-data-need-not-have-an-h-one-lifting</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-arbitrary-pullback-does-not-define-a-chow-operation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-arbitrary-selected-columns-miss-dominant-direction</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-arc-length-is-not-continuous-under-uniform-convergence</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-arcsine-not-differentiable-at-endpoints</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-arcsine-of-sine-is-not-the-identity</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-average-cluster-size-does-not-determine-unequal-size-design-effect</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-backward-euler-scalar-stability-not-matrix-contractivity</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-backward-heat-amplifies-small-high-frequency-errors</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bad-cover-circle-cech-misses-h1</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bar-invariance-and-mod-q-congruence-without-balancedness</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-based-circle-loops-with-the-same-endpoints-need-not-be-path-homotopic</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bch-truncation-fails-when-higher-commutators-do-not-vanish</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bernoulli-needs-x-at-least-minus-one</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bertini-characteristic-p-failure</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-best-rank-two-cp-approximation-may-not-exist</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bijective-birational-not-isomorphism-cusp-reprise</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-birational-does-not-imply-isomorphic</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-blowup-arbitrary-base-change-failure</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-blowup-singular-center-not-smooth</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bmo-functions-need-not-be-globally-integrable</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-borel-fixed-point-needs-completeness</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-both-supports-cannot-be-singletons-when-n-is-greater-than-one</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bott-samelson-words-related-by-a-braid-need-not-be-isomorphic-bimodules</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundary-accumulation-does-not-force-holomorphic-identity</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundary-convergent-power-series-no-larger-holomorphic-disc</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundary-h-two-regularity-needs-domain-regularity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-boundary-mode-changes-laplace-rate</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundary-null-has-nonstandard-lr-limit</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundary-point-values-are-not-defined-by-an-lp-class</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundary-w-two-p-regularity-needs-c-one-one-type-control</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-continuous-cannot-be-replaced-by-all-bounded-measurable-functions</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-discontinuous-elliptic-coefficients-do-not-force-h-two-regularity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-form-without-coercivity-need-not-be-solvable</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-influence-does-not-imply-positive-breakdown</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-measurable-nondivergence-coefficients-do-not-give-schauder-estimates</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-not-totally-bounded</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-open-set-with-nonnull-boundary</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-spectrum-covariance-lower-rate-must-be-capped</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-bounded-total-derivative-on-a-nonconvex-domain-need-not-give-global-lipschitz</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundedness-does-not-replace-pointwise-relative-compactness</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundedness-is-not-topological</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-boundedness-of-first-moments-alone-does-not-give-uniform-integrability</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-box-topology-diagonal-not-continuous</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-branching-filtration-need-not-split-in-modular-characteristic</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-brownian-hitting-time-is-almost-surely-finite-but-not-integrable</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-c-four-and-v-four-can-share-a-nonfaithful-cycle-index</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-c-infinity-up-to-boundary-density-is-domain-sensitive</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-c-two-minus-a-complex-line-is-a-domain-of-holomorphy</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-c0-is-not-reflexive</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-c0-unit-ball-is-not-dentable</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-c6-and-two-triangles-share-a-degree-sequence</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-calderon-zygmund-operators-need-not-map-linfinity-to-linfinity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-calderon-zygmund-strong-lone-bound-fails</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-calling-one-prime-destroys-uniqueness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cancellative-monoid-not-a-group</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-canonical-and-quasi-canonical-bases-need-not-coincide</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-canonical-bidual-map-need-not-be-surjective</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-canonical-map-hyperelliptic-not-embedding</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cantor-function-is-not-w-one-one-despite-being-absolutely-continuous-off-a-null-set</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cantor-intersection-needs-vanishing-diameters</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cantor-measure-is-atomless-but-not-absolutely-continuous</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cantor-point-that-is-not-an-endpoint</loc>
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<loc>https://alphabetamath.cc/item/cex-carleson-maximal-operator-is-not-strong-type-one-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-category-o-is-not-extension-closed-in-all-g-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cauchy-davenport-fails-for-a-composite-modulus</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cauchy-input-has-no-degree-one-chaos</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cauchy-mean-value-quotient-form-needs-a-nonvanishing-derivative</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cauchy-product-of-convergent-series-diverges</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cauchy-rationals-no-rational-limit</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cauchys-theorem-does-not-extend-to-composite-divisors</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cech-refinement-map-not-canonical-on-cochains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cellularity-does-not-make-every-cell-module-simple</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cellwise-vanishing-obstructions-with-incompatible-choices-need-not-give-a-global-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-centerless-does-not-imply-semisimple</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-centralizer-containment-is-not-necessary-for-block-induction</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cg-artin-positive-lift-is-not-a-homomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cg-faithful-canonical-realization-need-not-be-reflection-faithful</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cg-i2-five-is-not-crystallographic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cg-interval-partition-with-nonmonotone-endpoints-is-not-a-congruence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cg-inversion-sets-do-not-compute-meets-and-joins</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cg-parabolic-quotient-interval-eulerian-claim-fails</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cg-rank-two-inversion-set-violating-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cg-shrinking-edge-ray-is-locally-finite-but-not-complete</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-chacon-correlation-subsequence-prevents-mixing</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-changing-a-connection-changes-the-form-but-not-its-de-rham-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-changing-a-framing-can-change-the-pontryagin-thom-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-changing-the-line-bundle-sign-dualizes-the-borel-weil-answer</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-changing-the-tensor-equality-convention-changes-the-crystal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-characteristic-cauchy-data-may-be-nonunique-or-incompatible</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-characteristic-initial-data-for-a-fully-nonlinear-equation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-characteristic-line-data-do-not-determine-a-one-dimensional-wave</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-chebyshev-bounds-do-not-give-the-prime-number-theorem</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-chinese-remainder-without-coprimality</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-circular-curve-defeats-vector-valued-mean-value-equality</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-classical-column-pivoted-qr-is-not-strong-with-factor-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-classical-parabolic-corner-regularity-needs-compatible-initial-and-boundary-data</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-clifford-algebra-need-not-be-semisimple</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-clifford-square-sign-changes-low-rank-algebra</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-closed-and-bounded-not-compact-in-the-sup-metric</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-closed-bounded-in-q-not-compact</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-closed-graph-fails-without-completeness</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-closed-orbit-does-not-imply-stability-positive-dimensional-stabilizer</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-closed-set-with-an-isolated-point-is-not-perfect</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-closed-subset-does-not-determine-closed-subscheme</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-closed-unbounded-euclidean-subset-not-compact</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-closure-of-ball-smaller-than-closed-ball</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-clt-can-fail-with-infinite-variance-under-square-root-n-scaling</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cochain-cup-product-is-not-graded-commutative-on-the-nose</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-coercive-form-need-not-be-symmetric</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cohomology-class-obstructs-a-global-symplectomorphism</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-collapse-with-a-nonsplit-extension-problem</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-colliding-column-colors-do-not-identify-a-jacobian</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-collinear-design-coefficient-risk-unidentifiable</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-collinear-design-fails-re-and-incoherence</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-collisions-destroy-freeness-of-coordinate-permutation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-common-component-bezout-sum-not-finite</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-common-divisors-of-zero-have-no-greatest-element</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-common-jump-prevents-riemann-stieltjes-integrability</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-commutative-monoids-are-semiadditive-and-not-additive</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-commutative-target-erases-the-a2-wall-crossing</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-commuting-endomorphisms-need-not-be-diagonalisable</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-compact-convergence-without-uniform-convergence</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-compact-does-not-imply-hilbert-schmidt</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-compact-peter-weyl-is-not-a-direct-sum-decomposition-for-noncompact-regular-representations</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-compact-set-without-jordan-content</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-compact-solid-without-jordan-volume</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-compactness-is-not-preserved-by-strong-operator-limits</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-comparison-needs-nonnegativity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-completed-product-sections-need-not-be-pointwise-measurable</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-completeness-is-not-topological</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-complex-conjugation-is-a-sphere-homeomorphism-not-holomorphic</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-complex-conjugation-preserves-unoriented-angles-but-is-not-conformal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-complex-continuous-multiplicative-map-not-the-standard-exponential</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-complex-power-series-not-uniform-on-its-open-disc</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-complex-squaring-is-not-globally-invertible</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-complex-step-absolute-value-returns-the-wrong-derivative</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-components-differ-from-quasicomponents</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-componentwise-algebra-action-need-not-define-a-tensor-action</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-composite-coordinate-proximal-rate-needs-penalty-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-composite-strong-convexity-alone-does-not-give-coordinate-factor</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-composition-factors-do-not-determine-the-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-composition-of-limits-fails</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-composition-of-relations-is-not-commutative</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-condensation-needs-monotonicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-condition-number-depends-on-the-chosen-norm-and-scaling</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conditional-linear-sum-does-not-force-product-convergence</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-conditionally-convergent-euler-product-rearrangement</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conditioning-does-not-preserve-strict-inequalities</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-cone-level-set-has-a-rank-drop-at-the-apex</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conformal-coverage-under-distribution-shift</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conformal-rare-subgroup-poor-conditional-coverage</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-congruence-need-not-preserve-trace-or-determinant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conjugacy-alone-does-not-classify-braid-closures</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conjugate-gradients-can-break-on-a-symmetric-indefinite-system</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conjugate-gradients-does-not-apply-to-a-nonsymmetric-invertible-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conjugation-does-not-send-distinct-parts-to-odd-parts</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-connected-domain-need-not-be-star-shaped</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-connected-even-degree-bowtie-is-not-a-cycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-connected-graphs-are-not-hereditary</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conormal-left-map-not-injective</loc>
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<loc>https://alphabetamath.cc/item/cex-conservative-fv-weak-limit-need-not-be-entropic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-conservative-sph-can-clump-under-positive-pressure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-consistent-marginals-alone-do-not-specify-joint-laws</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-consistent-mass-p1-fem-diffusion-fails-positivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-constant-coefficients-do-not-compute-a-nontrivial-monodromy-system</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-constant-functions-are-equicontinuous-not-pointwise-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-constant-presheaf-not-sheaf-disconnected-open</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-constant-sheaf-not-flasque</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuity-alone-does-not-give-delta-method</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuity-alone-does-not-imply-finite-quadratic-variation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuity-alone-does-not-satisfy-a-dini-modulus</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuity-does-not-imply-absolute-fourier-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuity-from-above-without-finite-first-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuous-bijection-not-a-homeomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuous-calculus-does-not-contain-discontinuous-spectral-projections</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuous-cantor-image-raises-hausdorff-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuous-fourier-series-need-not-converge-everywhere</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuous-function-of-unbounded-variation</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-continuous-function-with-divergent-fourier-series-at-a-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuous-functional-calculus-cannot-produce-every-spectral-projection</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-continuous-injection-on-a-non-interval-need-not-be-monotone</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-continuous-map-destroying-cauchyness</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-continuous-ode-with-nonunique-delayed-solutions</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-contraction-on-an-incomplete-space</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-contravariant-hom-need-not-be-right-exact</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-convergence-in-distribution-need-not-be-in-probability</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-convergence-in-probability-need-not-be-almost-sure</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-convergence-in-probability-need-not-imply-lp-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-convex-flux-riemann-formula-fails-for-a-nonconvex-flux</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-convex-function-on-closed-convex-set-discontinuous-at-the-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-convex-function-with-empty-subdifferential-at-a-boundary-point</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-convex-maximum-set-need-not-be-a-face</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-convolution-of-two-tempered-distributions-need-not-exist</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cook-levin-enumerates-all-branches</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-coordinate-vectors-do-not-converge-weakly-to-zero-in-ell-one</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-coproduct-preserving-left-exact-module-functor-is-not-tensor</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-correct-scale-trimming-slab-radius-four-is-false</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-coset-multiplication-by-a-nonnormal-subgroup</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cospectral-graphs-need-not-be-isomorphic</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-countable-car-representations-are-not-all-fock</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-countable-levels-do-not-suffice-for-konig</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-countable-partitions-can-be-strictly-better-than-finite-ones-for-a-complex-measure</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-countably-many-concentric-circles-give-an-injective-immersion-not-an-embedding</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-counting-every-lower-central-generator-with-weight-one</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-counting-measure-on-zero-one-shows-the-dominating-measure-needs-sigma-finiteness</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-credible-posterior-set-with-zero-frequency-coverage</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-critical-lagrange-point-evaluation-on-h1-in-two-dimensions</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-critical-level-sugawara-formula-undefined</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-critical-levels-cannot-always-be-interchanged-across-a-connecting-trajectory</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-critical-sobolev-embedding-is-not-compact</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-critical-trace-compactness-fails-by-tangential-dilation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-critical-value-can-have-a-smooth-level-set</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-critical-w-one-n-does-not-embed-in-linfinity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cross-group-contamination-violates-partial-interference</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-crouzeix-raviart-below-trace-threshold</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ctrl1-terminal-constraints-break-pointwise-control-vi</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cube-root-of-two-is-not-algebraically-constructible</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-curved-normal-family-statistic-incomplete</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cusp-level-set-has-a-rank-drop-at-the-origin</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cyclic-block-descent-may-cycle-outside-hypotheses</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cyclic-prime-square-extension-does-not-split</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cyclic-subgroups-do-not-give-integral-induction-in-general</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-cyclic-sylow-does-not-alone-imply-a-normal-p-complement</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-daha-a1-eigenvalue-separation-fails-at-q-one</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-decreasing-convergence-without-an-integrable-start-does-not-preserve-the-integral</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dedekind-kummer-without-the-index-hypothesis</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degenerate-ellipticity-allows-nonconstant-solutions-with-interior-zero-sets</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degenerate-gaussian-scale-prior-can-break-arbitrary-concentration-rate</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degenerate-q-ij-polynomials-destroy-the-faithful-basis-route</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degenerate-surface-parametrization-collapses-to-a-curve</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degree-is-not-defined-by-top-homology-for-self-maps-of-s-zero</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degree-p-squared-purely-inseparable-extension-is-not-simple</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degree-two-g-minus-one-not-always-basepoint-free</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degree-two-g-not-always-very-ample</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degree-zero-does-not-imply-a-sphere-map-is-constant</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degree-zero-line-bundle-no-section</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-degree-zero-projection-is-exact-cocontinuous-but-not-graded-tensor</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-delaunay-tetrahedral-sliver</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-delete-only-relator-rewriting-can-require-lengthening</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-delete-only-relator-rewriting-is-order-dependent</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-delete-only-relator-rewriting-misses-ba</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-deleting-stay-put-moves-does-not-preserve-computation</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dense-set-of-measure-zero</loc>
<lastmod>2026-08-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-density-continuity-fails-unequal-speed-routing</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dependent-equality-constraints-have-nonunique-multiplier-vectors</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dependent-level-samples-bias-product-estimator</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dependent-variables-need-not-factor-expectation</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dieudonne-borel-measure-on-omega-one-plus-one-is-not-regular</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-different-unstabilized-normal-bundles-can-have-nonisomorphic-thom-data</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-differentiable-with-unbounded-derivative-is-not-lipschitz</loc>
<lastmod>2026-08-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-differentials-purely-inseparable-field-nonzero</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-differentiation-under-an-improper-integral-without-domination</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dilations-can-destroy-tightness-on-an-unbounded-domain</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-dimension-empty-set-minus-infinity-needed</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dimension-formula-fails-for-three-subspaces</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dimension-one-binary-digit-set-with-zero-length</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-diminishing-adaptation-alone-does-not-imply-strong-law</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dini-needs-a-compact-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dini-needs-a-continuous-limit</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dini-needs-continuous-approximants</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dini-needs-monotonicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dirac-on-euclidean-space-is-not-fredholm</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dirac-threshold-sharp</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-direct-q-one-substitution-in-quantum-denominators</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-directional-derivatives-without-total-differentiability</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-directional-sparsity-is-not-symmetric</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dirichlet-density-alone-does-not-give-a-counting-asymptotic</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dirichlet-density-does-not-mean-integer-natural-density</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dirichlet-function-is-positive-but-has-zero-lebesgue-integral</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dirichlet-has-no-limit-anywhere</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dirichlet-is-not-riemann-integrable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-dirichlet-is-nowhere-continuous</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-disc-algebra-is-not-dense-without-self-adjointness</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-discontinuous-logarithmic-functional-equation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-discontinuous-midpoint-convex-hamel-function</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-discontinuous-multiplicative-cauchy-solution</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-discontinuous-right-hand-side-with-no-local-solution</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-distinct-borel-measures-can-represent-the-same-c-c-functional</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-distinct-point-count-needs-multiplicity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-distinct-polynomials-can-induce-the-same-finite-field-function</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-distinct-quadratic-forms-have-the-same-polar-form-in-characteristic-two</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-distinct-subspaces-of-the-dual-can-have-the-same-preannihilator</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-divergent-blaschke-sum</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-divergent-probability-sum-without-independence</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-divides-a-product-without-dividing-a-factor</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dj-bridge-untwisted-conjugation-changes-the-module</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-domain-tensor-algebraic-closure-reducible</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-doob-lp-maximal-inequality-excludes-p-equals-one</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-doubled-origin-diagonal-not-closed</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-doubled-origin-valuative-nonuniqueness</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-doubling-ergodicity-depends-on-the-invariant-measure</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dual-functor-is-not-covariant</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-dvr-only-test-unsafe-without-hypotheses</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-e-to-n-z-converges-chordally-to-infinity-on-the-right-half-plane</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-e-to-one-over-z-shows-essential-singularities-break-the-argument-principle</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-e-to-z-is-meromorphic-on-c-but-not-on-the-riemann-sphere</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-edge-deletion-alone-cannot-prove-induced-removal</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ell-one-and-ell-infinity-are-not-reflexive</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-elliptic-eigenvalues-need-not-be-simple</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-elliptic-fredholm-solvability-can-fail-at-an-eigenvalue</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-embedding-not-order-preserving</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-embedding-the-column-space-alone-does-not-control-ls-residual</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-empty-set-has-no-sup</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-enumerating-relator-consequences-does-not-decide-nontriviality</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-actions-on-k-zero-do-not-imply-isomorphic-derived-autoequivalences</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-central-character-does-not-give-every-verma-embedding-direction</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-dominant-moduli-can-make-power-iteration-cycle</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-finitely-many-moments-do-not-determine-a-law</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-homology-does-not-imply-homotopy-equivalence</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-iterated-integrals-do-not-imply-l-one-integrability</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-multiple-modes-double-laplace-constant</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-probability-events-need-not-be-independent</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-size-intervals-with-different-mobius-values</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equal-total-degree-does-not-classify-maps-from-a-disconnected-domain-componentwise</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equality-almost-surely-is-not-pointwise-equality</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equivalent-categories-need-not-be-isomorphic</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-equivalent-metrics-need-not-come-from-equivalent-norms</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-erdos-ko-rado-fails-below-two-k</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-euler-characteristic-alone-does-not-classify-compact-surfaces</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-euler-characteristic-does-not-determine-signature</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-euler-equality-alone-does-not-imply-perfectness</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-euler-lagrange-stationarity-does-not-imply-a-minimum</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-euler-moments-diverge-for-cubic-dissipative-sde</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-euler-totient-need-not-be-the-unit-group-exponent</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-eulerian-not-hamiltonian</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-eulerian-statistic-need-not-be-mahonian</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-even-polynomial-algebra-is-not-dense</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-every-compact-set-is-conformally-removable</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-every-total-computable-function-is-primitive-recursive</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-evt-and-ivt-fail-over-a-non-complete-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-evt-fails-on-the-open-interval-and-on-the-half-line</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-evt-fails-without-compactness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exact-np-hardness-implies-no-constant-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-excess-tail-functional-does-not-bound-trimmed-mean</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-excision-fails-without-the-closure-inside-interior-hypothesis</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exp-one-over-z-is-essential-and-omits-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exp-z-one-z-two-has-invertible-complex-jacobian-and-is-not-injective</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-expansion-shock-is-weak-but-not-entropic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exponent-sum-is-not-a-complete-braid-normal-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exponential-is-a-holomorphic-surjection-of-c-onto-c-times-not-an-automorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exponential-local-biholomorphism-is-not-proper</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exponential-not-uniformly-continuous-on-r</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exponential-product-limit-not-uniform-on-r</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-extension-by-zero-differs-direct-image</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-extension-by-zero-without-support-away-from-the-boundary-is-not-smooth</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-extensionality-is-needed-for-injective-collapse</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-exterior-dirichlet-uniqueness-needs-growth-or-decay-control</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-extra-sqrt-m-after-standard-error-studentization-diverges</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-factorial-generating-series-is-not-rational</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-factorial-power-series-has-radius-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-faithful-transitive-action-need-not-be-free</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-fas-zero-tau-breaks-fine-root</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-fatou-can-be-strict-and-domination-can-fail-simultaneously</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-fejer-means-need-not-converge-uniformly-for-discontinuous-data</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-feller-negligibility-cannot-be-removed-from-the-converse</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fermat-fails-at-an-endpoint</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-fibrewise-subschemes-without-flatness-do-not-form-a-hilbert-family</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-filtered-colimits-need-not-commute-with-infinite-products-in-set</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-filtered-vector-spaces-fail-the-coimage-image-axiom</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-filtered-vector-spaces-form-an-additive-category-with-all-kernels-and-cokernels-that-is-not-abelian</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-final-time-face-is-not-part-of-the-parabolic-boundary</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-additivity-alone-does-not-prove-infinite-cw-uniqueness</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-bit-flips-cannot-defeat-a-free-ultrafilter</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-cofinite-set-function-is-not-a-premeasure</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-dimensional-does-not-imply-finite-or-locally-finite</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-dimensional-lie-supermodules-need-not-be-semisimple</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-fibres-not-finite-morphism</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-fibres-not-finite-open-immersion</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-length-and-finite-hom-do-not-imply-finite-category</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-mean-functional-without-l2-influence-curve</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-normalization-does-not-make-the-curve-regular-before-blowups</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-quadratic-variation-does-not-imply-finite-total-variation</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-simple-module-classes-do-not-imply-semisimplicity-for-a-commutative-vertex-algebra</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-speed-does-not-imply-strong-huygens</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-support-makes-high-degree-moment-gram-singular</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-target-interpolation-does-not-state-an-infinite-endpoint</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-type-based-modules-need-not-have-finite-basis-compatible-envelopes</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-type-module-not-locally-free</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-type-not-finite-presentation-nonnoetherian-base</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-variance-does-not-imply-subgaussian-tail</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-finite-variance-is-not-the-same-as-compact-support</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-first-moment-threshold-one-is-not-enough</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-first-resolvent-estimate-does-not-give-hille-yosida-bound</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-first-row-padding-before-the-partition-threshold-is-undefined</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fitting-centralizer-without-solvability</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fixed-affine-cover-nonseparated-intersections</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fixed-neighbor-irregular-derivative-not-consistent</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fixed-point-congruence-fails-without-p-group-hypothesis</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fixed-time-nondifferentiability-does-not-prove-nowhere-differentiability</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fixing-the-boundary-only-setwise-changes-the-disk-mapping-class-group</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-flat-finite-type-not-open-without-presentation-warning</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-flat-hyperplanes-do-not-have-spherical-stationary-phase-decay</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-flat-not-smooth-nodal-family</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-flat-smooth-function-has-no-holomorphic-extension</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-floater-hormann-cd1-seminorm-rate-fails</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-forcing-is-not-upward-monotone-to-weaker-conditions</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-forgetting-labels-can-close-a-nonlooping-coordinate-path</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-formal-composition-with-nonzero-constant</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-formal-nonunit-has-no-inverse</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-forward-euler-negative-concentration-despite-stability</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-four-closed-sets-can-cover-s2-without-antipodal-pairs</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-four-dividing-n-forces-a-nonprimitive-two-square-representation</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fourier-inversion-need-not-hold-at-every-point-of-an-l-one-representative</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fourier-restriction-is-not-defined-on-lp-equivalence-classes-pointwise</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fourier-transform-of-an-l-one-function-need-not-be-integrable</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-frattini-image-under-a-nonsurjective-homomorphism</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-free-action-need-not-be-transitive</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-free-module-rank-fails-over-an-endomorphism-ring</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-free-ultrafilter-finitely-additive-probability</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-freezing-coefficients-cannot-absorb-a-fixed-large-oscillation-on-arbitrarily-small-balls</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-frobenius-cycle-type-needs-good-reduction</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-frobenius-not-smooth</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-frobenius-zero-tangent-map-not-formally-etale</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fubini-fails-without-l-one-integrability</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-full-dual-of-infinite-group-algebra-has-no-algebraic-coproduct</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-full-lsqr-can-amplify-data-noise</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fully-faithful-need-not-be-essentially-surjective</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-functors-need-not-preserve-monomorphisms</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-fundamental-group-depends-on-base-field</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-g-mod-h-need-not-have-an-invariant-measure</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gadget-correctness-needs-only-one-direction</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gap-amplification-alone-controls-alphabet</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gaps-tending-to-infinity-need-not-be-hadamard-lacunary</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gauge-of-a-nonbalanced-set-is-not-a-seminorm</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gauss-sum-sign-is-not-canonical-without-conventions</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gauss-sum-sign-without-a-complex-embedding</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gaussian-reduction-is-not-strictly-natural-for-arbitrary-chain-maps</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gelfand-transform-of-a-banach-algebra-need-not-be-isometric</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-generalization-after-open-assumption</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-generalized-pell-solutions-need-not-all-be-convergents</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-generating-family-without-pi-system</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-generic-target-smoothness-needs-smooth-source</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-genus-zero-without-rational-point-not-p1</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-geometric-cardinality-is-not-homotopy-invariant</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-geometric-power-series-not-uniform-on-its-open-interval</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-global-energy-identity-needs-integrability-or-decay</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-global-harnack-comparison-needs-connectedness</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-global-sections-epimorphism-fails-lift</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-global-sections-not-right-exact</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-globally-generated-not-very-ample</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-gmres-can-stagnate-on-a-nonnormal-matrix-with-moderate-conditioning</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-grandi-series-abel-summable-but-divergent</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-graph-of-x-sin-one-over-x-is-not-rectifiable</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-grazing-event-time-error-is-not-linearly-bounded</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-greedy-order-on-p-four</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-green-functions-need-not-exist-with-the-naive-boundary-regularity</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-grouped-series-converges-original-diverges</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-groups-of-order-p-cubed-need-not-be-abelian</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-h-two-estimate-needs-an-ltwo-kernel-term-without-injectivity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-h0-not-euler-characteristic-before-serre-vanishing</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-haar-averaging-does-not-produce-a-finite-measure-for-a-noncompact-group</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hahn-banach-extension-need-not-be-unique</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-half-graph-pairs-have-macroscopic-irregularity</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<loc>https://alphabetamath.cc/item/cex-half-norm-fails-the-triangle-inequality-on-two-indicators</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-half-open-interval-neither-open-nor-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-half-replacement-prevents-covariance-only-mean-recovery</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hamilton-path-not-hamilton-cycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hamiltonian-not-eulerian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hard-lefschetz-fails-for-a-non-dominant-degree-two-element</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hardy-littlewood-sobolev-strong-p-equals-one-endpoint</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-harmonic-on-a-punctured-domain-need-not-extend</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-harnack-estimate-needs-an-additive-forcing-term</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-harnack-requires-nonnegativity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-heat-equation-does-not-have-finite-propagation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-heine-borel-fails-in-ell-two</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-heine-cantor-fails-without-compactness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-henstock-kurzweil-integrability-is-not-absolute</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-heteroskedasticity-invalidates-ols-blue</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hh-coideal-with-nonzero-counit-does-not-give-quotient-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hh-infinite-dimensional-tensor-dual-identification-fails</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hh-infinite-dual-module-is-not-rational</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hh-nondegenerate-symmetrizing-trace-does-not-imply-semisimplicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hh-perfect-symmetrizing-trace-does-not-imply-semisimple</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hh-rank-one-tensor-action-is-not-faithful</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hh-separate-action-and-coaction-fail-hopf-compatibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-high-frequency-oscillations-violate-uniform-translation-control</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-higher-elliptic-regularity-cannot-exceed-the-forcing-regularity-by-more-than-two-derivatives</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-hilbert-monoid-factorisation-not-unique</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hilbert-schmidt-does-not-imply-trace-class</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hilbert-transform-does-not-map-linfinity-to-linfinity</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-hilbert-transform-is-not-strong-type-one-one</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hmm-marginal-modes-are-not-sequence-map</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hmm-zero-evidence-has-no-posterior-map</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-holomorphic-function-on-an-annulus-with-nonzero-closed-contour-integral</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-holomorphic-zero-set-in-two-variables-is-neither-isolated-nor-bounded</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hom-is-not-exact</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-homeomorphism-type-does-not-determine-smooth-structure-in-dimension-seven</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-homology-is-not-an-exact-functor</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hopf-conclusion-needs-a-strict-nonconstant-extremum</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hopf-lax-without-convex-superlinear-coercivity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hopf-lemma-needs-a-boundary-geometry-hypothesis</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-hp-degree-independent-sipdg-penalty-loses-coercivity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-identical-distribution-without-independence-can-defeat-the-mean-law</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-identical-e-two-pages-with-different-later-differentials</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-identical-one-step-marginals-do-not-determine-a-markov-chain</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-identifiability-alone-does-not-imply-posterior-consistency</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-identifiable-model-with-insufficient-abc-summary</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-identifiable-nonconstant-summary-loses-parameter</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-identity-is-compact-iff-the-space-is-finite-dimensional</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-identity-on-two-points-is-not-ergodic</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ignoring-monodromy-gives-the-wrong-serre-e-two-page</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-iid-bootstrap-inconsistency-at-absolute-mean-kink</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-iid-cauchy-averages-have-no-deterministic-weak-centering</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-iid-strong-law-fails-at-infinite-absolute-mean</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ilu0-product-can-create-fill-outside-input-pattern</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-image-morphism-not-closed</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-imaginary-root-spaces-need-not-have-multiplicity-one</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-importance-weight-ess-misses-target-region</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-improper-filter</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-incidence-vectors-dependent-over-the-two-element-field-and-independent-over-the-reals</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-indefinite-and-semidefinite-matrices-fail-positive-diagonal-cholesky</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-indefinite-classes-have-cycles-of-reduced-forms</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-independent-events-need-not-be-closed-under-unions-of-overlapping-pairs</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-independent-set-that-does-not-span</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-indicator-of-a-fat-cantor-set-is-not-integrable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-indicators-of-unit-interval-translates-converge-almost-everywhere-but-not-in-measure</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-indicators-of-unit-interval-translates-show-egorov-needs-finite-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-induction-axiom-necessary</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-inelastic-bouncing-ball-has-zeno-accumulation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-infinite-branching-is-not-enough-for-konig</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-infinite-mode-regular-weyl-representations-are-inequivalent</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-infinite-product-diverges-though-the-series-converges</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-infinite-ramsey-fails-with-infinitely-many-colours</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-infinite-sets-delta-system-hypothesis</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-informative-censoring-does-not-identify-event-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-inhomogeneous-equation-not-projectively-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-injective-transpose-does-not-imply-surjectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-inseparable-map-riemann-hurwitz-naive-fails</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-integrable-based-sl-two-tensor-triples-need-not-be-balanced</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-integrable-stopping-time-alone-does-not-suffice-for-arbitrary-martingale-increments</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-integral-total-pontryagin-multiplicativity-cannot-ignore-two-torsion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-interior-estimates-cannot-use-distance-zero-to-the-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-interior-of-a-union-is-larger</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-interior-regularity-does-not-imply-boundary-regularity</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-intersection-form-not-negative-definite-on-all-divisors</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-intersection-of-shrinking-intervals-not-open</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-intersection-of-ultrafilters-not-ultrafilter</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-intrinsic-variance-alone-does-not-control-covariance-pilot</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-invalid-spatial-lower-bound-can-prune-global-minimum</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-invariant-character-need-not-extend-linearly</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-invariant-subspace-need-not-reduce-an-operator</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-invertible-derivative-without-c-one-local-inverse</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-invertible-matrix-can-fail-unpivoted-lu-at-the-first-pivot</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-ip-equals-pspace-needs-no-degree-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-irrational-flow-on-a-symplectic-torus-is-symplectic-but-not-hamiltonian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-irrational-rotation-is-not-weakly-mixing</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-irrationals-are-not-f-sigma</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-irreducible-multiplicity-data-is-not-canonical-outside-type-i</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-irregular-summability-matrix</loc>
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</url>
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<loc>https://alphabetamath.cc/item/cex-isomorphic-associated-graded-objects-need-not-give-isomorphic-filtered-objects</loc>
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<loc>https://alphabetamath.cc/item/cex-isomorphic-hecke-classes-do-not-by-themselves-prove-homotopy-equivalent-complexes</loc>
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<loc>https://alphabetamath.cc/item/cex-isomorphic-middle-groups-do-not-determine-equivalent-extensions</loc>
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<loc>https://alphabetamath.cc/item/cex-it-asymptotic-source-channel-threshold-does-not-give-zero-error-at-finite-blocklength</loc>
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<loc>https://alphabetamath.cc/item/cex-it-fidelity-data-processing-does-not-prove-qre-dpi</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-it-kl-is-directional-and-can-be-infinite</loc>
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<loc>https://alphabetamath.cc/item/cex-jacobi-symbol-one-does-not-imply-a-square</loc>
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<loc>https://alphabetamath.cc/item/cex-jensen-can-fail-without-probability-normalization</loc>
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<loc>https://alphabetamath.cc/item/cex-k-four-is-planar-but-not-three-colourable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-k-three-three-satisfies-the-planar-edge-bound</loc>
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<loc>https://alphabetamath.cc/item/cex-k-topology-is-not-uniformizable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-k-zero-categorification-alone-does-not-identify-a-global-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-kac-formula-needs-ergodicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-kelley-cofinite-set-is-not-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-knapp-rules-out-extension-below-the-tomas-exponent</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-kolmogorov-complexity-is-an-absolute-integer</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-kolmogorov-extension-alone-does-not-give-a-continuous-version</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-konig-fails-on-triangle</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-kronecker-composition-subalgebra-is-proper</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-ks-weak-actions-do-not-supply-pentagon-coherence-data</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-l-one-not-subset-l-two-on-the-line</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-l-two-not-subset-l-one-on-the-line</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-l-zero-of-a-non-right-exact-functor-need-not-recover-the-functor</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-l1-bounded-martingale-need-not-converge-in-l1</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lagrange-multiplier-rule-needs-a-regular-constraint</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lattice-sample-covariance-not-positive-definite</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-laurent-nested-intervals-empty</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-lc-countably-incomplete-ultrapower</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lca-fourier-inversion-is-not-an-everywhere-statement-for-arbitrary-lone-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lebesgue-null-sets-need-not-have-zero-jordan-outer-content</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lebesgue-plus-counting-measure-has-no-lebesgue-decomposition-relative-to-lebesgue-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-left-and-right-duals-and-double-duals-need-not-collapse</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-left-coset-that-is-not-a-right-coset</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-left-to-right-exact-equivalence-need-not-preserve-the-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-leray-hirsch-fails-without-a-global-restricting-fiber-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lex-leading-term-not-found-by-unbalanced-substitution</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lhopital-converse</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lie-algebra-does-not-detect-nonsmooth-group-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lie-root-system-does-not-record-full-root-datum</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-limit-comparison-l-zero-one-directional</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-limit-differs-from-the-value</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-limit-not-unique-at-an-isolated-point</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-limit-point-compact-without-countable-compactness</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-limsup-infinite-not-attained-in-r</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-limsup-product-strict</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-limsup-subadditivity-strict</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lindelofness-is-not-productive-worked</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-line-with-two-origins</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-linear-and-cyclic-convolution-are-not-the-same-without-zero-padding</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-linear-bijection-need-not-preserve-jordan-content</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-linear-mixed-model-covariance-does-not-imply-ignorable-dropout</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-linearity-can-fail-without-integrability</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-linfinity-approximate-identity-need-not-converge-in-supremum-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-liouville-needs-one-sided-boundedness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-local-global-fails-for-a-cubic-curve</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-local-nilpotence-of-only-the-ei-does-not-imply-integrability</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-localisation-map-can-kill-a-nonzero-element</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-localising-at-a-set-containing-zero-gives-the-zero-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-locally-finite-type-not-finite-type</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-log-modulus-has-no-harmonic-conjugate-on-the-punctured-plane</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-log-one-plus-x-series-at-minus-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-logarithm-not-uniformly-continuous-on-positive-reals</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lower-semicontinuous-compact-function-without-a-maximum</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lp-boundary-data-need-not-lie-in-the-h-one-trace-range</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lp-convergence-need-not-imply-almost-sure-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lp-convergence-need-not-imply-lq-convergence-for-p-less-than-q</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-lp-functions-need-not-have-point-values</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-luzin-property-n-does-not-imply-absolute-continuity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-m-over-m-plus-n-has-noncommuting-iterated-limits</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-manipulating-the-euler-product-without-summability</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-marginal-subgaussianity-does-not-justify-mixture-confidence-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-markov-inequality-fails-without-nonnegativity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-mass-escapes-to-infinity-under-pointwise-convergence</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-maximal-matching-not-maximum-p4</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-maximal-not-greatest</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-maximal-proper-modules-need-not-be-disjoint-in-a-disconnected-graph</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-measurable-sections-do-not-imply-product-measurability</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-mercator-series-does-not-define-logarithm-globally</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-not-every-open-set-is-a-w-one-p-extension-domain</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-nowhere-dense-with-positive-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-np-means-not-polynomial</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-null-set-not-of-content-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-null-times-unbounded-need-not-be-null</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-numerical-rank-depends-on-the-declared-tolerance</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-o-minus-one-no-global-generators</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-objectwise-image-not-sheaf</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-observed-first-cause-does-not-identify-latent-failure-times</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-observed-paired-contrast-variance-is-not-effect-heterogeneity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-obstacle-admissible-set-can-be-empty-when-trace-and-obstacle-are-incompatible</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-obstacle-complementarity-product-needs-extra-regularity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-odd-rank-euler-class-need-not-vanish-with-two-torsion-coefficients</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omega-one-has-no-at-most-countable-cofinal-subset</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-cross-block-purity-breaks-the-transversal-conclusion</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-epsilon-closure-breaks-determinisation</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-exterior-corner-angles-from-a-geodesic-polygon</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-rosenbrock-stage-correction-loses-order-two</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-strictly-semistable-objects-breaks-hn-factorization</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-the-absolute-jacobian-reverses-sign</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-the-central-term-breaks-the-affine-gcm-bracket</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-the-exterior-root-weight-shifts-gives-the-wrong-dot-weight</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-omitting-the-rho-shift-breaks-kostants-formula</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-centred-ball-mean-identity-does-not-force-harmonicity</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-existing-iterated-integral-does-not-give-riemann-integrability</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-minus-two-plus-three-is-abel-but-not-cesaro-summable</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-observation-does-not-identify-a-smoothing-spline</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-over-sine-one-over-z-has-a-nonisolate-singularity-at-zero</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-over-x-is-not-uniformly-continuous-on-the-unit-interval</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-over-z-defeats-the-large-semicircle-estimate</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-over-z-has-a-nonremovable-puncture-in-one-variable</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-point-compactification-of-n-is-not-beta-n</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-one-subdivision-depth-does-not-make-all-singular-simplices-cover-small</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-open-action-set-no-minimizer</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-open-bounded-euclidean-subset-not-compact</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-open-cover-of-unit-interval-no-finite-subcover</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-open-cover-with-no-lebesgue-number</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-open-immersion-not-proper</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-open-mapping-fails-without-completeness</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-opposite-boundary-orientation-gives-the-wrong-sign-in-stokes</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-optional-stopping-fails-for-unbounded-simple-random-walk-hitting-time</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-orbit-count-is-not-set-size-divided-by-group-order</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-orbit-set-need-not-represent-quotient-sheaf</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordered-field-not-archimedean</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-acyclicity-forgets-basis-and-group-ring-torsion</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-acyclicity-over-z-does-not-detect-group-ring-torsion</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-barycentric-subdivision-cannot-fix-a-nonconstant-simplicial-edge</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-cohomology-does-not-give-noncompact-poincare-duality</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-importance-sampling-infinite-variance-under-light-tailed-proposal</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-intersection-number-alone-does-not-give-the-lkb-pairing</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-jucys-murphy-projection-formulas-do-not-survive-content-collision</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-tensor-product-fails-for-clifford-orthogonal-sums</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-trace-on-a-p-singular-unipotent-element</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ordinary-traces-on-p-singular-elements-do-not-define-brauer-characters</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-orientation-reversing-homeomorphism-is-quasiconformal</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-oscillatory-step-function-improper-integral-diverges</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-outer-induction-is-not-the-kronecker-product</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-outer-multiplicity-is-not-the-semistandard-tableau-count</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-overlapping-cycles-need-not-commute</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-p-regular-and-p-restricted-are-not-the-same-label</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pa36-positive-twist-global-sections-fail</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pa36-singular-localization-and-parabolic-kernel</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pair-count-normalized-sample-acvf-not-positive-semidefinite</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pairwise-positive-correlation-does-not-imply-prds</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pairwise-trivial-intersection-is-not-a-direct-sum</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-paracompactness-is-not-open-hereditary</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-paracompactness-is-not-productive</loc>
<lastmod>2026-08-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-partial-derivatives-without-continuity</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-particle-filter-proposal-misses-target-support</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-particle-gibbs-missing-path-support</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pasting-fails-for-an-infinite-closed-cover</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-path-dependent-parallel-transport-on-the-sphere</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pathwise-riemann-stieltjes-integration-does-not-construct-the-brownian-ito-integral</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pcp-allows-symbol-reordering-within-dominoes</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pe04-underintegrated-burgers-collocation-entropy-growth</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pe05-centered-source-produces-spurious-current</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pe12-linear-ritz-does-not-commute</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-peano-surface-linewise-minimum-without-an-extremum</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-peano-unequal-mixed-partials</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pell-units-need-not-be-all-quadratic-field-units</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-periodic-nonneutral-source-has-no-poisson-solution</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-periodic-perturbation-preserves-the-gamma-recurrence-and-factorial-values</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-permuting-meridian-conjugacy-classes-without-fixing-the-boundary-word-is-not-artin</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-phase-field-sav-modified-energy-not-physical-energy</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-place-permutation-is-not-a-nondegenerate-hecke-generator</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-plancherel-measure-is-not-uniform-on-partitions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-poincare-wirtinger-needs-connectedness</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-poincare-without-mean-trace-or-zero-set-normalisation-fails</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-point-evaluation-at-zero-is-not-well-defined-on-l-p-of-unit-interval</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointed-sets-are-not-additive</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointwise-bootstrap-ar1-variance-mismatch</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointwise-bootstrap-does-not-preserve-dependent-pair-law</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointwise-bounded-but-not-equicontinuous</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointwise-boundedness-without-a-uniform-bound-on-an-incomplete-domain</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointwise-cdf-convergence-at-a-jump-is-not-required</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointwise-convergent-functions-need-not-converge-as-distributions-without-local-control</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointwise-finite-dimensionality-does-not-imply-fi-finite-generation</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-pointwise-limit-discontinuous-at-zero-signals-mass-escape</loc>
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<loc>https://alphabetamath.cc/item/cex-pointwise-limit-of-integrable-functions-can-be-nonintegrable</loc>
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<loc>https://alphabetamath.cc/item/cex-pointwise-shock-values-do-not-affect-the-weak-solution</loc>
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<loc>https://alphabetamath.cc/item/cex-pointwise-strong-laws-do-not-imply-uniform-law</loc>
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<loc>https://alphabetamath.cc/item/cex-pointwise-values-do-not-determine-the-lie-bracket-at-a-point</loc>
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<loc>https://alphabetamath.cc/item/cex-poisson-commuting-functions-with-dependent-differentials-do-not-give-liouville-arnold-coordinates</loc>
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<loc>https://alphabetamath.cc/item/cex-poisson-integral-need-not-recover-discontinuous-data-at-the-jump</loc>
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<loc>https://alphabetamath.cc/item/cex-poisson-integral-on-the-half-space-is-not-unique-without-growth-control</loc>
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<loc>https://alphabetamath.cc/item/cex-polar-coordinates-are-not-globally-injective</loc>
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<loc>https://alphabetamath.cc/item/cex-polar-coordinates-do-not-give-a-chart-at-the-origin</loc>
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<loc>https://alphabetamath.cc/item/cex-polynomial-division-fails-for-a-nonunit-leading-coefficient</loc>
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<loc>https://alphabetamath.cc/item/cex-polynomial-rodl-does-not-force-the-whole-graph-to-be-restricted</loc>
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<loc>https://alphabetamath.cc/item/cex-polynomial-size-implies-uniform-generation</loc>
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<loc>https://alphabetamath.cc/item/cex-positive-abc-tolerance-changes-posterior-target</loc>
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<loc>https://alphabetamath.cc/item/cex-positive-characteristic-failure-of-lies-theorem</loc>
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<loc>https://alphabetamath.cc/item/cex-positive-determinant-does-not-imply-positive-definite</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-positive-ext-does-not-vanish-for-an-injective-first-variable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-positive-gradient-reverses-stable-and-unstable-dimensions</loc>
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<loc>https://alphabetamath.cc/item/cex-positive-kernel-second-moment-does-not-imply-nondegenerate-projections</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-positive-pair-densities-alone-do-not-force-a-triangle</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-positive-recurrence-without-aperiodicity-does-not-give-total-variation-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-positive-sectional-curvature-with-no-fixed-lower-bound-on-a-noncompact-manifold</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-positive-semidefinite-hessian-without-strict-convexity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-power-of-a-product-in-a-nonabelian-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-power-sums-do-not-form-an-integral-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-power-sums-do-not-generate-in-characteristic-two</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-power-weight-fails-at-both-a-p-endpoints</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-powers-locally-uniform-not-uniform-on-closed-disc</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-powers-on-the-unit-interval-converge-pointwise-not-uniformly</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-presheaf-bounded-continuous-functions-not-sheaf</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-presheaf-cokernel-needs-sheafification</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-primality-is-not-inherited-by-induced-subgraphs</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-principal-bundle-classification-can-fail-without-numerability</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-principal-complex-powers-exponent-law</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-process-valid-under-one-null-but-not-composite-null</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-kernel-blowup-defeats-a-global-grid-inference</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-measure-ae-equality-is-not-pointwise-equality-of-integrands</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-measure-need-not-be-unique-without-sigma-finiteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-of-complete-measures-need-not-be-complete</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-of-two-distributions-is-not-canonically-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-of-two-infinite-groups-need-not-be-hyperbolic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-of-two-quadratic-nonresidues-modulo-a-composite</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-of-two-subgroups-not-a-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-product-of-uniformly-continuous-functions-need-not-be-uniformly-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-progressive-map-without-fixed-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-proj-graded-ring-not-faithful</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-projection-branch-locus-is-not-singular-locus</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-projection-is-not-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-proper-finiteness-fails-noncoherent</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-proper-not-affine-positive-dimensional</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-proper-not-necessarily-projective</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-proper-subspace-with-an-equinumerous-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-properness-is-needed-for-the-compact-boundary-package</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-pseudocompact-noncompact-particular-point-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-pseudoinversion-is-discontinuous-at-a-rank-changing-diagonal-family</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-psi-of-one-over-x-has-no-limit-at-zero</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-purely-inseparable-base-change-nonreduced</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-pushforward-qc-needs-quasi-separated</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-qa-14-query-parallelism-does-not-give-exponential-search</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-qa-20-sparse-oracle-does-not-give-term-list</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-qa-21-unknown-input-reflection</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/cex-radial-boundary-limit-does-not-force-tangential-limit</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-radius-does-not-determine-boundary-convergence-of-a-complex-power-series</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-radix-two-recursion-does-not-directly-apply-to-odd-length</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-ramified-frobenius-has-no-canonical-lift</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-rankine-hugoniot-alone-does-not-give-uniqueness</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-ratio-inconclusive-root-decides</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-rational-cherednik-category-o-not-semisimple-at-half</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-rational-isotropy-is-not-integral-representation</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-rational-map-singular-curve-not-extend-uniquely</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rational-map-with-indeterminacy</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rational-modules-need-not-be-semisimple-in-characteristic-p</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rational-points-in-unit-square-have-no-jordan-content</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rational-power-laws-need-positive-base</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rational-valued-character-need-not-be-defined-over-the-rationals</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rationals-in-an-interval-are-disconnected</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-raw-prplus-loses-descent-and-safeguard-restarts</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-real-bezout-needs-algebraic-closure</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-real-part-is-nowhere-complex-differentiable</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-real-projective-two-space-is-not-unoriented-null-cobordant</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-recognizable-means-total</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-recurrence-is-not-a-property-shared-by-different-communicating-classes</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-recursion-theorem-needs-source-file-access</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-reducible-polynomial-quotient-is-not-a-field</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-reductions-may-reverse-yes-and-no</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-reentrant-corner-poisson-solution-not-h2</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-regular-bijection-not-isomorphism-cusp</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-regular-conditional-laws-are-not-unique-on-null-conditioning-values</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-regular-expression-syntax-is-its-denoted-language</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-regular-graphs-are-not-hereditary</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-regular-not-smooth-purely-inseparable-point</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rejection-is-divergence</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-relative-homology-is-not-the-homology-of-the-set-difference</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-relativized-separations-prove-unrelativized-separations</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rellich-fails-on-rn-by-translations</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rellich-fails-without-uniform-tail-control</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-reordering-a-conditional-basis-can-destroy-convergence</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-repeated-unit-root-causes-linear-parasitic-growth</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-repeating-constraints-amplifies-the-gap</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-residue-sequences-need-not-separate-when-e-is-at-most-n</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-reusing-random-bits-amplifies-success</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-reversing-boundary-orientation-reverses-flux</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-reversing-orientation-preserves-a-contour-integral</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-reversing-the-contact-extremum-reverses-the-viscosity-inequality</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ricci-lower-bound-does-not-control-every-sectional-curvature-in-dimension-at-least-three</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-riemann-inequality-not-equality-special-divisor</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-riemann-lebesgue-has-no-universal-rate</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-riemann-sums-along-one-sequence-of-tagged-partitions-do-not-suffice</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-riesz-potential-integral-can-diverge-at-the-upper-endpoint</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-right-continuity-is-necessary-for-lebesgue-stieltjes-measures</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-right-continuous-psi-has-the-wrong-perron-endpoint</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-right-exact-module-functor-without-coproduct-preservation-is-not-tensor</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ring-homomorphism-not-preserving-identity</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-ringed-space-map-not-locally-ringed</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-roe-jump-property-does-not-imply-entropy-admissibility</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rolle-fails-over-a-non-complete-field</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-root-limit-one-decides-nothing</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-row-equivalent-matrices-can-have-different-column-spaces</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-row-padding-does-not-preserve-a-kronecker-coefficient-before-stability</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-rudin-bounded-spikes-are-not-equicontinuous</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-s-three-has-trivial-center</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-saga-linear-factor-fails-under-standard-initialization</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-cardinality-without-a-canonical-bijection</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-complex-lie-algebra-with-distinct-global-groups-sl-two-and-pgl-two</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-complexification-with-different-killing-form-signatures</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-descent-set-different-inversion-number</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-discriminant-does-not-imply-proper-equivalence</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-finite-quotients-do-not-trivially-identify-abstract-groups</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-intrinsic-plane-with-different-extrinsic-curvature-after-bending</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-middle-group-with-inequivalent-extension-maps</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-represented-integers-do-not-imply-proper-equivalence</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-sign-intersection-points-cannot-be-whitney-cancelled-orientedly</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-same-topology-different-cauchy-sequences</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-savitch-stores-the-whole-configuration-graph</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-schauder-estimates-fail-at-the-holder-endpoint-alpha-one</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-scheme-not-determined-by-underlying-space</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-schwarz-lantern-polyhedral-areas-diverge</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-schwarz-naive-coarse-space-misses-conductive-mode</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-second-derivatives-of-the-fundamental-solution-are-not-locally-integrable-absolutely</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-sector-angle-changes-under-the-sign-convention</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-self-adjoint-part-need-not-be-associative-subalgebra</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-self-adjointness-cannot-be-dropped-from-the-order-calculus</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-semicontinuous-function-almost-everywhere-equal-to-no-riemann-integrable-function</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-semistable-locus-depends-on-linearization</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-separability-is-not-hereditary-worked</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-separable-nonnormal-extension-with-trivial-automorphism-group</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-separately-continuous-not-jointly-continuous</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-separating-algebra-without-constants-is-not-dense</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-sequential-closure-strictly-inside-closure</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-sequential-limits-not-unique</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-sequential-uniform-boundedness-needs-a-complete-domain</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-sequentially-continuous-not-continuous</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-serre-duality-without-properness</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-serre-page-collapse-does-not-split-the-abutment</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-set-distance-is-not-a-metric</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-set-partitions-with-the-same-block-sizes-can-be-distinct</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-set-theoretic-fibre-loses-multiplicity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-setwise-endpoints-do-not-make-a-braid-pure</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-setwise-puncture-preservation-does-not-define-the-pure-mapping-class-group</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-sharp-frequency-cutoffs-do-not-have-uniform-lone-kernels</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-sharpp-is-a-language-class</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<loc>https://alphabetamath.cc/item/cex-sigma-n-and-pi-n-are-disjoint</loc>
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<loc>https://alphabetamath.cc/item/cex-signorini-nodal-contact-feasibility-needs-convex-obstacle</loc>
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<loc>https://alphabetamath.cc/item/cex-sir-l2-bound-from-conditional-means-is-false</loc>
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<loc>https://alphabetamath.cc/item/cex-size-without-cancellation-does-not-give-a-principal-value-operator</loc>
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<loc>https://alphabetamath.cc/item/cex-sl2-r-complementary-series-destroys-property-t</loc>
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<loc>https://alphabetamath.cc/item/cex-small-residual-does-not-certify-positivity</loc>
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<loc>https://alphabetamath.cc/item/cex-smc-clt-class-does-not-ensure-target-moment</loc>
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<loc>https://alphabetamath.cc/item/cex-smc-residual-clt-fails-at-integer-weight-boundary</loc>
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<loc>https://alphabetamath.cc/item/cex-smc-time-bound-fails-with-varying-proposals</loc>
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<loc>https://alphabetamath.cc/item/cex-smooth-does-not-imply-real-analytic-for-general-pde</loc>
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<loc>https://alphabetamath.cc/item/cex-smooth-interior-data-do-not-repair-incompatible-dirichlet-corner-values</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-smooth-linewise-minimum-without-an-extremum</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-sobolev-embedding-on-an-unbounded-domain-needs-the-full-norm-or-decay</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-soergel-character-grading-alone-does-not-prove-category-o-koszulity</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-solution-count-trichotomy-fails-over-a-finite-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-solvable-group-need-not-be-an-m-group</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-sparse-gap-truth-causes-empirical-bayes-credible-set-undercoverage</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-sparsity-does-not-pass-to-subsets</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-specht-irreducibility-fails-without-the-characteristic-zero-hypothesis</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-spectrum-can-shrink-in-a-larger-banach-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-sphere-is-not-the-boundary-of-the-ball</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-spherical-and-antispherical-normalizations-give-different-polynomials</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-sqrt-k-differences-null-not-cauchy</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-square-modulo-each-prime-does-not-ignore-the-two-part</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-squaring-on-units-is-not-a-homomorphism-nonabelian-warning</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-standard-midpoint-nystrom-not-operator-norm-convergent</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-step-function-has-no-locally-integrable-weak-derivative</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-strict-contraction-without-a-fixed-point</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-strictly-decreasing-gaps-no-limit</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-strong-continuity-does-not-imply-operator-norm-continuity</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-strong-maximum-principle-needs-connectedness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-strongly-continuous-unitary-group-need-not-be-norm-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-su-two-and-so-three-share-a-root-system-but-are-not-isomorphic</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-subset-closed-under-addition-but-not-scaling</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-sum-and-product-totalisations-can-differ-on-infinite-diagonals</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cex-test-supermartingale-supremum-threshold-need-not-be-attained</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-algebraic-character-group-without-compact-open-topology-is-not-pontryagin-duality</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-bernstein-holder-one-half-endpoint-can-fail</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-bidisc-minus-the-origin-is-not-holomorphically-convex</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-box-topology-disconnects-a-product-of-connected-spaces</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-braid-category-is-braided-but-not-symmetric</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-c0-unit-ball-has-no-extreme-points</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-cantor-function-fails-luzin-property-n</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-cartesian-product-is-not-associative</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-central-character-does-not-determine-the-primitive-ideal</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-central-product-decomposition-of-an-extraspecial-group-is-not-unique</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-cfl-pumping-lemma-characterizes-cfls</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-circle-and-line-have-isomorphic-one-dimensional-lie-algebras-but-are-not-isomorphic-lie-groups</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-classical-composition-of-absolutely-continuous-functions-is-not-absolutely-continuous</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-closed-angular-form-on-the-punctured-plane-is-not-exact</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-closure-of-a-cw-cell-need-not-be-a-closed-ball</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-collapsing-recursion-has-no-solution-on-the-integers</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-complementary-form-loses-positivity-beyond-the-unitary-interval</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-composition-of-two-absolutely-continuous-functions-need-not-be-absolutely-continuous</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-core-circle-of-a-mobius-band-has-no-integral-oriented-self-intersection</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-cup-product-of-arbitrary-abelian-group-valued-cochains-is-not-canonical</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-degenerate-ariki-theorem-does-not-imply-the-nondegenerate-one</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-deleted-tychonoff-plank-is-not-normal</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-density-ratio-is-undefined-on-zero-marginal-fibres</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-diamond-and-pentagon-lattices-are-not-distributive</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-doubling-functor-on-set-is-not-representable</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-empty-family-is-not-erdos-hajnal</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-empty-set-is-not-a-surjective-image-of-n</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-eta-series-represents-the-continuation-where-the-dirichlet-series-diverges</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-factorial-gap-series-has-the-unit-circle-as-a-natural-boundary</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-figure-eight-and-round-circle-are-not-regularly-homotopic-as-oriented-immersions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-figure-eight-is-an-immersed-image-not-an-embedded-submanifold</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-first-mean-value-theorem-needs-a-one-signed-weight</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-five-cycle-is-bull-free-but-not-perfect</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-free-group-on-two-generators-is-not-amenable</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-full-algebraic-dual-of-a-verma-module-is-not-in-o</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-full-fock-space-is-not-automatically-the-irreducible-basic-module</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-full-weight-lattice-does-not-integrate-to-every-central-quotient-group</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-hardy-littlewood-maximal-operator-is-not-strong-type-one-one</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-harmonic-series-shows-the-defining-series-diverges-at-one</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-hawaiian-earring-is-not-a-cw-complex-with-its-circle-cells</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-ideal-x-y-in-a-bivariate-polynomial-ring-is-not-principal</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-identity-on-f-two-has-no-cyclic-vector</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-image-of-an-intersection-is-smaller-than-the-intersection-of-the-images</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-induced-permutation-does-not-determine-a-braid</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-integers-are-not-a-sidon-set</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-integral-kronecker-map-need-not-be-an-isomorphism</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-inversion-crossed-homomorphism-of-c-two-to-z-is-not-a-homomorphism</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-kernel-row-of-a-morphism-of-short-exact-sequences-need-not-be-short-exact</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-koch-curve-is-not-rectifiable</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-lexicographic-order-on-integer-pairs-is-not-a-well-order</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-logarithmic-ramsey-bound-is-not-an-erdos-hajnal-bound</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-long-line-is-locally-euclidean-and-hausdorff-but-not-a-manifold-under-the-library-convention</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-ltwo-unit-sphere-is-not-weakly-closed-in-an-infinite-dimensional-hilbert-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-mean-value-inequality-is-attained</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-members-of-an-object-do-not-form-a-group</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-mertens-conjecture-is-false</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-minimal-derivative-is-symmetric-not-self-adjoint</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-natural-filtration-need-not-be-right-continuous-before-augmentation</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-one-form-y-dx-is-path-dependent</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-one-norm-comes-from-no-inner-product</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-opposite-of-abelian-groups-does-not-satisfy-ab5</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-ordered-to-unordered-two-point-quotient-is-not-one-to-one</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-ordinary-chain-rule-fails-for-brownian-motion</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-pointwise-limit-of-continuous-functions-need-not-be-continuous</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-power-set-of-a-union-is-larger-than-the-union-of-the-power-sets</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-product-of-harmonic-functions-need-not-be-harmonic</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-product-of-two-unions-is-larger-than-the-union-of-the-two-products</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-pullback-on-cohomology-reverses-composition-order</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-pumping-lemma-characterizes-regular-languages</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-punctured-disc-has-an-irregular-boundary-point-and-a-nonsolvable-datum</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-punctured-disc-is-connected-but-not-simply-connected</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-punctured-plane-separates-c-complement-from-spherical-complement</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-quaternion-extension-of-c-two-by-c-four-does-not-split</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-quotient-of-a-tree-can-have-cycles</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-reflected-sphere-embedding-is-regularly-homotopic-but-not-isotopic-to-the-standard-one</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-regular-bgg-complex-cannot-be-used-unchanged-at-a-singular-weight</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-relative-floating-point-model-excludes-overflow-underflow-and-invalid-operations</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-residue-cocycle-depends-on-invariant-form-normalization</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-same-number-of-removable-p-hooks-does-not-replace-the-core-test</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-same-trace-can-have-different-path-lengths</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-samuel-map-need-not-preserve-the-original-uniformity</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-second-kind-inclusion-exclusion-formula-does-not-count-permutations-by-cycles</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-shapovalov-form-is-not-positive-definite-in-general</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-shift-is-a-nonidentity-order-automorphism</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-short-exact-sequence-to-s-n-does-not-prove-b-n-torsion-free</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-sine-integral-is-improperly-riemann-integrable-and-not-lebesgue-integrable</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-skeleton-of-set-cannot-be-made-strict-by-identification</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-standard-contact-plane-field-is-not-integrable</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-tautological-line-over-rp-infinity-has-no-finite-rank-complement</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-top-square-formula-does-not-define-all-lower-squares</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-the-translation-semigroup-is-not-analytic</loc>
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<loc>https://alphabetamath.cc/item/cex-the-uct-splitting-is-not-natural</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-underlying-bar-contraction-is-not-equivariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-underlying-quotient-graph-does-not-determine-the-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-unit-interval-indicator-has-nonintegrable-maximal-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-unitary-dual-need-not-be-hausdorff</loc>
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<loc>https://alphabetamath.cc/item/cex-the-universal-coefficient-splitting-cannot-in-general-be-chosen-naturally</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-untwisted-e-two-page-misses-monodromy-in-a-mapping-torus</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-volume-coordinate-expression-changes-sign-under-a-reflection</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-whole-affine-hecke-algebra-is-not-one-cyclotomic-klr-block</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-whole-partition-fock-space-is-not-the-basic-representation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-the-zero-countable-infinity-cocountable-measure-space-breaks-p-equals-one-duality</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-there-is-no-field-with-six-elements</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-three-point-outer-measure-has-only-trivial-caratheodory-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-three-squares-fail-for-seven-modulo-eight</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-threefold-classification-is-not-global</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-thresholded-sparse-covariance-rate-unbounded-at-superexponential-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-tietze-fails-in-a-t1-space-that-is-not-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-time-inhomogeneous-chain-cannot-be-encoded-by-one-kernel-without-enlarging-state</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-tonelli-fails-without-sigma-finiteness-on-the-diagonal</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-topological-abelian-groups-are-additive-and-not-abelian</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-topologically-not-uniformly-equivalent</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-topologists-sine-curve-connected-not-path-connected</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-torsion-free-abelian-groups-do-not-form-an-abelian-category</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-torsion-free-nilpotent-group-with-torsion-in-abelianization</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-total-quotient-ring-of-a-nondomain-need-not-be-a-field</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-total-variation-can-exceed-the-absolute-value-of-the-set-value</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-totally-bounded-not-compact</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-trace-of-products-is-not-cyclic-without-summability</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-trace-theorem-fails-on-a-standard-outward-cusp-without-domain-control</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-transfinite-induction-fails-when-the-minimum-is-exempted</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-transitive-does-not-force-minimal-normal-subgroups-transitive</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-translation-semigroup-is-not-strongly-continuous-on-linfinity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-transpose-range-need-not-be-norm-dense</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-trivial-kernel-does-not-imply-surjective</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-truncated-fields-need-not-be-local</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-truncated-kernel-loses-boundary-constant-reproduction</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-truth-at-one-assignment-does-not-survive-substitution</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-closed-convex-sets-need-not-be-strongly-separated</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-disjoint-nonmeasurable-sets-can-have-a-measurable-union</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-distinct-chain-maps-inducing-the-same-homology-map</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-equivalent-higher-extensions-with-no-single-isomorphism-of-middle-terms</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-formally-distinct-words-that-become-the-same-object</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-homogeneous-need-not-be-two-transitive</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-l-two-functions-can-have-convolution-outside-l-two</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-latin-squares-need-not-be-orthogonal</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-maps-into-an-indiscrete-space-agreeing-on-a-dense-set</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-monomorphisms-representing-the-same-subobject</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-morphisms-agreeing-on-every-member-need-not-be-equal</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-noncompatible-atlases-on-the-real-line</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-nonconjugate-real-cartan-subalgebras</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-nonhomotopic-leaf-loops-can-have-the-same-holonomy-germ</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-point-outer-measure-need-not-be-regular</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-projective-resolutions-with-nonisomorphic-first-syzygies</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-radon-nikodym-derivatives-can-differ-on-a-null-set</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-two-visits-alias-random-slope-and-residual-variance</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unbased-homotopic-based-maps-need-not-induce-the-same-based-homotopy-map-without-basepoint-transport</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unbounded-closed-set-not-compact</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unbounded-domain-does-not-suffice-for-fodor</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unbounded-punctured-harmonic-singularity-is-not-removable</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unbounded-set-has-no-sup</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unbounded-with-convergent-subsequence</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uncorrected-random-permutation-pvalue-can-be-zero</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uncorrelated-random-variables-need-not-be-independent</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uncountable-class-has-nonmeasurable-empirical-supremum</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uncountable-zero-dimensional-binary-digit-set</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-undecidable-means-no-instance-can-be-answered</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-undersampling-identifies-two-distinct-pure-frequencies</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-understated-thinning-envelope-is-invalid</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unfiltered-l-infinity-maurer-cartan-sum-is-undefined</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniform-bijection-with-non-uniform-inverse</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniform-boundedness-fails-on-an-incomplete-domain</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniform-convergence-does-not-control-derivatives</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniform-convergence-does-not-force-integral-convergence-on-an-infinite-measure-space</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniform-maximum-has-n-rate-not-root-n</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniform-moving-support-invalidates-naive-cramer-rao-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniform-null-p-value-is-anti-conservative</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniform-payoff-convergence-does-not-imply-gradient-convergence</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-uniformly-not-lipschitz-equivalent</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-union-of-filters-not-filter</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unique-critical-point-is-a-nonglobal-strict-local-minimum</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-uniqueness-does-not-require-local-lipschitz-continuity</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-uniqueness-of-beltrami-solutions-without-normalization</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unit-complex-sum-strict-with-distinct-summands</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unit-group-modulo-fifteen-is-not-cyclic</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unit-length-interval-need-not-embed-in-real-line-mod-integers</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-univariate-clean-quantile-count-exponent-is-false</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-universal-weyl-c-star-algebra-has-nonregular-representations</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-universality-decides-halting</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unnormalized-ribbon-trace-is-not-unframed-markov-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unramified-not-flat-closed-immersion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unrestricted-diagonalization-respects-any-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unrestricted-graded-natural-transformations-are-not-determined-by-the-regular-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unrestricted-variable-step-ratios-amplify-bdf2-starter-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unseparated-m-estimator-is-inconsistent</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-unshifted-weyl-orbits-do-not-classify-central-characters</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unsigned-bruhat-edge-sums-need-not-square-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-unsigned-half-angle-formula</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-unsymmetrized-q-parameters-break-the-cartan-normalization</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-untwisted-motivic-integration-fails-for-one-arrow-quiver</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-upper-semicontinuous-need-not-attain-its-infimum</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-using-inward-normal-first-reverses-the-boundary-term</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-using-multiplicity-one-for-imaginary-roots-gives-the-wrong-affine-denominator</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-valid-iv-does-not-identify-ate-without-further-restrictions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-vanishing-lefschetz-number-allows-fixed-points</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-vanishing-stable-characteristic-classes-does-not-make-two-embeddings-isotopic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-vanishing-tangent-space-does-not-imply-rigidity-with-automorphisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-variable-capture-changes-satisfaction</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-vc-entropy-exponent-cannot-be-uniform-in-r</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-vector-bundle-classification-without-numerability-can-fail</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-viscosity-solutions-need-not-be-unique-when-the-boundary-condition-is-not-imposed-in-a-comparison-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-visible-artin-relations-alone-do-not-prove-presentation-completeness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-vitali-covering-theorem-needs-a-fine-cover</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-volterra-bounded-derivative-not-riemann-integrable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-vortex-field-is-closed-but-not-exact-on-the-punctured-plane</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-w-one-p-is-not-an-algebra-below-the-continuity-threshold</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-w-one-p-point-evaluation-is-unbounded-in-the-subcritical-and-higher-dimensional-critical-cases</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-w-one-p-to-lq-bound-fails-for-q-greater-than-p-star-by-dilation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-wall-crossing-functors-do-not-commute</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-wave-energy-need-not-be-conserved-through-an-open-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-wave-formula-with-sphere-area-and-ball-volume-confused</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-weak-and-norm-topologies-differ-on-ell-one-despite-identical-convergent-sequences</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-weak-boundary-inequality-does-not-suffice-for-rouche</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-closure-can-exceed-sequential-weak-closure</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-law-can-fail-without-tail-control</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-law-does-not-imply-strong-law</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-maximum-principle-needs-boundedness-or-control-at-infinity</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-maximum-principle-needs-the-zero-order-sign</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-null-does-not-imply-mixed-assignment-centering</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-sparsity-does-not-imply-directional-sparsity</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-sparsity-does-not-imply-sparsity</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-star-and-weak-topologies-on-a-dual-can-differ</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-star-compact-does-not-imply-weak-star-sequentially-compact</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weak-tilted-tests-do-not-imply-almost-sure-consistency</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weakly-measurable-need-not-be-strongly-measurable</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weighted-am-gm-needs-normalized-nonnegative-weights</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-weil-divisor-not-cartier-singular-cone</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-whitehead-theorem-fails-without-cw-type</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-whitehead-vanishing-does-not-apply-to-the-nilpotent-radical</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-wiener-inversion-needs-nonvanishing</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-x-inverse-dlambda-on-zero-one-shows-finiteness-is-needed-in-the-epsilon-delta-criterion</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-x-squared-is-not-uniformly-continuous-on-r</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-x-squared-sine-one-over-x-squared-is-differentiable-everywhere-but-not-absolutely-continuous</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-xxz-unit-circle-generator-not-self-adjoint</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-yangian-one-root-bethe-equation-does-not-guarantee-completeness</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-z-does-not-have-property-t</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-z-four-not-isomorphic-z-two-squared</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-z-mod-n-is-not-a-free-z-module</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-z-mod-one-is-not-a-field</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-z-one-z-two-is-not-regular-in-z-two-at-the-origin</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-z-over-n-shows-why-hurwitz-needs-the-or-constant-clause</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-z-sqrt-d-units-need-not-equal-ok-units</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-z-squared-is-not-hyperbolic</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-zariski-product-topology-too-coarse</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cex-zariski-space-nonhausdorff-yet-separated-scheme</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zariski-topology-not-hausdorff</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-angular-momentum-level-with-nonfree-points-is-singular</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-average-treatment-effect-does-not-imply-fisher-sharp-null</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-derivative-on-a-disconnected-open-set-without-constancy</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-directional-derivatives-without-continuity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-divisor-equation-not-cartier</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-euler-class-does-not-in-general-imply-a-nowhere-zero-section</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-extension-of-a-nonzero-boundary-function-creates-a-jump</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-hessian-does-not-classify-a-critical-point</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-ideal-prime-not-maximal-in-z</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-iterated-integrals-without-a-double-integral</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-lefschetz-number-does-not-imply-no-fixed-points</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-residue-does-not-force-a-removable-singularity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cex-zero-scalar-curvature-does-not-imply-flatness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-zero-times-infinity-indeterminate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-zorn-hypothesis-fails</loc>
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<url>
<loc>https://alphabetamath.cc/item/cex-zp-is-not-the-integral-closure-of-z-in-qp</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-bernstein-set-is-not-lebesgue-measurable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-bijective-quasi-isometry-between-finitely-generated-groups-is-a-bilipschitz-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-bounded-vector-field-on-all-of-euclidean-space-is-complete</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-cartesian-closed-category-with-an-initial-object-has-strict-initial-objects</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-chain-map-between-acyclic-complexes-has-acyclic-cone</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-circle-loop-is-nullhomotopic-iff-its-degree-is-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-closed-embedded-submanifold-of-a-complete-riemannian-manifold-is-complete-in-the-induced-metric</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-closed-euclidean-submanifold-has-a-smooth-neighbourhood-retraction</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-closed-form-is-flow-invariant-when-its-contraction-is-exactly-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-closed-oriented-manifold-has-no-top-form-with-nonzero-integral-that-is-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-cocomplete-locally-small-abelian-category-with-a-generator-satisfies-the-special-adjoint-functor-theorem-hypotheses-dually-with-representatives-supplied</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-codimension-one-foliation-defined-by-a-closed-one-form-has-zero-godbillon-vey-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-colimit-of-a-set-valued-functor-is-the-set-of-connected-components-of-its-category-of-elements</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-compact-hausdorff-space-is-tychonoff</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-compactly-supported-smooth-euclidean-vector-field-is-complete</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-complete-locally-small-category-with-a-small-coseparating-set-and-saft-intersections-is-cocomplete</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-complex-character-is-irreducible-iff-its-self-inner-product-is-one</loc>
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<loc>https://alphabetamath.cc/item/cor-a-continuous-bijection-of-compact-hausdorff-spaces-is-a-homeomorphism-by-conservativity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-continuous-functor-to-set-from-a-chosen-well-powered-saft-category-is-representable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-continuous-image-of-a-lebesgue-measurable-set-can-be-nonmeasurable</loc>
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<loc>https://alphabetamath.cc/item/cor-a-continuous-map-from-a-closed-subset-extends-smoothly-exactly-when-it-has-a-continuous-extension-and-is-smooth-near-the-subset</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-continuous-preimage-of-a-lebesgue-measurable-set-can-be-nonmeasurable</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-a-contractible-complex-is-acyclic</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-curl-free-c1-field-on-a-star-shaped-open-subset-of-r3-is-conservative</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-cw-complex-with-no-cells-in-adjacent-dimensions-has-zero-cellular-boundary</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-discrete-embedded-submanifold-is-closed-locally-and-countable</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-divergence-free-field-has-zero-outward-flux-through-a-glued-elementary-solid</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-finite-dimensional-nilpotent-lie-algebra-has-a-codimension-one-ideal-containing-any-given-proper-subalgebra</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-finite-group-with-an-irreducible-complex-character-of-degree-greater-than-one-is-nonabelian</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-finite-p-group-has-only-the-trivial-simple-module-in-characteristic-p</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-finite-primitive-group-has-at-most-two-minimal-normal-subgroups</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-finitely-generated-group-with-a-word-metric-is-a-quasi-geodesic-space</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-fixed-point-free-sphere-map-has-antipodal-degree</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-flat-closed-oriented-surface-has-euler-characteristic-zero</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-function-with-nonempty-domain-is-injective-exactly-when-it-has-a-left-inverse</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-functor-between-additive-categories-preserving-finite-products-is-additive</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-galois-connection-satisfies-fgf-equals-f-and-gfg-equals-g</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-geodesic-segment-before-its-first-conjugate-point-is-locally-energy-minimizing</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-gradient-flow-has-no-nonconstant-periodic-or-recurrent-orbits</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-graph-has-an-even-number-of-odd-degree-vertices</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-group-acting-freely-on-a-positive-even-sphere-has-at-most-two-elements</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-group-acting-freely-without-inversions-on-a-tree-is-free</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-lie-algebra-with-nilpotent-adjoint-representation-has-a-central-series</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-linear-subspace-has-a-complement</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-local-isometry-from-a-complete-connected-manifold-has-geodesically-complete-target-image</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-map-homotopic-to-a-homotopy-equivalence-is-a-homotopy-equivalence</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-measurable-function-on-a-finite-measure-subset-of-rn-agrees-off-a-small-set-with-a-continuous-function</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-measurable-subgroup-of-rn-of-positive-measure-is-rn</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-morphism-between-universal-delta-functors-is-determined-in-degree-zero</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-morphism-in-an-abelian-category-is-monic-exactly-when-its-kernel-is-zero-and-epic-exactly-when-its-cokernel-is-zero</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-morphism-of-short-exact-sequences-with-invertible-outer-maps-is-invertible</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-morse-function-on-a-compact-manifold-has-finitely-many-critical-points</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-nonreal-eigenvector-produces-an-invariant-real-two-plane</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-nonvanishing-vector-field-has-locally-parallel-integral-curves</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-nonzero-compactly-supported-final-profile-is-not-reached-by-whole-space-heat-flow</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-nonzero-degree-map-to-a-connected-manifold-is-surjective</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-nonzero-period-obstructs-exactness-and-bounding</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-null-cobordant-cycle-has-zero-intersection-with-a-disjoint-boundary</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-p-classes-are-open-in-the-exponent</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-positively-curved-closed-oriented-surface-has-positive-euler-characteristic</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-preadditive-category-with-a-zero-object-has-zero-morphisms-in-the-published-sense</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-projective-or-injective-resolution-is-unique-up-to-nonunique-homotopy-equivalence</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-proper-injective-immersion-is-an-embedding</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-reflective-subcategory-of-a-complete-category-is-complete</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-restricted-set-contains-a-large-stable-set-or-clique</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-retract-of-a-contractible-space-is-contractible</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-right-adjoint-is-left-exact-and-a-left-adjoint-is-right-exact</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-right-adjoint-preserves-ends-and-a-left-adjoint-preserves-coends</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-row-reduction-is-a-product-of-elementary-matrices</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-second-proof-that-adjoints-are-unique</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-semigroup-with-unbounded-generator-cannot-be-operator-norm-continuous-at-zero</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-sequence-of-chain-maps-is-exact-exactly-when-it-is-exact-degreewise</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-short-exact-sequence-stays-exact-after-tensoring-exactly-when-its-tor-boundary-obstruction-vanishes</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-short-exact-sequence-with-acyclic-middle-identifies-neighbouring-homology</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-simple-eigenvalue-has-one-dimensional-eigenspace</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-smooth-map-from-lower-to-higher-dimension-cannot-be-surjective</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-smooth-section-can-be-perturbed-transverse-to-the-zero-section</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-split-short-exact-sequence-admits-the-direct-sum-resolution</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-submersion-is-transverse-to-every-embedded-submanifold</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-sufficiently-large-shift-is-coercive</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-unique-quadratic-subfield-of-the-p-th-cyclotomic-field</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-vector-bundle-is-trivial-if-and-only-if-it-has-a-global-frame</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-a-weakly-contractible-cw-complex-is-contractible</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-abel-ruffini-for-the-general-polynomial</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-abel-test-for-improper-integrals</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-abelian-normal-subgroups-of-faithful-primitive-actions-are-regular</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-abelian-p-groups-of-order-pn-are-counted-by-partitions</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-abelian-subgroups-of-hyperbolic-groups-are-virtually-cyclic</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-absolute-and-unconditional-convergence-agree-universally-iff-finite-dimensional</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-absolute-integral-of-one-is-path-length</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-absolute-value-and-powers-of-a-martingale-are-submartingales</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-abstract-parabolic-smoothing</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-ac-iff-well-ordering</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-ac-iff-zorn</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-adapted-classes-compute-derived-functors</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-adaptive-mcmc-containment-from-uniform-drift-minorization</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-additive-categories-are-closed-under-passage-to-the-opposite</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-additivity-of-the-nonnegative-lebesgue-integral</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-adjoint-has-the-same-singular-values</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-aep-typical-set-probability-and-size-bounds</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-afem-constant-convection-weak-wellposedness</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-algebra-maximal-ideals-as-points-over-algebraically-closed-field</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-algebraic-set-coordinate-duality-complete</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-closed-points-detect-radicals</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-domain-maximal-ideal-height-equals-dimension</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-normalization-is-finite</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-qc-sheaf-determined-global-sections</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-radical-ideal-point-separation</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-scheme-isomorphism-ring-isomorphism</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-scheme-quasi-compact</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-affine-schemes-separated</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-ale-exact-splitting-residual-orders</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-algebraic-closures-are-isomorphic-over-the-base</loc>
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<loc>https://alphabetamath.cc/item/cor-algebraic-connectivity-characterises-connectedness</loc>
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<loc>https://alphabetamath.cc/item/cor-algebraic-extensions-of-perfect-fields-are-separable</loc>
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<loc>https://alphabetamath.cc/item/cor-algebraic-integer-minimal-polynomial-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-algebraically-constructible-numbers-have-power-of-two-degree</loc>
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<loc>https://alphabetamath.cc/item/cor-algebras-for-a-closure-operator-monad-are-its-fixed-points</loc>
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<loc>https://alphabetamath.cc/item/cor-all-abelian-groups-of-order-n-cyclic-iff-n-squarefree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-all-four-classical-braid-models-realize-the-artin-presentation</loc>
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<loc>https://alphabetamath.cc/item/cor-all-integral-pell-solutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-all-relevant-characteristic-numbers-vanish-on-null-cobordant-manifolds</loc>
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<loc>https://alphabetamath.cc/item/cor-almost-everywhere-monotone-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-almost-sure-convergence-of-an-independent-series-is-a-zero-one-event</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-alpha-narrow-graphs-have-large-cliques-or-stable-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-alternating-group-is-normal-and-has-half-the-elements</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-amalgamation-along-an-isomorphism-recovers-the-other-factor</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-abelian-category-that-is-a-preorder-is-trivial</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-additive-category-is-an-ab-enriched-category-with-a-zero-object-and-finite-biproducts</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-element-of-finite-order-acts-diagonalisably-over-an-algebraically-closed-field-of-characteristic-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-exact-functor-preserves-and-reflects-quasi-isomorphisms-when-conservative</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-extension-determines-a-well-defined-h-two-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-extraspecial-p-group-has-class-two-and-derived-subgroup-of-order-p</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-extraspecial-p-group-has-no-complement-to-its-centre</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-extraspecial-p-group-is-a-product-of-two-maximal-abelian-subgroups</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-h-free-graph-has-a-linearly-large-induced-subgraph-whose-graph-or-complement-has-bounded-maximum-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-injective-immersion-from-a-compact-manifold-is-an-embedding</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-irreducible-chain-is-either-recurrent-or-transient</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-object-of-a-braided-category-carries-canonical-braid-actions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-operator-has-at-most-dimension-many-distinct-eigenvalues</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-an-oriented-sphere-self-map-is-a-homotopy-equivalence-iff-its-degree-is-plus-or-minus-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-analytic-semigroups-are-operator-norm-differentiable-away-from-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-angle-sum-comparison-for-small-geodesic-triangles</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-annihilator-detects-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-antidominant-verma-modules-are-simple</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-any-adjoint-between-additive-categories-is-additive</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-arbitrarily-large-finite-models-give-infinite-model</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-arbitrary-product-measure-for-standard-borel-probability-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-arc-length-accumulation-derivative-is-speed</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-archimedean-reciprocal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-area-as-a-line-integral-for-elementary-regions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-argument-principle-counts-preimages</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-artin-tate-integral-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-artinian-local-henselian-via-nilpotent-maximal-ideal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-artinian-quotients-and-localisations</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-arzela-ascoli-subsequence-theorem-for-proper-metric-targets</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ascoli-arzela-for-compact-hausdorff-domains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ascoli-arzela-for-compact-metric-domains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-associated-primes-empty-iff-module-zero-noetherian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-associated-primes-of-a-cyclic-module-are-primes-of-element-annihilators-modulo-ideal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-asymptotic-density-of-coprime-pairs</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-atkinson-in-calkin-algebra-language</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-aubin-nitsche-h-r-plus-s-rate-under-primal-and-dual-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-average-order-of-divisor-counting-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-average-order-of-divisor-sum-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-average-order-of-euler-totient</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-average-order-of-two-square-representations</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-baire-sequence-space-is-homeomorphic-to-the-irrationals</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-balanced-bracket-words-are-counted-by-the-catalan-numbers</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ball-mean-value-property-for-harmonic-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-banach-error-estimates</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-banach-space-with-a-schauder-basis-is-separable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-base-change-finite-type-and-products</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-based-connected-coverings-isomorphic-iff-equal-subgroups</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-basel-sum-by-residues</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-basic-cohen-model-fails-well-orderability-and-choice</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-basic-cohen-model-finite-set-continuity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bauer-maximum-principle</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bell-number-binomial-recurrence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bem-p0-galerkin-rate-for-h1-density</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-beppo-levi-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bessel-potential-spaces-are-hilbert-and-complete</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-best-affine-predictor-from-one-random-variable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-best-polynomial-approximation-errors-vanish</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-betti-number-is-rank-in-minimal-resolution</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bgg-euler-character-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bgg-resolution-has-length-the-number-of-positive-roots</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bieberbach-second-coefficient-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bijective-birational-to-normal-isomorphism-under-finiteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-binary-quadratic-form-equivalence-is-decidable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-binary-trees-are-counted-by-the-catalan-numbers</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-binary-trees-satisfy-b-equals-one-plus-z-b-squared</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-binary-words-avoiding-a-fixed-factor-have-a-rational-generating-function</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-binary-words-have-generating-function-one-over-one-minus-two-x</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-binomial-theorem-consequences</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bipartite-extremal-density-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-birational-smooth-proper-curves-isomorphic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-birkhoff-ergodic-theorem-for-ergodic-probability-systems</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-birkhoff-strong-law-for-iid-coordinate-shifts</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bishop-volume-upper-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bivariate-normal-full-conditional-kernels</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-block-defect-groups-are-p-radical</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-blowing-up-a-vertex-preserves-the-erdos-hajnal-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-blowup-birational-integral-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-blowup-unique-up-to-unique-isomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bmo-lp-oscillation-norms-are-equivalent</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bolzano-weierstrass-in-rn</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-bonnet-myers-fundamental-group-is-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-borel-iff-analytic-and-coanalytic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-borel-weil-bott-euler-character-is-the-weyl-character</loc>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/cor-cocontinuous-additive-module-functors-admit-right-adjoints</loc>
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<loc>https://alphabetamath.cc/item/cor-codimension-one-frobenius-criterion</loc>
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<loc>https://alphabetamath.cc/item/cor-coefficient-trace-residue-agreement</loc>
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<loc>https://alphabetamath.cc/item/cor-cofinality-of-a-cardinal-power</loc>
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<loc>https://alphabetamath.cc/item/cor-cohen-macaulay-modules-have-no-embedded-associated-primes</loc>
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<loc>https://alphabetamath.cc/item/cor-commuting-nearby-group-elements-have-commuting-logarithms-under-the-stated-domain-hypotheses</loc>
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<loc>https://alphabetamath.cc/item/cor-compact-domain-maps-are-uniformly-continuous</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-compact-groups-are-type-i-and-direct-integrals-collapse-to-discrete-sums</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-compact-hausdorff-partitions-of-unity</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-compact-operator-iff-approximation-numbers-tend-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-compact-regular-level-surfaces-have-finite-patch-covers</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-compact-riemann-surface-has-meromorphic-function</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-compactly-supported-smooth-functions-are-dense-in-wkp-of-rn</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-comparison-and-uniqueness-for-the-bounded-cylinder-heat-problem</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-complete-connected-riemannian-manifolds-are-proper-length-spaces</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-complete-local-domain-finite-over-a-regular-power-series-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complete-local-rings-are-henselian</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-complete-reducibility-for-compact-lie-groups</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-complete-splitting-in-a-cyclotomic-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-completely-metrizable-spaces-are-baire</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-completely-multiplicative-dirichlet-series-euler-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-completion-preserves-cohen-macaulayness-two-directions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-analytic-functions-have-local-primitives</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-exponential-cartesian-form-modulus-and-eulers-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-jacobian-determinant-is-multiplicative</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-k-theory-ahss</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-k-theory-of-spheres</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-numbers-are-a-quadratic-real-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-power-series-coefficient-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-power-series-sums-are-analytic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-power-series-sums-have-derivatives-of-all-orders</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-semisimple-lie-algebras-are-classified-by-finite-disjoint-unions-of-dynkin-diagrams</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-specht-restriction-branching-rule</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-complex-trigonometric-and-hyperbolic-addition-formulas</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-components-of-open-subsets-of-rn-are-polygonally-connected</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-compositions-have-generating-function-x-over-one-minus-two-x</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-compositions-with-k-parts-are-counted-by-binomial-coefficients</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-conditional-cauchy-schwarz-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-conditional-expectation-as-a-measurable-function-of-the-conditioning-variable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-conditional-lp-contraction</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-conjugate-elements-are-related-by-an-automorphism-of-an-algebraic-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-connected-components-partition-the-vertex-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-connected-cover-of-a-simply-connected-space-is-trivial</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-connected-lie-subgroups-with-the-same-lie-algebra-are-equal-as-immersed-subgroups</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-connected-nilpotent-lie-groups-are-discrete-central-quotients-of-bch-groups</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-connected-projective-variety-h0-o</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-conservative-fields-are-path-independent-and-have-zero-circulation</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-continued-fraction-convergents-are-reduced</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-continuous-complex-derivative-gives-c1-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-continuous-extension-from-a-dense-subset-r</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-continuous-functionals-of-the-scaled-posterior-converge</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-continuous-functions-are-borel-measurable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-continuous-image-of-an-interval-is-an-interval</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-continuous-logarithmic-functions-form-a-one-parameter-family</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-contour-integral-of-a-constant-is-an-endpoint-increment</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-contractible-iff-identity-nullhomotopic</loc>
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<url>
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<loc>https://alphabetamath.cc/item/cor-contractible-spaces-are-path-connected</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-contraction-hille-yosida-theorem</loc>
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<loc>https://alphabetamath.cc/item/cor-contraction-of-maximal-ideals-integral-extension</loc>
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<loc>https://alphabetamath.cc/item/cor-contravariant-yoneda-lemma</loc>
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<loc>https://alphabetamath.cc/item/cor-convergent-series-are-cesaro-and-abel-summable</loc>
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<loc>https://alphabetamath.cc/item/cor-converse-of-lagrange-for-finite-abelian-groups</loc>
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<loc>https://alphabetamath.cc/item/cor-convex-differentiable-functions-have-continuous-derivatives</loc>
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<loc>https://alphabetamath.cc/item/cor-convex-domains-are-domains-of-holomorphy</loc>
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<loc>https://alphabetamath.cc/item/cor-convex-functions-on-open-convex-sets-are-continuous</loc>
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<loc>https://alphabetamath.cc/item/cor-convex-subsets-of-rn-are-contractible</loc>
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<loc>https://alphabetamath.cc/item/cor-convolution-approximate-identities-from-fourier-multipliers</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-convolution-of-conjugate-l-p-and-l-q-functions-is-continuous-and-vanishes-at-infinity</loc>
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<loc>https://alphabetamath.cc/item/cor-coordinate-random-elements-on-a-countable-product-are-independent</loc>
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<loc>https://alphabetamath.cc/item/cor-countable-choice-and-omega-one-cofinality</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-countable-independent-copies-exist</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-countable-los-vaught-test</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-countable-products-and-g-delta-subspaces-of-polish-spaces-are-polish</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-countable-transitive-models-of-fixed-zfc-fragments</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-countable-union-and-omega-one-regularity-fail-in-the-feferman-levy-model</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-countably-additive-part-of-ba-is-ell-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-countably-many-discontinuities-integrable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-covariance-vanishes-under-independence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cox-partial-likelihood-asymptotic-normality</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cramers-rule-over-a-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-critical-holder-boundary-at-zero-from-the-brownian-lil</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cross-product-is-hodge-star-of-the-wedge</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cubic-defect-gives-second-order-for-symmetric-multirate-composition</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-curl-vanishes-exactly-when-a-field-is-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cut-time-does-not-exceed-first-conjugate-time</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cycle-integral-of-a-derivative-vanishes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cyclic-fixed-points-detect-rational-representations</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-cyclotomic-extensions-are-abelian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cyclotomic-field-splits-a-finite-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-cyclotomic-hecke-blocks-inherit-a-nontrivial-z-grading</loc>
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<loc>https://alphabetamath.cc/item/cor-de-moivre-laplace-central-limit-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-de-rham-cohomology-depends-only-on-the-underlying-homotopy-type</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-de-rham-cohomology-of-a-finite-disjoint-union-is-the-direct-sum</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-de-rham-cohomology-of-punctured-euclidean-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-de-rham-vector-space-comparison-with-continuous-singular-cohomology</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-deck-group-of-a-regular-covering</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-deformation-cohomology-of-a-smooth-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-degree-additive-proper-curve</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-degree-descends-picard-curve</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-degree-descends-to-circle-loop-classes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-degree-factors-into-separable-and-inseparable-degrees</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-degree-is-an-integer-and-independent-of-the-regular-value</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-degree-of-f-adjoin-an-nth-root-by-coset-order</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-degree-three-line-bundle-embeds-genus-one-plane-cubic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-degree-zero-line-bundle-section-trivial</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-delta-one-sets-are-exactly-decidable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-dense-range-iff-transpose-is-injective</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-density-characterised-by-annihilator-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-density-inversion-from-an-integrable-characteristic-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-depth-as-first-nonzero-ext</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-depth-bounded-by-number-of-ideal-generators</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-depth-depends-only-on-radical</loc>
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<loc>https://alphabetamath.cc/item/cor-depth-lemma-unequal-depth-equalities</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-depth-of-a-finite-local-module-at-most-its-dimension</loc>
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<loc>https://alphabetamath.cc/item/cor-depth-zero-iff-ideal-contained-in-an-associated-prime</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-derivations-represented-by-differentials</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-derivative-operators-are-continuous-for-local-uniform-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-derivatives-have-no-removable-or-jump-discontinuities</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-derived-composition-isomorphism-under-total-acyclicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-derived-long-exact-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-derived-subgroups-of-symmetric-and-alternating-groups</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-determinant-is-a-polynomial-in-the-matrix-entries</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-determinant-is-alternating-multilinear-in-the-rows</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-determinant-is-invariant-under-similarity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-determinant-multiplicativity-from-the-top-exterior-power</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-determinant-of-an-inverse</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-determinant-vanishes-with-a-zero-or-repeated-column</loc>
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<loc>https://alphabetamath.cc/item/cor-deterministic-ito-integrals-are-gaussian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-dfas-and-nfas-recognize-the-same-languages</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-diagonal-lattice-paths-with-a-prescribed-endpoint-are-counted-by-a-binomial-coefficient</loc>
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<loc>https://alphabetamath.cc/item/cor-diagonal-self-intersection-is-the-euler-number-of-tm</loc>
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<loc>https://alphabetamath.cc/item/cor-diameter-rigidity-from-toponogov-under-a-sectional-lower-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-diffeomorphism-pushforward-preserves-lie-brackets</loc>
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<loc>https://alphabetamath.cc/item/cor-diffeomorphisms-preserve-interior-and-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-differentiable-approximants-with-a-vanishing-derivative-at-a-point</loc>
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<loc>https://alphabetamath.cc/item/cor-dihedral-groups-as-semidirect-products</loc>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/cor-dimension-drops-under-a-parameter</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-dimension-of-image-plus-generic-fibre</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-dimensional-heisenberg-uncertainty-inequality</loc>
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<loc>https://alphabetamath.cc/item/cor-distinct-partitions-have-product-generating-function</loc>
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<loc>https://alphabetamath.cc/item/cor-distinct-specht-modules-are-inequivalent</loc>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/cor-euler-trail-characterisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-eulerian-numbers-are-symmetric</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-eulerian-polynomial-exponential-generating-function</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-evaluation-is-monic-and-coevaluation-is-epic-for-nonzero-objects</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-every-adjunction-induces-a-comonad-on-the-other-side</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-block-has-an-indecomposable-module-of-full-defect-vertex</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-every-category-monadic-over-set-is-complete</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-chain-map-factors-as-a-cofibration-like-inclusion-followed-by-a-homotopy-equivalence</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-every-classical-braid-group-is-linear</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-closed-embedded-submanifold-has-a-smooth-neighbourhood-retraction</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-closed-subset-of-a-manifold-is-the-zero-set-of-a-smooth-nonnegative-function</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-compact-connected-abelian-subgroup-is-contained-in-a-maximal-torus</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-compact-lie-group-is-isomorphic-to-a-closed-matrix-lie-group</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-compact-smooth-manifold-admits-an-excellent-morse-function</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-complex-polynomial-splits-into-linear-factors</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-connected-covering-of-circle-is-regular</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-continuous-map-between-smooth-manifolds-is-homotopic-to-a-smooth-map</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-distinguished-open-is-compact</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-face-of-an-elementary-solid-region-is-outward-oriented</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-finite-dimensional-characteristic-zero-lie-algebra-is-a-matrix-lie-algebra</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-finite-dimensional-representation-is-a-direct-sum-of-highest-weight-modules</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-finite-group-is-finitely-presented</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-graph-on-at-most-three-vertices-has-the-erdos-hajnal-property</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-grothendieck-category-has-enough-injectives-and-every-object-admits-an-injective-resolution</loc>
<lastmod>2026-09-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-immersion-is-locally-an-embedding</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-irreducible-complex-character-occurs-in-the-induction-of-an-irreducible-constituent-of-its-restriction</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-local-ring-is-its-localisation-at-its-maximal-ideal</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-module-admits-a-projective-resolution</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-module-admits-an-injective-resolution</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-module-is-a-quotient-of-a-free-module</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-nonconstant-polynomial-has-a-root-in-an-extension</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-nonfrattini-element-belongs-to-a-minimal-generating-set</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-open-subset-of-a-manifold-is-the-cozero-set-of-a-smooth-function</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-real-polynomial-factors-into-linear-and-irreducible-quadratic-factors</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-short-exact-sequence-of-smooth-vector-bundles-splits</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-smooth-manifold-admits-a-riemannian-metric</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-smooth-vector-field-on-a-compact-manifold-is-complete</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-spanning-set-contains-a-basis</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-submersion-is-an-open-map</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-subset-of-r-of-positive-outer-measure-contains-a-nonmeasurable-subset</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-system-of-parameters-is-regular-in-a-cohen-macaulay-module</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-tangent-vector-is-the-velocity-of-a-smooth-curve</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-vector-space-has-a-basis</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-every-vector-subbundle-has-a-smooth-complement</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-exact-finite-tensor-functors-have-right-projective-kernels</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-exact-hotelling-one-sample-test</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-exact-module-tensor-functors-correspond-to-right-flat-bimodules</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-exact-polyhedral-selective-tests-and-confidence-sets</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-exceptional-divisor-smooth-center-normal-bundle</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-existence-and-scaling-of-d-dimensional-brownian-motion</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-existence-of-left-and-right-haar-measures</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-existence-rational-function-bounded-pole</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-expander-independent-sets-coloring-and-diameter</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-expectation-agrees-with-the-finite-weighted-sum</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-expectation-linearity-monotonicity-and-modulus-bound</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-expectation-of-an-indicator-is-probability</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-expected-exit-time-solves-the-poisson-equation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-explicit-polynomial-time-constant-degree-expanders-exist</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-exponential-brownian-martingale</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-exponential-is-a-bijection-onto-positive-reals</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-exponential-reciprocal-and-positivity</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-ext-can-be-computed-from-any-injective-resolution-of-the-second-variable</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-ext-can-be-computed-from-any-projective-resolution-of-the-first-variable</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-extended-euclidean-bezout-coefficients</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-extended-green-hall-bialgebra</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-extension-of-k-morphisms-into-abelian-schemes</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-extensions-with-coprime-kernel-and-quotient-split</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-factor-hensel-implies-simple-root-hensel</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-factor-images-intersect-in-the-amalgamated-subgroup</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-factor-theorem-over-a-commutative-ring</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-factorisation-of-a-nonzero-integer</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-factors-embed-in-a-free-product-with-amalgamation</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-faithful-transitive-actions-are-core-free-coset-actions</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-faithfully-flat-descent-of-finite-generation</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-faithfully-flat-ring-maps-are-injective</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-feferman-levy-omega-one-has-countable-cofinality</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-feferman-model-has-no-free-ultrafilter-on-omega</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-feferman-model-refutes-bpi</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-few-induced-copies-force-a-linearly-large-induced-subgraph-with-bounded-maximum-degree</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-field-finite-type-over-a-field-is-a-finite-extension</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-field-kunneth-isomorphism-for-homology-of-products</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-fields-of-characteristic-zero-and-finite-fields-are-perfect</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-fields-of-fractions-are-unique-over-the-domain</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-abelian-group-cyclic-iff-one-invariant-factor</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-basis-energy-model-has-c1-response</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-c-prime-one-sixth-presentations-have-solvable-word-problem</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-codimensional-subspaces-are-complemented</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-complex-measures-admit-integrable-radon-nikodym-densities</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-cw-real-vector-bundle-has-orthogonal-complement-under-ac</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-dimensional-inner-product-spaces-have-orthonormal-bases</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-dimensional-irreducible-representations-of-a-solvable-complex-lie-algebra-are-one-dimensional</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-dimensional-normed-spaces-are-banach</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-dimensional-representations-are-completely-reducible-when-char-k-does-not-divide-group-order</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-dimensional-subspaces-are-closed</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-dimensional-subspaces-are-complemented</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-finite-dimensional-unitary-representations-separate-points-of-a-compact-lie-group</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<loc>https://alphabetamath.cc/item/cor-finite-direct-sums-preserve-chain-conditions</loc>
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<loc>https://alphabetamath.cc/item/cor-finite-eilenberg-watts-is-a-biequivalence</loc>
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<loc>https://alphabetamath.cc/item/cor-finite-flat-noetherian-modules-are-projective</loc>
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<loc>https://alphabetamath.cc/item/cor-finite-one-sided-exactness-is-equivalent-to-existence-of-the-corresponding-adjoint</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-finite-premeasure-extension-is-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-finite-projective-planes-are-symmetric-two-designs</loc>
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<loc>https://alphabetamath.cc/item/cor-finite-purely-inseparable-extensions-have-prime-power-degree</loc>
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<loc>https://alphabetamath.cc/item/cor-finite-ramsey-by-konig-compactness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-finite-range-comparison-for-arbitrary-target</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-finite-rank-operators-are-norm-dense-in-compact-hilbert-space-operators</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-finite-register-arithmetic-coder-average-length</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-finite-relay-compress-forward-noisy-network-coding-bound</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-finite-type-algebra-over-a-principal-ideal-domain-is-noetherian</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-finitely-generated-pro-p-homomorphisms-are-surjective-iff-surjective-mod-frattini</loc>
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<loc>https://alphabetamath.cc/item/cor-finitely-generated-projective-kg-modules-are-injective-and-conversely</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-finitely-generated-torsion-free-modules-over-a-pid-are-free</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-flat-modules-preserve-intersections-of-ideals</loc>
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<url>
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<loc>https://alphabetamath.cc/item/cor-forced-heat-solutions-are-smooth-away-from-the-source-time-diagonal</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/cor-fourier-transform-is-a-topological-automorphism-of-schwartz-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-fox-sudakov-quantitative-induced-density-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-frattini-free-finite-p-groups-are-elementary-abelian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-frattini-subgroup-is-contained-in-the-fitting-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-frattini-subgroup-of-a-finite-two-group-is-the-square-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-free-groups-of-rank-at-least-two-have-subgroups-of-every-finite-rank</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-free-product-factor-maps-are-injective</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-free-product-of-infinite-cyclic-groups-is-free</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-ftc-integral-function-differentiable-almost-everywhere</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-full-faithful-essentially-surjective-small-target-characterises-equivalence</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-fundamental-group-of-two-dimensional-torus</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-fundamental-theorem-of-calculus-from-stokes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-fundamental-theorem-of-finitely-generated-abelian-groups-from-pid-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-g-to-the-group-order-is-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-gaft-recovers-the-free-group-and-abelianisation-adjoints</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-galois-prime-decomposition-efg</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-gamblers-ruin-expected-duration</loc>
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<loc>https://alphabetamath.cc/item/cor-gamblers-ruin-hitting-probability-from-optional-stopping</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-gmres-minimizes-the-residual-over-the-affine-krylov-space</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-graded-specht-classes-form-a-basis-of-the-module-grothendieck-group</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-group-algebra-is-not-semisimple-when-char-k-divides-group-order</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-hamiltonian-flow-has-zero-divergence-with-respect-to-symplectic-volume</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/cor-hartogs-figure-obstruction-to-domain-of-holomorphy</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-heat-equation-has-infinite-propagation-in-the-positive-kernel-class</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-high-dimensional-smooth-poincare-for-homotopy-spheres-bounding-a-contractible-manifold</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-higher-homotopy-groups-are-iterated-loop-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hilbert-transform-is-an-ltwo-isometry-and-squares-to-minus-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hodge-star-is-an-isometry-and-squares-to-a-sign</loc>
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<loc>https://alphabetamath.cc/item/cor-holder-inequality-for-random-variables</loc>
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<loc>https://alphabetamath.cc/item/cor-holomorphic-function-ring-integral-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-holomorphic-function-with-holomorphic-conjugate-is-constant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-holomorphic-functional-calculus-in-the-wiener-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-holomorphic-functions-are-closed-for-local-uniform-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-holomorphic-functions-are-real-analytic-and-smooth</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-holomorphic-functions-in-several-variables-are-smooth</loc>
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<url>
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<loc>https://alphabetamath.cc/item/cor-holomorphic-logarithm-has-the-logarithmic-derivative</loc>
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<loc>https://alphabetamath.cc/item/cor-holomorphic-mean-value-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-holomorphic-roots-homologically-simply-connected-domains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hom-functors-are-continuous-and-send-colimits-to-limits</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hom-functors-on-a-preadditive-category-are-left-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hom-of-finite-modules-is-finite-over-a-noetherian-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homogeneous-polynomial-becomes-hyperplane-section</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homological-gaussian-elimination-preserves-homotopy-type-and-homology</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homology-of-a-degreewise-split-direct-sum-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homology-of-good-pairs-is-reduced-homology-of-the-quotient</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homology-of-spheres</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homotopic-maps-induce-the-same-map-on-singular-homology</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homotopy-equivalence-bijection-on-path-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homotopy-groups-of-a-cw-complex-depend-on-finite-skeleta-in-each-representative</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-homotopy-relative-and-path-homotopy-are-equivalence-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hook-divisibility-defect-zero-vanishing-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hopf-formula-is-independent-of-the-free-presentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hopf-lax-is-a-contraction-in-the-supremum-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hopf-lax-preserves-a-modulus-of-continuity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-horizontal-pieri-rule</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-huffman-code-lengths-are-within-one-bit-of-entropy</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hyperbolic-groups-have-solvable-word-problem</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-hypersurface-singular-locus-gradient</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ideal-divisibility-reverses-inclusion-dedekind</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ideal-real-arithmetic-code-average-length</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ideals-in-a-dedekind-domain-are-two-generated</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-idempotent-endomorphisms-are-diagonalisable-projections</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-idempotents-lift-uniquely-in-a-henselian-pair</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-identity-on-an-infinite-dimensional-normed-space-is-not-compact</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-iid-finite-variance-strong-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-iid-finite-variance-weak-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-iid-strong-law-implies-the-weak-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-image-and-preimage-round-trips-detect-injectivity-and-surjectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-improper-integral-tails-tend-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-improper-integral-test-for-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-in-a-preadditive-category-the-coequalizer-of-a-parallel-pair-is-the-cokernel-of-their-difference</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-in-a-preadditive-category-with-a-zero-object-a-morphism-is-epic-exactly-when-its-cokernel-is-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-inactive-dmc-cost-constraint-recovers-capacity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-inclusion-exclusion-is-boolean-mobius-inversion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-indecomposable-finite-abelian-groups-are-cyclic-prime-power</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-indefinite-henstock-kurzweil-integral-is-a-primitive</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-independent-nonidentical-finite-variance-strong-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-independent-replicate-mean-clt</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-independent-set-and-vertex-cover-are-np-complete</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-independent-set-is-no-larger-than-a-finite-spanning-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-and-coindex-swap-under-negation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-n-handles-cap-boundary-spheres</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-of-a-cycle-is-locally-constant-and-vanishes-far-from-its-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-of-a-full-rank-integer-sublattice-is-the-absolute-determinant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-one-iff-whole-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-one-trajectory-moduli-spaces-are-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-p-subgroups-of-finite-p-groups-are-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-tower-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-index-zero-handles-create-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-indexed-omega-one-delta-system</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-induced-and-intrinsic-adic-filtrations-are-equivalent</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-infinite-dimensional-closed-unit-ball-is-not-compact</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-infinite-ramsey-for-dedekind-infinite-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-infinitely-many-primes-congruent-to-one-modulo-three</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-inhomogeneous-dirichlet-data-reduce-to-zero-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-inhomogeneous-weak-dirichlet-problem-by-a-trace-lifting</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-initial-subsequences-of-a-regular-sequence-are-regular</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-initial-values-determine-a-linear-recurrence-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-injective-holomorphic-derivative-nonzero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-injective-or-monotone-derivative-is-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-injective-regular-ck-map-is-a-ck-diffeomorphism-onto-its-image</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-injectives-have-costandard-filtrations</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-injectivity-removes-the-lp-kernel-term-from-a-global-w-two-p-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-inner-product-induces-a-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integer-partitions-have-euler-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integers-requiring-four-squares</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integrability-of-absolute-values-products-and-lattice-operations</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integrable-hardy-functions-have-vanishing-moments-in-the-atomic-range</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-closure-of-a-dedekind-domain-in-a-finite-separable-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-cohomology-detects-adjacent-homology-torsion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-elements-form-a-subring</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-exponential-addition-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-extension-lifts-finite-prime-chains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-logarithm-agrees-with-natural-logarithm</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-logarithm-is-strictly-increasing</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-logarithm-reciprocals-and-integer-powers</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-of-an-exact-compactly-supported-top-form-on-a-boundaryless-manifold-is-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integral-over-a-null-set-vanishes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-integrality-of-the-j-invariant-fourier-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-interior-laplacian-gradient-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-intermediate-cohomology-o-d-projective-space-vanishes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-intermediate-field-degrees-divide</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-interval-uncountable</loc>
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<loc>https://alphabetamath.cc/item/cor-inverse-by-row-reducing-an-augmented-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-inverse-image-preserves-meets-and-direct-image-preserves-joins</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-inverse-matrix-by-adjugate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-inverse-of-an-invertible-operator-is-a-polynomial-in-the-operator</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-invertible-matrix-has-unit-determinant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-involutions-are-counted-by-standard-tableaux</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ip-is-closed-under-complement</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-irrationals-uncountable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-irreducible-characters-are-orthonormal-class-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-irreducible-polynomial-is-separable-iff-derivative-nonzero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-irreducible-polynomials-exist-over-finite-fields-in-every-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-irreducible-real-polynomial-has-degree-one-or-even-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-irreducible-real-polynomials-have-degree-one-or-two</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-irreducible-representations-have-degree-at-most-the-group-order</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-irreducible-symmetric-group-character-values-are-power-sum-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-isomorphic-lie-algebras-give-locally-isomorphic-but-not-necessarily-isomorphic-connected-lie-groups</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-isotopic-embeddings-have-diffeomorphic-complements</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-it-fano-with-erasure-or-out-of-alphabet-estimates</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-iwasawa-criterion-for-faithful-finite-actions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-jacobi-symbol-minus-one-obstructs-square</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-jacobian-determinant-of-a-holomorphic-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-jacobian-presentation-differentials</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-jensen-zero-counting-bound</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-jordan-block-data-controls-eigenspaces-and-polynomials</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-jordan-content-finite-additivity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-jordan-content-under-a-c-one-diffeomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-jucys-murphy-elements-commute-pairwise</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-k-five-and-k-three-three-are-nonplanar</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kac-moody-kostant-multiplicity-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kernel-composition-and-transformations-use-balanced-tensor-products</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kernel-of-a-constant-rank-submersion-is-integrable</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-kernel-of-the-action-on-the-frattini-quotient-is-a-p-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kernel-of-the-universal-central-extension-is-the-schur-multiplier</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kirchhoff-eigenvalue-product-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kleisli-and-eilenberg-moore-categories-are-equivalent-for-an-idempotent-monad</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-kleisli-and-eilenberg-moore-have-the-extremal-adjunction-universal-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kolmogorov-strong-law-for-independent-uniformly-bounded-variances</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kolmogorov-two-series-sufficiency</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kolmogorov-zero-one-law-from-reverse-martingales</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kostant-cohomology-in-degrees-zero-and-top</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kostant-euler-character-recovers-the-weyl-numerator</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-koszul-complex-invariant-under-invertible-generator-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-koszul-complex-resolves-a-regular-quotient</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-koszul-homology-flat-base-change</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-koszul-homology-localises</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-koszul-homology-supported-on-sequence-vanishing-set</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-kronecker-coefficients-are-nonnegative-integers-and-s3-symmetric</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kunneth-over-a-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-kunneth-when-one-homology-family-is-flat</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-l-is-properly-contained-in-pspace</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-l-one-approximate-identities-converge-uniformly-on-compacta-for-continuous-functions</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-l-one-convergence-has-an-almost-everywhere-convergent-subsequence</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-l-one-l-infinity-and-l-two-bounds-interpolate-to-l-p-l-p-prime</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-l-p-convergence-implies-convergence-in-measure</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-l-p-convergent-sequences-have-almost-everywhere-convergent-subsequences</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-l-p-norm-recovery-by-unit-l-q-pairings</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-l2-inverse-error-budget-and-cross-term-condition</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-lacunary-series-lp-membership-is-coefficient-ell-two</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-lagrange-multiplier-rule-for-graph-constraints</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-lagrange-multiplier-rule-for-one-regular-constraint</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-lambda-identity-minus-compact-has-index-zero</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-landweber-discrepancy-stopped-convergence-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-large-almost-pure-pair-hypotheses-yield-a-complete-or-anticomplete-blockade</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-large-schroder-numbers-as-a-binomial-sum-of-catalan-numbers</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-largest-invariant-factor-is-the-minimal-polynomial</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-laurent-coefficients-independent-of-radius</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-laurent-nested-intervals</loc>
<lastmod>2026-08-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-laurent-not-lub-complete</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-law-of-the-brownian-maximum</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-lax-milgram-inverse-has-norm-at-most-one-over-alpha</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lax-shock-inequalities-for-convex-scalar-laws</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-layer-cake-formulas-for-random-variables</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lc-large-cardinal-implication-ledger</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-leaf-and-coleaf-deletion-preserves-the-erdos-hajnal-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lebesgue-measure-is-invariant-under-orthogonal-linear-maps</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lebesgue-measure-is-the-lebesgue-stieltjes-measure-of-the-identity</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-lebesgue-outer-measure-is-regular-with-borel-measurable-hulls</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lebesgue-sigma-algebra-is-the-completion-of-borel-lebesgue-measure</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-lefschetz-number-is-homotopy-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lefschetz-number-of-the-identity-is-the-euler-characteristic</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-left-adjoints-preserve-colimits</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-left-and-right-semisimplicity-agree</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-length-is-additive-in-short-exact-sequences</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-length-of-the-graph-of-a-c1-function</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-levi-factors-are-noncanonical-but-unique-up-to-inner-unipotent-conjugacy</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-lie-derivative-commutes-with-the-exterior-derivative</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-lifted-path-endpoints-depend-only-on-path-homotopy</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-liminf-is-least-subsequential-limit</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-limit-comparison-test-for-improper-integrals</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-line-meets-degree-d-curve-counted-with-multiplicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-linear-elliptic-control-projection-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-linear-isoperimetric-bound-for-finite-c-prime-one-sixth-presentations</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-linear-maps-with-finite-dimensional-domain-are-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-linfinity-embeds-continuously-into-bmo</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-linfinity-maximum-bound-for-scalar-entropy-solutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-liouville-theorem-for-plane-harmonic-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-liouville-theorem-in-several-complex-variables</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lipschitz-maps-do-not-increase-hausdorff-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lipschitz-ode-uniqueness-and-stability-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-littlewood-richardson-coefficients-have-conjugation-symmetry</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-extrema-and-saddles-from-the-morse-index</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-formula-for-distance-from-the-center-of-a-normal-neighborhood</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-holder-regularity-implies-fourier-convergence-at-a-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-holomorphic-roots-nonvanishing-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-integrability-beltrami-structures</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-koszul-acyclicity-iff-regular-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-level-set-cone-at-a-morse-critical-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-mean-value-property-is-enough</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-minima-of-convex-functions-are-global</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-minima-of-convex-functions-on-rn-are-global</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-multiplicity-count-holomorphic-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-newton-convergence-for-midpoint-bvp-collocation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-newton-convergence-for-shooting-bvp-residual</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-normal-form-for-immersions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-local-normal-form-for-submersions</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-local-rings-have-only-trivial-idempotents</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-local-zero-count-via-rouche</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-localisation-commutes-with-finite-intersections-of-submodules</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-localisation-commutes-with-kernels-images-and-cokernels</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-localisation-dimension-does-not-increase</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-localisation-is-unique-up-to-unique-isomorphism</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-localisations-of-regular-local-rings-are-regular</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-locally-bounded-meromorphic-poles-are-removable</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-locally-compact-hausdorff-spaces-are-cech-complete</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-locally-integrable-weakly-harmonic-functions-are-smooth</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-locally-uniformly-convergent-holomorphic-series</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-log-modulus-of-a-holomorphic-function-is-plurisubharmonic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-logarithmic-derivative-of-a-normally-convergent-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-logrank-fisher-randomization-pvalue-valid</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lower-limit-line-is-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lower-positive-sectional-curvature-forces-conjugate-points</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lp-fourier-series-converges-almost-everywhere-for-p-greater-than-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lp-is-uniformly-convex-for-one-less-p-less-infinity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-lyapunov-central-limit-theorem</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-lyapunov-moment-inequality-on-a-probability-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-m-groups-are-solvable</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-ma-and-not-ch-implies-suslin-hypothesis</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-mackey-little-group-reduction-for-an-abelian-normal-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-major-index-generating-function-is-q-factorial</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-majority-sat-is-pp-complete</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-maps-between-oriented-spheres-are-homotopic-iff-their-degrees-agree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-markov-inequality-for-random-variables</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-mass-conservation-for-integrable-entropy-solutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-matching-minimax-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-matern-mesh-ratio-conditioning-bound</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-matrix-coefficients-are-uniformly-dense-in-continuous-functions-on-a-compact-lie-group</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-matrix-rank-equals-the-rank-of-its-linear-map</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-matrix-rank-nullity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-matrix-rings-are-noncommutative-in-dimension-at-least-two</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-maxima-and-minima-of-two-w-one-p-functions-are-w-one-p</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-maximal-chains-in-affine-domains-have-equal-length</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-maximal-chains-irreducible-variety-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-maximal-compact-subgroups-exist-and-are-conjugate-in-a-connected-finite-center-semisimple-lie-group</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-maximal-ideal-and-residue-field-of-zp</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-maximal-ideals-are-prime</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-maximal-integral-manifolds-partition-the-manifold</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-maximal-subgroups-of-a-finite-p-group-are-frattini-hyperplanes</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-maximum-modulus-on-the-distinguished-boundary-of-a-polydisc</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-maximum-principle-real-part-holomorphic-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-mean-value-theorem</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-measurable-functions-admit-dominated-simple-approximations</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-meromorphic-functions-on-a-domain-form-a-field</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-meromorphic-functions-on-a-plane-domain-are-holomorphic-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-meromorphic-functions-on-the-plane-are-entire-quotients</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-meromorphic-great-picard-theorem</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-meromorphic-little-picard-theorem</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-meshfree-joint-refinement-consistency</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-metric-spaces-admit-subordinate-partitions-of-unity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-metrizability-and-first-countability-are-hereditary</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-metrizable-cech-complete-iff-completely-metrizable</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-midpoint-quadrature-strang-error-for-p1</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-milnor-homotopy-seven-spheres-are-homeomorphic-to-s-seven</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-milnor-sphere-bundles-with-euler-number-plus-or-minus-one-are-homotopy-seven-spheres</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimal-generating-sets-of-a-finite-p-group-have-equal-size</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimal-generators-over-a-local-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimal-polynomial-divides-characteristic-polynomial</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimal-prime-has-height-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimal-prime-over-a-nonzerodivisor-has-height-one</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimal-recurrence-and-reduced-denominator</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimisers-are-classical-when-elliptic-regularity-applies</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimum-degree-two-forces-a-cycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-minimum-tangent-dimension-and-homogeneous-regularity</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-minkowski-convex-body-theorem-at-equality</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-minuscule-tensor-product-rule</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-misspecified-iid-bvm-under-kv-regularity</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-ml-estimate-for-complex-line-integrals</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-mlmc-complexity-for-poisson-tau-leaping</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-mlmc-euler-finite-l2-and-weak-cost-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-mlmc-euler-hms-autonomous-cost-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-mobius-dirichlet-series-reciprocal-zeta</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-mobius-inversion-for-finite-posets</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-mod-two-evenness-does-not-by-itself-supply-a-whitney-move</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-module-finite-affine-map-quasi-finite</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-module-tensor-products-are-unique-up-to-unique-isomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-modulus-powers-of-holomorphic-functions-are-subharmonic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-monic-resultant-is-unchanged-modulo-f</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-monoid-objects-in-a-symmetric-monoidal-category-form-a-symmetric-monoidal-category</loc>
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<loc>https://alphabetamath.cc/item/cor-moore-penrose-image-and-kernel-identities</loc>
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<loc>https://alphabetamath.cc/item/cor-morphisms-equal-on-dense-open-reduced-source</loc>
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<loc>https://alphabetamath.cc/item/cor-morse-critical-point-sum-is-the-euler-characteristic</loc>
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<loc>https://alphabetamath.cc/item/cor-morse-euler-characteristic-identity</loc>
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<loc>https://alphabetamath.cc/item/cor-morse-gradient-zero-contributes-minus-one-to-the-index-power-lambda</loc>
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<loc>https://alphabetamath.cc/item/cor-morse-homology-recovers-the-morse-inequalities</loc>
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<loc>https://alphabetamath.cc/item/cor-motion-of-a-completely-integrable-hamiltonian-is-linear-on-invariant-tori</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-motzkin-numbers-as-a-binomial-sum-of-catalan-numbers</loc>
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<loc>https://alphabetamath.cc/item/cor-multiplicity-of-an-irreducible-summand-is-a-character-inner-product</loc>
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<loc>https://alphabetamath.cc/item/cor-multivariable-taylor-formula-with-peano-remainder</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-multivariate-polynomial-ring-over-a-domain-is-a-domain</loc>
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<loc>https://alphabetamath.cc/item/cor-na-best-polynomial-approximation-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-na-closed-newton-cotes-eight-panel-peano-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-na-composite-trapezoid-even-power-expansion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-na-diagonal-diffusion-scheme-converges-under-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-na-mini-element-pressure-mass-block-spectrum</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-na-mini-element-pressure-mass-schur-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-na-practical-dpg-poisson-quasioptimality-estimator</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-na-sampled-smooth-d4-besov-best-m-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nakayama-generators-modulo-an-ideal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nat-addition-well-defined</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-necklace-count-via-cycle-index</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-necklaces-over-an-m-letter-alphabet</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-negative-expected-dimension-generic-intersections-are-empty</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nerode-classes-give-the-canonical-minimal-dfa</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-neumann-solutions-are-unique-modulo-componentwise-constants</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nevanlinna-picard-theorems</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-newton-leibniz-with-finitely-many-exceptional-points</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nikiforov-applies-to-every-linearly-large-induced-subgraph</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nilpotent-groups-and-finite-p-groups-are-solvable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nilpotent-ideal-pair-is-henselian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nilpotent-similarity-classified-by-power-ranks</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nilradical-as-intersection-of-primes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-no-common-component-projective-plane-intersection-is-zero-dimensional</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-no-isolated-holomorphic-singularities-in-several-complex-variables</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-no-morse-smale-trajectories-for-nonpositive-index-drop</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-no-nonconstant-map-proper-variety-to-affine-line</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-no-nontrivial-number-field-has-discriminant-plus-or-minus-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-no-nontrivial-number-field-is-unramified-over-q</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-no-removable-cycle-length-strip-forces-a-character-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-no-sigma-algebra-is-countably-infinite</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-noether-normalisation-dimension-lower-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-noether-normalisation-module-finiteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-noetherian-from-finitely-many-noetherian-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-noetherian-local-domain-dimension-zero-iff-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-noetherian-modules-are-hopfian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-noetherian-spectrum-has-finitely-many-irreducible-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-non-intersecting-monotone-path-pairs-are-counted-by-a-two-by-two-determinant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nonconstant-entire-function-has-dense-image</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nonconstant-negative-gradient-trajectories-strictly-decrease-the-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nonempty-hereditary-class-contains-the-null-graph</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nonhalting-is-not-recognizable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nonintegral-entire-order-bounds-canonical-genus</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-noninvertible-elliptic-shifts-form-a-discrete-set-in-the-self-adjoint-case</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nonnegative-harmonic-function-with-an-interior-zero-vanishes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nonnegative-predictable-transforms-preserve-submartingale-gains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nontrivial-degree-zero-line-bundle-no-sections</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nontrivial-finite-p-group-is-cyclic-iff-generator-rank-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nontrivial-tree-has-two-leaves</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-norm-recovered-from-the-dual-unit-ball</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normal-operator-norm-equals-spectral-radius</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normal-operator-with-zero-spectrum-is-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normal-p-core-lies-in-every-block-defect-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normal-subgroup-induction-irreducibility-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normal-subgroups-are-exactly-kernels</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normal-sylow-subgroup-of-a-normal-subgroup-is-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalisation-plane-curve-germ</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalised-positive-definite-functions-correspond-to-probability-measures</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalization-resolves-singularities-of-curves</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalization-unique-up-to-unique-isomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalized-circle-integral-about-its-centre-is-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalized-cochains-compute-group-cohomology</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalized-haar-measure-on-a-compact-lie-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalized-haar-probability-on-a-compact-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normalized-positive-type-functions-correspond-to-pointed-cyclic-representations</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-normed-space-completions-are-uniquely-linearly-isometric</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-nowhere-differentiable-functions-are-residual-in-c01</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-nowhere-zero-section-forces-the-euler-class-to-vanish</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nowhere-zero-vector-field-forces-zero-euler-characteristic</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-nspace-is-closed-under-complement-above-logspace</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-nth-prime-asymptotic</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-null-homotopic-maps-induce-zero-on-homology</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-number-of-abelian-groups-of-a-given-finite-order</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-number-of-labelled-simple-graphs</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-number-of-monic-irreducible-polynomials-over-a-finite-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-number-of-primitive-roots-modulo-n</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-number-of-primitive-roots-modulo-odd-prime-power</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-number-of-simple-kg-modules-equals-number-of-p-regular-conjugacy-classes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-number-of-solutions-of-a-binomial-congruence</loc>
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<url>
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<loc>https://alphabetamath.cc/item/cor-polynomial-ring-noetherian-implies-coefficient-ring-noetherian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-polynomial-ring-on-a-finite-family-agrees-with-the-iterated-construction</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-polynomial-ring-over-a-domain-is-a-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-polynomial-ring-over-a-field-is-a-pid</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-polynomial-ring-over-a-field-is-euclidean</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-polynomial-rodl-implies-erdos-hajnal-for-a-finite-family</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-polynomials-in-commuting-diagonalisable-endomorphisms-are-diagonalisable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-polynomials-of-degree-at-most-four-are-solvable-by-radicals</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-polynomials-over-an-infinite-domain-are-determined-by-values</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-pontryagin-duality-is-a-contravariant-involution</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positive-codimension-immersed-submanifolds-are-null</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positive-definite-hessian-implies-strict-convexity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positive-density-measures-assign-positive-volume-to-nonempty-open-sets-and-metric-balls</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positive-dimensional-operator-over-an-algebraically-closed-field-has-an-eigenvalue</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positive-entire-harmonic-functions-are-constant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positive-negative-part-and-truncation-calculus-in-w-one-p</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positive-reaction-restores-coercivity-without-dirichlet-poincare</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positive-relative-consistency-of-ch-and-gch</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-positivity-of-kazhdan-lusztig-polynomials-and-structure-constants</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-post-hitting-chain-restarts-from-the-hit-state</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-posterior-r-c-d-exists-for-standard-borel-parameter</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-potentials-differ-by-a-componentwise-constant</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-power-congruence-solution-count-modulo-a-prime</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-power-series-convergence-dichotomy</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-power-series-sums-are-continuous</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-power-series-sums-are-smooth-with-coefficient-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-power-sums-are-orthogonal-for-the-hall-inner-product</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-power-sums-generate-when-factorial-is-invertible</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-premeasure-induced-set-function-is-an-outer-measure</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-prescribed-principal-parts-compact-riemann-surface</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-primary-projections-are-polynomials-in-the-endomorphism</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-prime-bull-free-graphs-are-basic</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-prime-containing-an-ideal-avoiding-an-element</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-prime-ideals-and-dimension-of-a-dvr</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-prime-iff-euclid-property</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-prime-number-theorem</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-prime-order-group-is-cyclic</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-prime-power-orders-admit-complete-families-of-orthogonal-latin-squares</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-prime-set-of-an-artinian-ring</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-prime-spectrum-insensitive-to-nilpotents</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-primes-of-a-prime-local-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-primes-of-a-principal-localisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-primitive-ideals-are-partitioned-by-dot-orbit-central-character</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-primitive-roots-modulo-prime</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-primitive-sums-of-two-squares-closed-under-products</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-primitives-of-a-continuous-function</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-primitivity-is-equivalent-to-maximality-of-a-point-stabilizer</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-principal-ideal-domains-are-noetherian</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-principal-localisation-spectrum-is-distinguished-open</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-principal-logarithm-is-holomorphic-on-the-slit-plane</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-principal-value-truncations-converge-almost-everywhere</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-product-of-invariant-factors-is-the-characteristic-polynomial</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-product-of-two-noetherian-rings-is-noetherian</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-product-schemes-over-base-exists</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projected-subgradient-fixed-step-square-root-rate</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-cohomology-finite-dimensional-field</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-dimension-is-the-largest-nondegenerate-ext-degree-when-finite</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-embedding-every-smooth-proper-curve</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-equations-dimension-bound</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-indecomposable-modules-have-trivial-vertex</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-plane-bezout-length-form</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-plane-curves-meet</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-standard-labels-lie-above-the-head</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-projective-variety-product-exists</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-proper-birational-normal-curve-isomorphism-off-finite-set</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-proper-local-diffeomorphisms-have-constant-finite-fibres</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-pspace-equals-npspace-and-is-closed-under-complement</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-pullback-carries-closed-forms-to-closed-forms-and-exact-forms-to-exact-forms</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-pullback-of-the-tangent-bundle-of-euclidean-space-is-trivial</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-punctured-rn-homotopy-equivalent-to-the-sphere</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-pure-braids-are-pure-punctured-disk-mapping-classes</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-pure-geometric-braids-are-the-fundamental-group-of-ordered-configurations</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-purely-inseparable-extensions-are-normal</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-q-is-meager-and-not-g-delta</loc>
<lastmod>2026-08-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-qc-cyclotomic-prime-norm-solvability</loc>
<lastmod>2026-10-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-qc-distance-corrects-t-errors-and-erasures</loc>
<lastmod>2026-10-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-qmd-ac-component-lan-to-bvm</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quadratic-congruence-discriminant-criterion</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-quadratic-forms-diagonalize-in-characteristic-not-two</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-quadratic-reciprocity-via-frobenius</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quarter-disc-inclusion-for-univalent-functions</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quasi-finite-algebra-is-source-locally-a-localization-of-a-finite-algebra</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quasi-finite-locus-open-finite-type-algebra</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quasi-isometries-are-exactly-the-coarsely-dense-quasi-isometric-embeddings</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quasi-isomorphism-criterion-from-a-filtered-map</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quiver-full-flag-pushforwards-are-semisimple-in-characteristic-zero</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quotient-dimension-does-not-increase</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quotient-of-a-henselian-local-ring-is-henselian</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-quotient-of-an-abelian-group-is-abelian</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-raabe-test</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-racah-speiser-tensor-product-algorithm</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-radical-ideal-has-finitely-many-minimal-primes-noetherian</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-radical-ideals-as-intersections-of-minimal-primes-noetherian</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-ramsey-recursion-and-diagonal-upper-bound</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-rank-and-nondegeneracy-are-congruence-invariants</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-rank-criterion-for-consistency</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/cor-rank-equals-number-of-nonzero-singular-values</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/cor-rank-of-a-compact-connected-lie-group-is-well-defined</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
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<loc>https://alphabetamath.cc/item/cor-rank-of-the-rational-representation-ring</loc>
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<loc>https://alphabetamath.cc/item/cor-samuel-compactification-agrees-with-completion-for-totally-bounded-spaces</loc>
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<loc>https://alphabetamath.cc/item/cor-samuel-compactification-is-unique</loc>
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<loc>https://alphabetamath.cc/item/cor-sauer-shelah-polynomial-bound</loc>
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<loc>https://alphabetamath.cc/item/cor-scalar-line-integral-of-one-is-arc-length</loc>
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<loc>https://alphabetamath.cc/item/cor-scaled-caccioppoli-inequality-on-concentric-balls</loc>
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<loc>https://alphabetamath.cc/item/cor-schur-index-divides-the-representation-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-schur-multiplier-of-a-finitely-presented-group-is-finitely-generated</loc>
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<loc>https://alphabetamath.cc/item/cor-schurs-lemma-for-irreducible-lie-algebra-representations</loc>
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<loc>https://alphabetamath.cc/item/cor-schwartz-convolution-and-product-transform-laws</loc>
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<loc>https://alphabetamath.cc/item/cor-second-borel-cantelli-lemma-under-pairwise-independence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-second-countable-lch-locally-finite-borel-measures-are-regular</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-second-derivative-sign-change-gives-an-inflection-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-second-green-identity-on-a-bounded-c-one-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-second-moment-is-the-expected-predictable-quadratic-variation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-second-moment-positive-probability-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-second-order-taylor-expansion-with-the-hessian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-second-supplement-via-cyclotomic-frobenius</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-segre-veronese-embedding</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-seifert-van-kampen-simply-connected-overlap</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-self-adjoint-algebra-generated-by-a-separating-family-is-dense</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-self-adjoint-extension-exists-iff-deficiency-indices-agree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-semantic-equivalence-under-substitution</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-semisimple-hamiltonian-actions-have-unique-equivariant-moment-map-when-one-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-semisimple-lie-algebras-are-centerless-and-perfect</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-semisimple-rings-are-noetherian-and-artinian</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-separable-and-purely-inseparable-extension-is-trivial</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-separable-banach-dual-ball-is-weak-star-sequentially-compact</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-separable-degree-is-at-most-extension-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-separable-degree-of-a-simple-extension-counts-distinct-roots</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-separable-infinite-dimensional-hilbert-space-is-ell-two</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-separable-reflexive-space-has-separable-dual</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-separated-uniformizable-iff-tychonoff</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-separately-continuous-bilinear-map-on-banach-spaces-is-jointly-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sequence-ideal-annihilates-koszul-homology</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sequential-criterion-for-nonexistence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-series-spline-sobolev-training-risk-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-serre-finite-generation-torsion-and-p-primary-transfer</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-serre-normality-criterion-two-directions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-set-cat-and-every-complete-category-are-cartesian-monoidal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-set-weighted-limits-and-colimits-exist-over-a-small-index-category-in-a-complete-or-cocomplete-target</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-shape-regular-affine-fe-primal-energy-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-shape-regular-fe-strang-error-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sheafification-idempotent</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-short-exact-sequences-of-vector-bundles-split-over-the-base</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-short-five-lemma-for-quasi-isomorphisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sign-from-disjoint-cycle-structure</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sign-is-the-unique-nontrivial-homomorphism-to-signs</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-signature-theorem-imposes-pontryagin-number-congruences</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-simply-connected-complete-nonpositively-curved-manifolds-have-unique-geodesics-between-points</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-simply-connected-proper-plane-domains-are-regular</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-simultaneous-upper-triangularization-of-solvable-lie-algebra-representations</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sin-x-over-x-limit</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sine-and-cosine-are-one-lipschitz</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-single-graph-erdos-hajnal-polynomial-rodl-and-viral-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-single-valued-continuation-on-simply-connected-domains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-singular-cohomology-is-homotopy-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-singular-cohomology-satisfies-the-eilenberg-steenrod-cohomology-axioms</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-small-complete-or-cocomplete-categories-are-preorders</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smb-limit-is-conditional-entropy-under-ac</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smolyak-chaos-coefficient-error-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-coefficients-and-boundary-make-elliptic-eigenfunctions-smooth</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-data-give-smooth-interior-solutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-functions-and-tensor-fields-extend-locally-across-the-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-functions-are-weakly-dense-in-distributions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-functions-separate-points-from-closed-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-partitions-subordinate-to-a-countable-coordinate-cover</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-projective-complete-intersections-general</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-proper-curve-finite-map-projective-line</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-variety-classical-scheme-conventions-agree</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smooth-weak-dirichlet-solutions-are-classical</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-smoothly-homotopic-maps-induce-the-same-de-rham-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sobolev-algebra-above-the-critical-index</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sobolev-duality-from-the-fourier-pairing</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sobolev-embeddings-transfer-from-rn-to-extension-domains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sobolev-inequality-for-w-one-p-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-socle-of-uncoloured-modular-restriction-is-the-sum-over-good-residues</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-solovay-model-has-no-banach-tarski-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-solovay-model-has-no-vitali-or-bernstein-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-solution-count-trichotomy-over-an-infinite-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-solvable-and-locally-finite-groups-are-amenable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-specialisation-order-is-prime-inclusion</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spectral-gap-gives-exponential-decay-of-a-self-adjoint-parabolic-semigroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spectral-projections-and-resolution-of-the-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spectrum-connected-iff-no-nontrivial-idempotents</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spectrum-is-a-contravariant-topological-functor</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spectrum-is-t-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spectrum-of-a-compact-operator-is-countable-with-only-zero-as-possible-accumulation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spectrum-with-structure-sheaf-locally-ringed</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sperner-from-symmetric-chains</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sperner-theorem-with-equality-cases</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spherical-complement-characterization-of-plane-simple-connectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-spin-dirac-index-formula-with-arbitrary-twist</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-splitting-field-of-a-product-is-the-composite-of-splitting-fields</loc>
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<loc>https://alphabetamath.cc/item/cor-splitting-fields-are-unique-up-to-base-isomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-splitting-fields-exist-for-finite-families</loc>
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<loc>https://alphabetamath.cc/item/cor-square-integrable-brownian-terminal-variables-have-ito-representations</loc>
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<loc>https://alphabetamath.cc/item/cor-square-matrices-form-a-ring</loc>
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<loc>https://alphabetamath.cc/item/cor-square-matrix-invertible-iff-determinant-is-a-unit</loc>
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<loc>https://alphabetamath.cc/item/cor-squared-distance-is-strictly-convex-along-geodesics-in-a-hadamard-manifold</loc>
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<loc>https://alphabetamath.cc/item/cor-squarefree-power-basis-discriminant-gives-ring-of-integers</loc>
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<loc>https://alphabetamath.cc/item/cor-stable-ar-long-run-variance-plug-in-consistency</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-standard-borel-spaces-have-countable-generating-and-measure-determining-algebras</loc>
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<loc>https://alphabetamath.cc/item/cor-standard-semantic-machine-properties-are-undecidable</loc>
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<loc>https://alphabetamath.cc/item/cor-standard-specializations-of-the-labelled-symbolic-method</loc>
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<loc>https://alphabetamath.cc/item/cor-stationary-irreducible-markov-shift-is-ergodic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-stein-tomas-for-compact-hypersurfaces-with-nonzero-curvature</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-steiner-triple-systems-force-v-congruent-one-or-three-mod-six</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-stem-fields-are-uniquely-f-isomorphic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-stochastic-galerkin-fe-interpolation-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-stokes-gives-zero-circulation-for-a-curl-free-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-stolz-cesaro-zero-over-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-stone-cech-compactification-is-unique-over-x</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-stone-cech-compactification-maps-onto-samuel-compactification</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-stone-cech-of-compact-hausdorff-space-is-itself</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-strict-convexity-gives-uniqueness-of-a-minimiser</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-strict-positivity-for-nontrivial-nonnegative-heat-solutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-strictly-convex-functions-have-at-most-one-minimizer</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-strictly-convex-functions-on-rn-have-at-most-one-minimizer</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-strong-lq-convergence-implies-strong-convergence-of-subcritical-powers</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-strong-maximum-principle-for-weak-elliptic-solutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-strong-morse-inequalities</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-strong-nullstellensatz-two-inclusions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-subcritical-compactness-for-w-one-p-zero-on-arbitrary-bounded-open-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-subdifferential-of-a-differentiable-convex-function-is-the-gradient</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-subgradient-zero-characterises-global-minima</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-subgroups-of-abelian-groups-are-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-submartingale-doob-decomposition-has-increasing-compensator</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-submodules-of-finite-free-pid-modules-are-free</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-subrepresentations-correspond-to-submodules-and-irreducibility-to-simplicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sufficiently-short-geodesic-segments-are-uniquely-minimizing</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sum-check-field-size-error-budget</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sum-of-reciprocals-of-primes-diverges</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sum-of-roots-of-unity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sum-of-squares-formula-for-irreducible-degrees</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sum-of-squares-of-standard-tableau-numbers</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-sums-of-two-squares-closed-under-products</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-supercompact-consistency-of-no-s-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-support-is-union-of-closures-of-associated-primes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-support-propagates-along-transport-characteristics</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-surface-area-of-revolution-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-suslin-tree-yields-nonproductive-ccc</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-suspension-isomorphism-in-reduced-singular-homology</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-bounded-increment-azuma-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-conjugacy-classes-are-indexed-by-cycle-types</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-galerkin-best-approximation-in-energy-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-group-class-equation-by-cycle-type</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-group-cycle-index-series-is-exponential</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-group-has-factorial-cardinality-again</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-lax-milgram-is-energy-minimisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-lovasz-local-lemma</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-matrices-are-congruent-to-diagonal-matrices</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symmetric-polynomial-values-on-roots-lie-in-the-base-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symplectic-manifolds-have-a-canonical-orientation-and-volume-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-symplectic-manifolds-have-no-local-invariants-beyond-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-syzygies-from-two-projective-resolutions-are-stably-isomorphic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-tangent-line-flex-multiplicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-taylor-lagrange-and-cauchy-remainders</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-taylor-remainder-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-temperley-lieb-nonzero-cell-forms-classify-simple-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-tensor-gauss-exact-chaos-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-tensor-product-with-a-quotient-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-tensor-products-of-finite-free-modules-and-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-tensor-products-of-integrable-highest-weight-modules-decompose</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-termwise-integration-of-a-real-power-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ternary-hilbert-one-place-principle</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ternary-isotropy-via-hilbert-symbol</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-abelian-group-c-star-algebra-recovers-pontryagin-duality</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-adjoint-representation-splits-into-simple-ideals</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-agreement-set-of-two-maps-into-a-hausdorff-space-is-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-aleph-and-beth-hierarchies-are-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-algebraic-numbers-in-c-form-an-algebraic-closure-of-q</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-artin-action-solves-the-braid-word-problem</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-averaging-principle</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-base-group-embeds-in-its-hnn-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-biproduct-of-morphisms-is-the-diagonal-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-bird-graph-is-generalized-nice</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-braid-group-word-problem-is-decidable-by-garside-normal-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-bull-graph-has-the-erdos-hajnal-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-canonical-map-from-a-lie-algebra-to-its-enveloping-algebra-is-injective</loc>
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<loc>https://alphabetamath.cc/item/cor-the-canonical-map-is-injective-iff-the-group-is-residually-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-center-is-a-polynomial-algebra-of-rank-many-generators</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-centralizer-of-a-noncentral-element-of-an-extraspecial-p-group-has-index-p</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-character-table-is-square-and-invertible</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-class-of-all-graphs-is-not-erdos-hajnal</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-class-of-extensions-is-a-set-whenever-derived-ext-one-is-a-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-commutant-of-a-cyclic-endomorphism-is-polynomial</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-complex-numbers-are-an-algebraic-closure-of-the-reals</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-cone-criterion-from-the-general-long-exact-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-the-curl-of-a-curl-of-a-c2-field</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/cor-trace-of-adjacency-power-counts-closed-walks</loc>
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<loc>https://alphabetamath.cc/item/cor-transcendence-degree-tower-additivity</loc>
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<loc>https://alphabetamath.cc/item/cor-transience-of-simple-symmetric-random-walk-in-dimension-at-least-three</loc>
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<loc>https://alphabetamath.cc/item/cor-translation-length-is-conjugacy-invariant-and-homogeneous</loc>
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<loc>https://alphabetamath.cc/item/cor-transverse-maps-are-dense-in-the-strong-smooth-topology</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-triangle-free-planar-edge-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-triangle-inequality-for-inner-product-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-triangulated-five-lemma</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-triangulations-of-a-convex-polygon-are-counted-by-the-catalan-numbers</loc>
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<loc>https://alphabetamath.cc/item/cor-trigonometric-parity-and-pythagorean-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-trigonometric-polynomials-are-dense-in-continuous-periodic-functions</loc>
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<loc>https://alphabetamath.cc/item/cor-trivial-amalgamation-is-the-free-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-trivial-holonomy-gives-a-product-foliated-neighbourhood</loc>
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<loc>https://alphabetamath.cc/item/cor-tubular-neighbourhoods-are-unique-up-to-ambient-isotopy</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-turning-angle-sum-for-a-simple-geodesic-polygon-in-the-plane</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-two-canonical-braided-composites-agree-exactly-when-their-underlying-braids-agree</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-two-out-of-three-for-acyclicity-in-a-short-exact-sequence-of-complexes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-two-sample-permutation-exact-under-equal-distributions</loc>
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<loc>https://alphabetamath.cc/item/cor-two-variable-hessian-determinant-test</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-tychonoff-spaces-have-compactifications-under-the-ultrafilter-lemma</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-type-a-finite-hecke-algebra-is-noncanonically-isomorphic-to-csn</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-type-a-hecke-decomposition-matrix-is-dominance-unitriangular</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-type-a-hecke-specht-modules-are-in-the-same-block-iff-their-labels-have-the-same-e-core</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-type-s-h-density-credible-band-calibration</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-ultrafilter-lemma-and-bpi-are-not-theorems-of-zf</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unbracketed-and-unordered-tensor-strings-are-well-defined-in-a-symmetric-monoidal-category</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unconditional-iff-absolute-in-r</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uncountable-polish-borel-hierarchy-is-strict</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-under-choice-every-epimorphism-in-set-splits</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniform-boundary-convergence-of-ball-poisson-integrals</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniform-integrability-characterizes-l1-convergence-under-probability-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniform-limit-of-smooth-functions-need-not-be-differentiable</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniform-limit-uniformly-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniform-picard-lindelof-for-nearby-initial-values</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniformized-generator-stationary-residual-certificate</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unique-continuation-for-harmonic-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unique-formal-root-with-constant-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unique-kth-root-modulo-prime-for-coprime-exponent</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-comparison-and-order-preservation-for-entropy-solutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-for-the-bounded-plane-dirichlet-problem</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-for-the-classical-dirichlet-problem</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-implies-existence-for-the-elliptic-dirichlet-problem</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-of-bounded-uniformly-continuous-viscosity-solutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-of-complex-power-series-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-of-finite-borel-measures-from-their-fourier-transforms</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-of-multivariable-power-series-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-of-the-l-one-fourier-transform</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-of-the-normalized-riemann-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-uniqueness-of-the-stationary-distribution-for-an-irreducible-positive-recurrent-chain</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unit-group-modulo-prime-is-cyclic</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unit-n-ball-volume-is-maximal-in-dimension-five</loc>
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<loc>https://alphabetamath.cc/item/cor-unit-n-ball-volume-tends-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unit-ranks-by-number-field-signature</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unitary-groups-converge-under-strong-resolvent-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-units-in-a-polynomial-ring-over-a-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-universal-cover-classification-riemann-surfaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-universal-delta-functors-extending-the-same-degree-zero-functor-are-uniquely-isomorphic</loc>
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<loc>https://alphabetamath.cc/item/cor-universal-property-of-the-complex-numbers</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-universe-is-the-class-union-of-its-stages</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-unramified-prime-decomposition-in-a-cyclotomic-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unraveling-covers-give-determinacy</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unrestarted-gmres-residual-norms-are-nonincreasing</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-unstable-disk-is-the-handle-core</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-upper-sectional-curvature-bounds-delay-conjugate-points</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-urysohns-lemma-closes-the-separation-chain</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-v-equals-l-gives-a-suslin-tree</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-vanishing-ext-one-implies-rigidity-of-deformation-classes</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-vanishing-moments-force-a-continuous-function-to-vanish</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-variance-adds-for-pairwise-independent-random-variables</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/cor-vector-valued-ftc-and-lipschitz-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/cor-verma-irreducibility-criterion-from-shapovalov-determinants</loc>
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<loc>https://alphabetamath.cc/item/ex-a-kazhdan-pair-for-a-compact-group</loc>
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<loc>https://alphabetamath.cc/item/ex-a-large-almost-pure-pair-extends-an-anticomplete-blockade</loc>
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<loc>https://alphabetamath.cc/item/ex-a-large-epsilon-restricted-induced-subgraph-gives-a-polynomial-clique-or-stable-set</loc>
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<loc>https://alphabetamath.cc/item/fs-a-cartesian-closed-category-has-all-finite-limits</loc>
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<loc>https://alphabetamath.cc/item/fs-a-cat-enriched-category-is-the-same-thing-as-a-strict-two-category</loc>
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<loc>https://alphabetamath.cc/item/fs-a-category-with-finite-products-and-finite-coproducts-has-biproducts</loc>
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<loc>https://alphabetamath.cc/item/fs-a-chain-map-is-determined-by-its-maps-on-homology</loc>
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<loc>https://alphabetamath.cc/item/fs-a-chart-domain-is-an-open-subset-of-euclidean-space</loc>
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<loc>https://alphabetamath.cc/item/fs-a-chordal-limit-of-holomorphic-functions-cannot-be-identically-infinity</loc>
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<loc>https://alphabetamath.cc/item/fs-a-coend-is-a-colimit-over-the-twisted-arrow-category-under-this-pages-convention</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-compact-hausdorff-group-is-profinite-without-total-disconnectedness</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-compact-subset-is-closed-in-every-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-comparison-map-between-resolutions-is-unique-as-a-chain-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-compatible-uniformity-is-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-complex-character-of-a-finite-group-is-always-a-homomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-complex-inner-product-is-symmetric</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-conical-limit-in-an-enriched-category-is-just-a-limit-in-the-underlying-category</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-connected-space-is-locally-connected</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-connected-space-is-path-connected</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-connection-is-c-infinity-linear-in-the-section-being-differentiated</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-continuous-function-is-differentiable-somewhere</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-continuous-function-of-bounded-variation-is-absolutely-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-continuous-function-on-a-compact-interval-has-a-rectifiable-graph</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-continuous-functor-on-a-complete-category-has-a-left-adjoint</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-continuous-real-function-on-any-subspace-of-a-normal-space-extends</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-convex-function-is-differentiable</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-convex-function-on-a-convex-set-is-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-countable-elementary-submodel-is-a-transitive-subset</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-critical-value-has-a-singular-level-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-degree-zero-natural-transformation-between-delta-functors-always-extends</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-degreewise-split-short-exact-sequence-of-complexes-has-zero-connecting-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-dense-set-of-outer-measure-zero-and-a-dense-set-of-full-inner-measure-cannot-coexist</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-derived-functor-is-canonical-without-supplied-replacement-data</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-dfa-transition-diagram-may-omit-a-sink-without-changing-totality</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-differentiable-function-has-a-continuous-derivative</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-divergence-free-field-has-zero-outward-flux-through-every-closed-surface</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-double-complex-totalisation-is-unambiguous-with-infinite-diagonals</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-family-of-vc-dimension-d-has-at-most-n-to-the-d-members</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-fibrewise-linear-continuous-bundle-map-is-automatically-smooth</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-finite-index-d-subgroup-of-a-rank-n-free-group-has-rank-dn</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-finite-patch-presentation-can-always-be-oriented-compatibly</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-finitely-generated-group-with-a-word-metric-is-a-geodesic-metric-space</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-free-action-always-has-a-manifold-orbit-space</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-a-function-with-closed-graph-is-continuous</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-a-functor-preserving-zero-morphisms-is-additive</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-a-general-mixed-tensor-field-has-a-pullback-by-every-smooth-map</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-generator-is-the-same-thing-as-a-projective-generator</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-generic-filter-belongs-to-the-ground-model</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-geodesic-stops-minimizing-exactly-at-its-first-conjugate-point</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-geodesic-triangle-on-every-surface-has-angle-sum-pi</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-group-of-order-p-to-an-even-power-can-be-extraspecial</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-group-with-r-conjugacy-classes-has-an-irreducible-of-degree-r</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-hahn-decomposition-is-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-homotopy-between-proper-maps-is-automatically-a-proper-homotopy</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-language-is-a-set-of-symbols</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-lebesgue-measurable-set-with-empty-interior-is-lebesgue-null</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-local-ode-solution-exists-on-the-whole-domain-of-the-vector-field</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-locally-uniform-limit-of-injective-holomorphic-functions-is-injective</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-maximal-ode-solution-has-a-closed-interval-domain</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-a-mobius-map-with-three-fixed-points-may-be-nonidentity</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-a-monad-is-a-monoid-object-in-the-endofunctor-category-for-every-category</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-a-monoid-object-in-the-endofunctor-category-is-the-definition-of-a-monad</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-a-monoidal-category-carries-at-most-one-symmetry</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-a-monoidal-functor-is-one-whose-structure-maps-are-isomorphisms</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-n-is-simple-for-all-n-at-least-four</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-nonconstant-meromorphic-function-on-the-plane-omits-at-most-one-sphere-value</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-nonconstant-scalar-holomorphic-function-in-dimension-at-least-two-can-have-an-isolated-zero</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-nonzero-one-form-has-a-nonzero-square-under-the-wedge-product</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-partition-of-unity-can-glue-manifold-valued-maps-by-taking-weighted-sums</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-plain-dynkin-diagram-classifies-real-forms</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-pointwise-bounded-sequence-of-continuous-functions-has-a-uniformly-convergent-subsequence</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-pointwise-limit-of-continuous-functions-need-not-be-continuous-ae</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-positive-semidefinite-hessian-gives-strict-convexity</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-preadditive-category-with-a-zero-object-has-binary-biproducts</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-quasi-isometry-is-continuous-or-bijective</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-quotient-of-a-tree-by-a-group-action-is-always-a-tree</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-real-form-is-merely-the-same-complex-lie-algebra-with-scalars-forgotten</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-reflective-inclusion-creates-colimits</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-regular-value-must-belong-to-the-image</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-retract-must-be-a-deformation-retract</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-root-system-determines-a-compact-connected-semisimple-group-up-to-isomorphism</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-section-curvature-lower-bound-makes-triangles-thinner-than-the-model</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-set-theoretic-section-of-an-extension-is-automatically-a-homomorphism</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-short-exact-sequence-of-vector-bundles-has-a-canonical-splitting</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-short-exact-sequence-splits-whenever-its-middle-object-is-isomorphic-to-the-biproduct-of-the-outer-two</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-shortest-walk-need-not-be-a-path</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-signed-measure-can-take-both-plus-infinity-and-minus-infinity</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-singular-cochain-is-a-finite-linear-combination-of-singular-simplices</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-smooth-density-is-the-same-thing-as-a-top-form-on-a-nonorientable-manifold</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-sparse-set-contains-a-stable-set-of-half-its-size</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-spectral-sequence-collapses-when-one-differential-is-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-split-minimal-polynomial-always-gives-diagonalisability</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-square-matrix-over-a-commutative-ring-is-invertible-iff-its-determinant-is-nonzero</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-a-subgroup-of-a-finitely-generated-free-group-is-finitely-generated</loc>
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<loc>https://alphabetamath.cc/item/fs-curve-velocities-in-two-charts-have-the-same-coordinate-tuple</loc>
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<loc>https://alphabetamath.cc/item/fs-darboux-theorem-makes-all-symplectic-manifolds-globally-symplectomorphic</loc>
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<loc>https://alphabetamath.cc/item/fs-direct-sum-and-product-totalisations-are-always-isomorphic</loc>
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<loc>https://alphabetamath.cc/item/fs-distinct-irreducible-complex-characters-of-a-finite-group-have-distinct-degrees</loc>
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<loc>https://alphabetamath.cc/item/fs-every-cycle-in-a-connected-plane-domain-is-null-homologous</loc>
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<loc>https://alphabetamath.cc/item/fs-every-divisor-of-the-group-order-is-an-irreducible-character-degree</loc>
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<loc>https://alphabetamath.cc/item/fs-every-dominant-weight-of-the-abstract-weight-lattice-integrates-to-every-compact-group-form</loc>
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<loc>https://alphabetamath.cc/item/fs-every-element-of-a-complex-semisimple-lie-algebra-is-semisimple</loc>
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<loc>https://alphabetamath.cc/item/fs-every-element-of-a-disconnected-compact-lie-group-lies-in-the-identity-components-maximal-torus</loc>
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<loc>https://alphabetamath.cc/item/fs-every-embedded-submanifold-is-an-open-subset-of-the-ambient-manifold</loc>
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<loc>https://alphabetamath.cc/item/fs-every-endomorphism-has-a-commuting-diagonal-plus-nilpotent-decomposition</loc>
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<loc>https://alphabetamath.cc/item/fs-every-endomorphism-has-jordan-form-over-its-base-field</loc>
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<loc>https://alphabetamath.cc/item/fs-every-enriched-category-has-constant-enriched-functors</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-finite-borel-measure-on-a-compact-hausdorff-space-is-regular</loc>
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<loc>https://alphabetamath.cc/item/fs-every-finite-dimensional-representation-of-a-reductive-lie-algebra-is-completely-reducible</loc>
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<loc>https://alphabetamath.cc/item/fs-every-finite-group-is-a-product-of-cyclic-prime-power-groups</loc>
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<loc>https://alphabetamath.cc/item/fs-every-finite-k-linear-abelian-category-is-semisimple</loc>
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<loc>https://alphabetamath.cc/item/fs-every-finite-reflection-invariant-set-of-vectors-is-a-crystallographic-root-system</loc>
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<loc>https://alphabetamath.cc/item/fs-every-finitely-presented-group-has-solvable-word-problem</loc>
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<loc>https://alphabetamath.cc/item/fs-every-function-g-times-g-to-m-is-a-factor-set</loc>
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<loc>https://alphabetamath.cc/item/fs-every-functor-with-a-left-adjoint-also-has-a-right-adjoint</loc>
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<url>
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<loc>https://alphabetamath.cc/item/fs-every-graph-with-at-least-four-vertices-has-a-nontrivial-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-hausdorff-locally-euclidean-space-is-a-manifold</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-henstock-kurzweil-integrable-function-is-a-derivative</loc>
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<url>
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<loc>https://alphabetamath.cc/item/fs-every-highest-weight-lambda-gives-a-finite-dimensional-simple-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-holomorphic-function-on-a-domain-continues-past-its-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-increasing-function-defines-a-lebesgue-stieltjes-measure</loc>
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<loc>https://alphabetamath.cc/item/fs-every-increasing-function-satisfies-newton-leibniz</loc>
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<loc>https://alphabetamath.cc/item/fs-every-l-p-cauchy-sequence-converges-pointwise-almost-everywhere</loc>
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<loc>https://alphabetamath.cc/item/fs-every-omega-one-tree-has-a-cofinal-branch</loc>
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<loc>https://alphabetamath.cc/item/fs-every-pointwise-assignment-of-a-tangent-vector-is-a-smooth-vector-field</loc>
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<loc>https://alphabetamath.cc/item/fs-every-poset-has-an-incidence-algebra</loc>
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<loc>https://alphabetamath.cc/item/fs-every-primitive-group-has-a-unique-minimal-normal-subgroup</loc>
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<loc>https://alphabetamath.cc/item/fs-every-quasi-isomorphism-is-an-isomorphism-of-complexes</loc>
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<loc>https://alphabetamath.cc/item/fs-every-representation-of-a-lie-algebra-is-completely-reducible</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-symmetric-submodel-satisfies-choice</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-symplectic-action-is-hamiltonian</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-symplectic-vector-field-has-a-global-hamiltonian-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-t1-space-is-hausdorff</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-tensor-is-an-elementary-tensor</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-tree-automorphism-fixes-a-vertex</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/fs-every-triangulated-subcategory-is-thick</loc>
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<url>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/fs-exponential-generating-functions-multiply-without-labelled-product-hypothesis</loc>
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<loc>https://alphabetamath.cc/item/fs-separable-degree-always-equals-extension-degree</loc>
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<loc>https://alphabetamath.cc/item/fs-separable-spaces-are-second-countable</loc>
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<loc>https://alphabetamath.cc/item/fs-sigma-n-and-pi-n-are-disjoint</loc>
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<loc>https://alphabetamath.cc/item/fs-simple-roots-are-pairwise-orthogonal</loc>
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<loc>https://alphabetamath.cc/item/fs-simply-connected-plane-domains-are-convex</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-simply-connected-plane-domains-are-star-shaped</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-sin-x-over-x-by-sector-areas</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-singular-values-are-absolute-values-of-the-eigenvalues</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-spherical-coordinates-are-globally-injective</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/fs-sum-check-computes-all-exponential-summands</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/fs-the-boundaries-of-a-complex-are-a-quotient-of-its-cycles</loc>
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<url>
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<loc>https://alphabetamath.cc/item/fs-the-cartan-matrix-equals-the-decomposition-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-the-catalan-numbers-satisfy-a-constant-coefficient-linear-recurrence</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-the-cayley-graph-of-a-group-does-not-depend-on-the-generating-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-the-central-binomial-quotient-is-an-integer-only-for-small-n</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-the-cfl-pumping-lemma-characterizes-cfls</loc>
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<loc>https://alphabetamath.cc/item/fs-the-characteristic-polynomial-determines-diagonalisability</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-the-closure-of-a-path-connected-set-is-path-connected</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-the-coefficients-of-every-cyclotomic-polynomial-lie-in-minus-one-zero-and-one</loc>
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<loc>https://alphabetamath.cc/item/fs-the-cohomology-connecting-morphism-lowers-degree</loc>
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<loc>https://alphabetamath.cc/item/fs-the-combinatorial-nullstellensatz-holds-without-the-top-coefficient-hypothesis</loc>
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<loc>https://alphabetamath.cc/item/fs-the-commutator-pairing-determines-an-extraspecial-p-group-up-to-isomorphism</loc>
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<loc>https://alphabetamath.cc/item/fs-the-commutator-pairing-needs-no-choice-of-a-central-generator</loc>
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<url>
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<loc>https://alphabetamath.cc/item/fs-the-connecting-morphism-depends-on-the-choices-made-in-its-construction</loc>
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<loc>https://alphabetamath.cc/item/fs-the-cotangent-bundle-uses-the-same-transition-matrices-as-the-tangent-bundle</loc>
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<loc>https://alphabetamath.cc/item/fs-the-cross-ratio-is-preserved-by-every-sphere-homeomorphism</loc>
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<loc>https://alphabetamath.cc/item/fs-vertex-and-edge-connectivity-always-agree</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-vertex-stabilizers-are-literally-the-chosen-vertex-groups-without-conjugacy</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-vitali-covering-theorem-holds-for-arbitrary-covers</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-von-neumann-mean-convergence-implies-birkhoff-pointwise-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-weak-mixing-implies-strong-mixing</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-weierstrass-factorization-is-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-weierstrass-preparation-is-unique-without-the-unit-condition</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-weyl-equidistribution-holds-for-every-rotation-angle</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-whole-semidirect-product-conjugacy-is-the-equivalence-relation-behind-first-cohomology</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-winding-number-depends-only-on-the-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-writing-e-two-double-arrow-h-is-a-complete-convergence-proof</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-yoneda-lemma-requires-a-small-category</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-yonedas-original-notation-agrees-with-the-modern-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-zero-complex-derivative-on-an-open-set-implies-constant</loc>
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<url>
<loc>https://alphabetamath.cc/item/fs-zero-derivative-almost-everywhere-implies-constancy</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zero-derivative-on-an-open-set-forces-constancy</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zero-hausdorff-dimension-implies-countability</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zero-integral-forces-everywhere-zero</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/fs-zero-mean-curvature-implies-a-submanifold-is-totally-geodesic</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zero-on-singletons-implies-zero-measure</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zero-product-property-modulo-n</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zero-second-derivative-decides-extremum</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zeta-minus-one-is-the-ordinary-sum-one-plus-two-plus-three-and-so-on</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zfc-determines-the-continuum-function</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zfc-proves-normal-moore-space-conjecture</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zfc-proves-there-is-an-inaccessible-cardinal</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zp-is-a-torsion-group-because-all-its-coordinate-groups-are-finite</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zp-is-cyclic-as-an-abstract-group</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/fs-zp-is-the-profinite-completion-of-z</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-3-manifold-boundary-kernel-is-lagrangian</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-based-self-map-of-the-punctured-disk-inducing-the-identity-on-pi-one-is-based-homotopic-to-the-identity</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-binomial-coefficient-with-top-below-a-prime-is-nonzero-modulo-that-prime</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-bipartite-layer-is-small-unless-a-large-comb-already-appears</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-bockstein-class-on-rp-two-times-rp-four-has-nonzero-integral-sq-three</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-boundary-fixed-punctured-disk-map-acting-trivially-on-pi-one-is-isotopic-to-the-identity</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-bundle-connection-is-local-and-restricts-to-open-sets</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-bundle-embedding-produces-its-grassmannian-classifying-map</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-c-zero-semigroup-is-uniformly-bounded-on-every-compact-time-interval</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-c1-map-from-r2-to-r-with-an-interval-of-critical-values</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-c1-map-is-locally-lipschitz-on-compact-coordinate-subsets</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-cancelling-disk-triad-has-an-exact-c2-boundary-scalar</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-cartan-eilenberg-resolution-totalizes-to-an-injective-resolution-in-the-required-derived-sense</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-cayley-graph-is-connected-exactly-when-its-defining-subset-generates-the-group</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-central-positive-braid-is-a-power-of-delta-squared-for-n-greater-than-two</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-central-product-of-two-quaternion-groups-is-a-central-product-of-two-dihedral-groups</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-chain-map-carries-cycles-to-cycles-and-boundaries-to-boundaries</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-clean-framed-whitney-bigon-has-an-adapted-tube</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-closed-discrete-subset-of-a-compact-space-is-finite</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-closed-moy-resolution-koszul-complex-computes-hochschild-homology-of-its-soergel-bimodule</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-closed-smooth-manifold-has-the-homotopy-type-of-a-finite-cw-complex</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-collar-identifies-boundary-local-homology-with-the-pair-fundamental-class</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-collar-product-region-deformation-retracts-onto-its-face</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-collared-whitney-disk-can-be-made-disjoint-from-an-entire-compact-immersed-image</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-codimension-one-leaf-with-finite-fundamental-group-has-trivial-holonomy-when-transversely-oriented</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-connected-one-dimensional-manifold-without-boundary-is-a-circle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-holonomy-free-codimension-one-foliation-is-a-fiber-bundle-over-its-leaf-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-leaf-near-a-compact-reference-leaf-is-a-one-sheeted-collar-graph</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-morse-trajectory-has-single-critical-alpha-and-omega-limits</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-remainder-estimate-forces-closed-range</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-riemannian-surface-has-a-uniform-short-geodesic-radius</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-scalar-identity-forces-finite-dimension</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-set-inside-a-bounded-open-set-admits-an-explicit-compactly-supported-cutoff</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-subspace-of-a-cw-complex-meets-only-finitely-many-cells</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-compact-surface-metric-extends-across-its-boundary</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-complement-induces-the-conjugation-action-on-the-kernel</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-complete-or-weakly-sparse-blockade-can-be-thinned-to-equal-subblocks-with-directional-sparsity</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-complete-or-weakly-sparse-blockade-yields-a-complete-subblockade-or-an-anticonnected-thinning</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-compressible-leaf-yields-a-vanishing-cycle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-configuration-loop-traces-a-geometric-braid</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-connected-cw-pair-has-a-model-without-low-relative-cells</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-continuous-map-of-compact-hausdorff-spaces-is-an-ultrafilter-algebra-homomorphism</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-contractible-relative-group-ring-complex-with-a-pi-one-isomorphism-gives-a-homotopy-equivalence</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-countable-coordinate-ball-cover-has-a-countable-locally-finite-shrinking</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-countable-coordinate-bump-map-embeds-a-manifold-in-countable-euclidean-data</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-degreewise-split-exact-complex-with-compatible-splittings-is-contractible</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-dense-bipartite-side-has-a-small-hitting-set</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-derivation-annihilates-constant-germs</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-descended-galois-orbit-idempotent-is-primitive</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-diagonal-path-that-changes-side-of-a-level-meets-it</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-dominant-cyclic-highest-weight-module-has-a-unique-simple-quotient</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-double-point-of-a-self-transverse-immersion-has-two-disjoint-embedded-sheet-disks</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-double-sum-over-finite-index-sets-may-be-interchanged</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-downward-closed-family-shatters-each-of-its-members</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-dyadic-scale-of-open-sets-defines-a-continuous-function</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-family-is-a-basis-exactly-when-its-conjugate-matrix-is-invertible</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-family-with-independent-incidence-vectors-has-at-most-n-members</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-fine-euclidean-approximation-lands-in-a-prescribed-tubular-neighbourhood</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-finite-abelian-group-is-a-quotient-of-a-power-of-a-cyclic-group</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-finite-characteristic-circuit-has-c2-regular-port-traces</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-finite-coordinate-bump-map-embeds-a-compact-manifold-in-some-euclidean-space</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-finite-cyclic-group-has-euler-totient-many-generators</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-finite-dimensional-algebra-separates-its-simple-modules</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-finite-dimensional-solvable-lie-algebra-has-a-codimension-one-ideal-over-an-algebraically-closed-characteristic-zero-field</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-finite-endpoint-of-a-maximal-unit-speed-geodesic-produces-a-cauchy-curve</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-finite-short-geodesic-network-gives-a-curvilinear-polygon-cellulation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-finitely-punctured-disk-retracts-to-a-wedge-of-circles</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-fixed-point-free-ball-map-produces-a-boundary-retraction</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-foliation-is-taut-if-and-only-if-it-has-no-dead-end-component</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-foliation-transverse-to-the-boundary-restricts-to-the-boundary</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-generic-isotopy-of-links-has-only-reidemeister-singular-times</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-generic-linear-projection-preserves-injectivity-and-immersion</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-generic-projection-can-preserve-properness</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-geometric-braid-slices-to-a-configuration-loop</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-given-ultrafilter-on-a-compact-hausdorff-space-has-a-unique-limit</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-graph-subgroup-is-a-complement-exactly-for-a-crossed-homomorphism</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-group-is-abelian-iff-every-conjugacy-class-is-a-singleton</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-group-with-the-fixed-point-property-is-amenable</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-half-dimensional-isotropic-subspace-forces-zero-signature</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-handle-decomposition-gives-a-relative-cw-complex</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-hatted-five-cycle-free-rooted-stable-tooth-comb-yields-a-large-pure-blockade-of-components</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-height-zero-diagram-represents-a-closed-braid</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-infinity-weights-satisfy-power-decay</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-k-handle-deformation-retracts-onto-its-cocore-and-outgoing-region</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-large-cy-restricted-subgraph-in-the-three-outcome-theorem-forces-a-smaller-scale-restricted-subgraph</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-large-set-contains-a-pattern-when-the-homogeneous-number-is-small</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-large-y-ten-thirds-restricted-induced-subgraph-forces-a-y-eleven-thirds-restricted-induced-subgraph</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-leafwise-loop-has-a-finite-transverse-double-point-representative</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-leafwise-path-determines-a-germ-of-transverse-diffeomorphism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-lie-subalgebra-distribution-is-involutive</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-lifted-cellular-homotopy-equivalence-has-a-contractible-algebraic-mapping-cone</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-limit-point-of-a-gradient-trajectory-is-critical</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-locally-compact-hausdorff-space-has-a-base-of-open-sets-with-compact-closure</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-locally-finite-sum-is-finite-near-the-compact-support-of-a-form</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-low-dimensional-disk-can-be-pushed-off-a-higher-cell</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-map-at-bounded-distance-from-a-quasi-isometric-embedding-is-a-quasi-isometric-embedding</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-map-of-nonzero-degree-between-spheres-is-surjective</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-maximal-layout-has-at-most-epsilon-inverse-blocks</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-measurable-direct-integral-of-unitary-representations-is-strongly-continuous</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-minimal-numerical-serre-kernel-obeys-the-quantum-casimir-constraint</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-module-meets-an-induced-subgraph-in-a-module</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-module-of-a-module-is-a-module</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-morphism-has-a-comparison-extension-between-the-supplied-injective-resolutions</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-morphism-has-a-comparison-lift-between-the-supplied-projective-resolutions</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-multiple-of-a-fork-surface-has-a-closed-compact-replacement</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-no-transversal-leaf-is-a-torus-via-the-finite-accessibility-boundary-sum</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-non-closed-leaf-of-a-codimension-one-foliation-meets-a-closed-transversal</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-noncompact-leaf-of-a-compact-c2-foliation-meets-a-positive-closed-transversal</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-nondegenerate-l1-representation-recovers-a-unitary-group-representation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-nontrivial-five-strand-braid-lies-in-the-burau-kernel</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-nonzero-dominant-section-is-determined-on-the-big-cell</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-nonzero-pi-class-on-a-torus-has-a-primitive-embedded-pi-root</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-nonzero-polynomial-in-several-variables-does-not-vanish-on-an-infinite-subring</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-nonzero-unitary-representation-of-a-compact-group-has-a-finite-dimensional-subrepresentation</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-nonzero-verma-homomorphism-is-injective</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-normal-summand-of-rank-at-least-two-surjects-on-the-framing-loop-obstruction</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-nullhomotopic-closed-transversal-yields-a-vanishing-cycle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-one-cube-average-and-maximal-function-forms-agree</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-one-handle-between-distinct-boundary-components-is-a-boundary-connected-sum</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-p-distribution-decay-from-maximal-cubes</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-p-dual-weight-and-nesting-properties</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-p-weighted-average-comparison-and-density-to-mass</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-p-weights-are-doubling</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-paired-immersed-cap-sweep-excludes-a-positive-closed-transversal</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-partition-is-determined-by-its-multiset-of-node-contents</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-pattern-inside-an-extension-set-produces-the-substitution</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-plane-arc-has-a-rectangular-neighborhood-by-schoenflies</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-polynomial-homogeneous-set-in-the-auxiliary-pattern-yields-a-y-four-restricted-union</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-positive-height-diagram-has-a-defect-region</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-positive-majorant-system-dominates-the-formal-cauchy-recursion</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-primitive-pi-torus-collar-has-contracting-longitude-and-exhausting-plane-caps</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-primitive-root-of-unity-and-its-prime-power-share-a-minimal-polynomial-over-the-rationals</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-proper-module-of-a-connected-graph-has-a-complete-neighbour</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-proper-verma-submodule-misses-the-highest-weight-line</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-punctured-disk-mapping-class-fixing-all-standard-adjacent-edges-is-a-boundary-twist-power</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-quasi-isometry-of-geodesic-spaces-has-a-controlled-coarse-inverse</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-quotient-mixed-block-witness-descends-to-two-member-blocks</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-rank-one-haar-average-is-a-nonzero-compact-intertwiner</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-reeb-component-obstructs-tautness</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-regular-weight-has-a-unique-dominant-dot-translate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-reiter-net-has-an-invariant-mean-cluster-point</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-relation-is-included-in-the-product-of-its-domain-and-range</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-rooted-stable-tooth-comb-with-a-cross-edge-between-two-blocks-contains-a-five-cycle</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-self-regular-set-of-intermediate-density-carries-many-induced-copies</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-self-transverse-immersion-has-no-double-points-when-n-is-greater-than-two-m</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-semisparse-blockade-can-be-sampled-to-anticonnected-blocks-with-nearly-pure-relations</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-sequence-in-a-hausdorff-space-has-at-most-one-limit</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-sequential-abelian-colimit-is-the-cokernel-of-one-minus-shift</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-set-of-positive-finite-measure-fills-most-of-a-dyadic-cube</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-simple-vanishing-cycle-produces-a-compact-leaf</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-small-regular-homotopy-removes-triple-points-and-preserves-transverse-branch-pairs</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-smooth-exhaustion-separates-the-locally-finite-chart-bands</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-smooth-finite-disk-arc-system-isotopy-extends-relative-boundary-and-marked-points</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-smooth-isotopy-of-compact-embedded-submanifolds-extends-to-an-ambient-isotopy</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-smooth-isotopy-of-links-can-be-put-in-general-position</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-smooth-three-manifold-with-h-one-z-two-and-h-two-zero-does-not-embed-in-s-four</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-co-p-five-free-graph-either-sparsifies-further-or-yields-a-pure-blockade-or-a-large-sparse-pair</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-co-p-five-free-graph-has-a-large-nearly-covered-sparse-pair</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-co-p-five-free-graph-yields-a-complete-or-anticomplete-blockade-or-a-sparser-subgraph</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-co-p-five-free-graph-yields-deeper-sparsification-or-a-complete-blockade-or-a-large-anticomplete-set</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-graph-either-sparsifies-further-or-yields-a-comb-or-a-large-sparse-pair</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-graph-has-a-prescribed-size-induced-subgraph-of-bounded-maximum-degree</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-graph-without-a-large-sparse-pair-has-a-large-nearly-covered-sparse-pair</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-p-five-free-graph-has-an-anticomplete-two-blockade</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sparse-set-has-small-self-density</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sphere-homeomorphism-extends-over-the-disk-by-the-alexander-trick</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sphere-with-a-product-neighbourhood-can-be-moved-off-a-lower-dimensional-submanifold</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-standard-stem-arc-system-can-be-straightened-by-boundary-and-puncture-fixed-ambient-isotopy</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-sufficiently-long-generator-extension-iteration-is-injective</loc>
<lastmod>2026-09-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-system-of-imprimitivity-gives-a-representation-of-the-transformation-algebra</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-taut-foliation-of-a-compact-connected-manifold-is-met-by-a-single-closed-transversal</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-topological-invariant-mean-yields-norm-approximately-invariant-densities</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-transitive-quasi-invariant-borel-g-space-is-ergodic</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-transposition-reverses-inversion-sign</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-triangulation-has-a-unique-triangle-on-the-closing-side</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-tubular-target-produces-a-submersive-finite-dimensional-perturbation-family</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-twice-differentiable-local-minimiser-has-nonnegative-second-variation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-two-element-indexed-product-is-in-bijection-with-a-cartesian-product</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-two-sided-coideal-in-an-enveloping-algebra-is-generated-by-its-primitive-part</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-ucb-invariant-mean-yields-a-topological-invariant-mean</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-uniformly-approximable-real-valued-map-is-continuous</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-union-of-parts-is-a-module-exactly-when-the-index-set-is</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vanishing-cycle-determines-a-nontrivial-limitwise-nullhomotopy-class</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vanishing-group-ring-coefficient-sum-pairs-off-opposite-signed-equal-labels</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vector-field-along-an-embedded-submanifold-extends-to-a-neighbourhood-and-globally-when-closed</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vector-line-integral-pulls-back-to-the-parameter-region</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vector-realises-the-minimal-polynomial</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-verma-composition-factor-has-the-same-central-character</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vertex-bijection-is-an-isometry-of-path-metrics-exactly-when-it-is-a-graph-isomorphism</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vertex-mixed-on-a-connected-set-mixes-on-an-edge</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vertex-mixed-on-a-quotient-block-yields-opposite-adjacency-on-two-member-blocks</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-vertex-mixed-on-an-anticonnected-set-yields-opposite-adjacency-on-a-nonedge</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-a-weak-equivalence-of-cw-complexes-has-vanishing-relative-homotopy-groups</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-weakly-sparse-set-has-a-large-sparse-subset</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-wedge-on-a-product-index-category-is-dinatural-in-each-variable-separately</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-wide-integral-geometric-layer-forces-a-property-star-blockade</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-wonderful-anticonnected-complete-or-sparse-blockade-yields-a-restricted-subgraph-or-a-large-anticomplete-pair</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a-word-whose-weight-is-coprime-to-its-length-has-a-trivial-shift-stabiliser</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a1-arbitrary-framing-cotangent-hecke-model</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a1-hecke-zero-section-excess-coefficients</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a1-nakajima-varieties-and-hecke-correspondence-are-points</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-a1-supported-chow-convolution-and-action</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-aalen-johansen-fixed-time-output-is-a-statistic</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abc-augmented-target-has-tolerance-posterior-marginal</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abel-jacobi-map-is-well-defined-and-base-point-independent</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abel-summation-by-parts</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-abel-summation-for-complex-series</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-abel-transform-of-cesaro-means</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-abelian-group-model-for-spectral-sequence-computations</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-abelian-scheme-base-change-and-products</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abelian-scheme-fibres-commutative-and-pointed-morphisms</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-abelian-scheme-fibrewise-constant-morphism-rigidity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abelian-scheme-universal-structure-sheaf-sections</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abelian-sheaves-admit-bounded-above-flat-resolutions</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abelian-sheaves-form-a-grothendieck-category</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abelian-sylow-fusion-in-its-normalizer</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-absolute-convergence-implies-convergence</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-absolute-real-powers-are-convex</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-absolute-value-does-not-increase-dirichlet-energy-or-change-ltwo-normalisation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-absolutely-continuous-upper-quantile-exact-tail-mass</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-absolutely-convergent-series-cauchy-product</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-absolutely-convergent-series-is-cauchy</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-absolutely-summable-fourier-coefficients-give-uniform-convergence</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-absolutely-summable-linear-filters-preserve-weak-stationarity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-abstract-residue-additivity</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-abstract-residue-basic-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-abstract-residue-trace-under-finite-free-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ac-supplies-countable-and-dependent-choice-for-banach-integration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ac-supplies-dependent-choice-for-vector-bundle-constructions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ac-supplies-sequential-choices-for-probability-constructions</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ac-zero-derivative-and-integral-reconstruction-under-countable-choice</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-acceptance-is-configuration-reachability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-acl-representatives-reconstruct-weak-gradients-by-fubini</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-action-map-fibres-and-stabilizer-subscheme</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-actions-related-by-automorphisms-give-isomorphic-semidirect-products</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-active-routes-in-a-finite-dag-have-active-paths</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-acyclic-assembly-by-exact-columns</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-acyclic-assembly-by-exact-rows</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-acyclic-direct-image-cohomology-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-acyclic-rows-and-columns-of-cech-double-complex</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-acyclicity-makes-the-simply-connected-middle-handle-matrix-unimodular</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adapted-continuous-processes-are-progressively-measurable</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-adapted-descending-field-near-a-compact-morse-band</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-adaptive-covariance-lepski-scale-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adaptive-cubic-unsuccessful-iteration-count</loc>
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<loc>https://alphabetamath.cc/item/lem-adaptive-em-predictable-grid-second-moment</loc>
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<loc>https://alphabetamath.cc/item/lem-adaptive-mcmc-block-perturbation-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-adaptive-mcmc-uniform-drift-minorization-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-adaptive-truncated-covariance-estimator-is-total</loc>
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<loc>https://alphabetamath.cc/item/lem-add-one-point-euler-characteristic</loc>
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<loc>https://alphabetamath.cc/item/lem-add-one-point-exact-sequence-line-bundle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-addable-nodes-of-a-partition-have-distinct-contents</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-addition-and-multiplication-of-marked-ideals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-addition-of-roofs-makes-an-additive-localization</loc>
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<loc>https://alphabetamath.cc/item/lem-additive-bounded-above-on-an-interval-is-linear</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additive-character-orthogonality-from-representation-orthogonality</loc>
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<loc>https://alphabetamath.cc/item/lem-additive-characters-are-one-dimensional-complex-representations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additive-cocontinuous-module-functors-form-a-category</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additive-constant-in-an-entropy-flux-does-not-change-the-entropy-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additive-heun-one-step-weak-expansion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additive-is-q-linear</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additive-kan-and-normalized-fibration-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additive-module-functor-preserves-colimits-iff-right-exact-and-coproduct-preserving</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additive-singular-cohomology-cross-product-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-additivity-and-compact-cell-support-control-the-infinite-cw-colimit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adelic-quotient-computes-h1-structure-sheaf</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adem-double-power-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adem-reduction-spans-by-admissible-composites</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjacent-column-garnir-relation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjacent-iid-finite-moment-vector-strong-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjacent-window-divided-difference-recurrence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjoining-a-vector-outside-the-span</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjoining-one-root-reduces-the-unsplit-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjoining-roots-of-unity-to-a-galois-extension-adds-an-abelian-kernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjoint-action-preserves-the-associated-graded-of-a-two-sided-ideal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjoint-casimir-is-positive-scalar</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjoint-of-a-coercive-sesquilinear-form-is-coercive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjoint-of-the-shifted-solution-operator-solves-the-adjoint-form-problem</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjoint-representation-of-an-affine-group-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjugate-inverse-formula-over-a-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjunct-formulas-are-mutually-inverse</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-adjunction-formula-for-effective-divisors-on-smooth-surfaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-admissible-cycle-around-a-compact-plane-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-admissible-density-domain-is-closed-convex-complete</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-admissible-is-chain</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-admissible-product-coordinate-normalizer-is-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-admissible-set-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-admissible-square-action-has-a-distinct-leading-monomial</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-admm-exact-subproblem-optimality-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-aep-implies-fixed-rate-lossless-coding</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-common-refinement-overlay-and-cardinality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-convection-quasi-orthogonality-under-fine-mesh</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-data-oscillation-reduction-under-marked-refinement</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-dorfler-marking-cardinality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-localized-galerkin-refinement-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-nvb-conforming-closure-and-cumulative-counting</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-nvb-shape-regularity-and-three-generation-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-p1-residual-representation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-afem-residual-estimator-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-afem-vertex-patch-poincare</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-affine-algebra-points-as-k-algebra-maps</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-algebraic-group-faithful-rational-representation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-affine-algebraic-whitney-strata-admit-finite-critical-strongly-plurisubharmonic-distance-exhaustions</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-blowup-algebra-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-blowup-chart-universal-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-central-coroot-from-the-transpose-null-ray</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-chart-quotients-for-invariant-sections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-closest-pairs-and-downward-facet-translation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-cone-dimension-projective-variety</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-current-fields-are-local</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-de-quivers-have-exponentially-many-indecomposables</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-deformations-obstruction-and-torsor</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-diagonal-and-front-back-shuffle-have-a-specified-chain-homotopy</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-dirichlet-trace-class-is-nonempty-convex-and-weakly-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-domain-chain-dimension-formula-step</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-domain-normalisation-dimension-lower-bound</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-domain-normalisation-dimension-upper-bound</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-etale-equivalence-relation-quotient</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-face-maps-satisfy-the-cosimplicial-identities</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-fibre-product-projections-stalk-maps</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-finite-field-hashes-are-pairwise-independent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-finite-type-scheme-coordinate-ring-finitely-generated</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-finite-type-source-immerses-in-relative-projective-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-form-integrable-on-bochner-l2</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-intersection-dimension-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-line-independence-in-the-definition-of-plurisubharmonicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-local-dimension-residue-transcendence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-module-sheaf-universal-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-morphism-cohomology-pushforward</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-morphism-local-on-target</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-morphism-separated</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-morphism-structure-sheaf-pushforward-localizes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-morphisms-have-one-sided-perverse-exactness</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-piola-transport-preserves-commuting-interpolation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-point-blowup-pushforward-vanishing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-product-topology-not-product-topology</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-pullback-weak-derivatives-and-scaling</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-qc-cech-unit-ideal-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-simplex-gauss-green-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-translation-derivation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-vacuum-character-at-level-k</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-vacuum-module-is-restricted</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affine-vacuum-module-pbw-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-affineness-from-unit-generating-global-sections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-base-change-of-standard-smooth-presentations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-differentials-localization-base-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-differentials-transitivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-differentials-universal-property</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-finite-field-extension-separable-factorization</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ag-flat-local-regularity-ascent-descent</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-geometric-regularity-field-tests</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-geometrically-regular-fibres-local-presentation</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-local-flatness-regular-parameters</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-polynomial-quotient-differentials</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-separable-residue-cotangent-sequence</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-standard-smooth-fibre-regular-parameters</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-standard-smooth-flatness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ag-standard-smooth-regular-geometric-fibres</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-aggregate-model-error-controls-proximal-candidate</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ahlfors-extension-of-line-quasisymmetric-maps</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ahss-e-one-page-is-cellular-cochains-with-theory-coefficients</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-airy-functions-have-negative-real-zeros</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-airy-series-coefficient-recurrence-and-tail</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ale-jacobi-geometric-conservation-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ale-periodic-face-motion-satisfies-discrete-gcl</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ale-schur-complement-positive-and-minimizes-energy</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ale-schur-residual-controls-interface-energy-error</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-alexandroff-urysohn-metrization-lemma</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-algebra-generated-by-finitely-many-integral-elements-is-module-finite</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-algebra-of-continuous-real-maps-on-a-space</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-algebra-operations-on-smooth-germs-are-representative-independent</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-algebra-with-countable-disjoint-unions-is-sigma</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-algebra-with-increasing-unions-is-sigma</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-algebraic-cancellation-does-not-yet-give-geometric-cancellation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-algebraic-integer-is-a-unit-iff-norm-is-plus-or-minus-one</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-algebraic-milnor-neighborhoods-admit-controlled-sector-transport</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-algebraic-open-inclusion-surjects-on-fundamental-groups</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-algebraic-set-finite-irreducible-components</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-all-charts-compatible-with-a-smooth-atlas-form-a-smooth-atlas</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-all-extremal</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-almost-invariant-vectors-and-positive-type-functions</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-almost-sure-convergence-event-is-measurable</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-alphabet-reduction-controls-size-and-degree</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-alternating-hook-induction-cancels-disconnected-rim-removals</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-alternating-kempe-paths-cannot-both-occur</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-alternating-multilinear-implies-antisymmetric</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-alternating-sequence</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-alternating-top-forms-are-determined-by-one-ordered-basis</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ample-divisor-positive-intersection-on-smooth-projective-surface</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ample-invariant-section-charts-are-affine</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ample-linearization-power-equivariant-embedding</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ample-pullback-finite-morphism</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ample-stable-positive-power</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ample-twist-of-line-bundle-is-very-ample</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ams-stationary-mean-dominates-tail-events</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-algebraic-integer-average-of-roots-of-unity-is-zero-or-constant</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-ambient-isotopy-preserves-the-orientation-of-an-invariant-round-sphere</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-analytic-germ-has-a-rational-geometric-majorant</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-antipode-is-unique</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-augmented-simplicial-cone-has-an-explicit-chain-contraction</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-elementary-expansion-has-zero-whitehead-torsion</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-embedding-into-r-n-gives-the-same-normal-bundle-identity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-extension-induces-a-well-defined-outer-action-on-the-kernel</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-extremal-cancellation-shortens-an-artin-substitution</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-hp-atom-has-uniform-hp-quasinorm</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-identity-relative-boundary-matrix-allows-cell-cancellation</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-immersion-into-r-n-gives-a-rank-n-minus-m-representative-of-the-stable-normal-bundle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-infinite-cap-center-trajectory-has-recurrent-common-plaque-interior-patches</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-injective-resolution-for-f-produces-a-g-acyclic-resolution-after-f</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-integrable-o-module-is-generated-by-dominant-maximal-weights</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-invariant-mean-produces-a-reiter-net</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-invariant-polynomial-is-determined-by-its-cartan-restriction</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-invariant-polynomial-of-curvature-is-closed</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-isomorphism-extends-across-a-simple-root-adjunction</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-isotopy-velocity-field-extends-over-a-tubular-neighbourhood</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-iterative-sparsification-step-for-sparse-co-p-five-free-graphs</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-l-two-class-invariant-in-modulus-under-all-translations-of-the-line-is-zero</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-lch-group-has-an-open-sigma-compact-subgroup</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-lkb-kernel-braid-fixes-every-standard-adjacent-edge-up-to-isotopy</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-odd-closed-walk-contains-an-odd-cycle</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-odd-permutation-reverses-oriented-simplex-sign</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-ultrafilter-algebra-determines-a-compact-hausdorff-topology</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-ultrafilter-algebra-map-is-the-unique-ultrafilter-limit</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-unshattered-set-reduces-a-monomial-on-a-family</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-an-x-sparse-blockade-iteration-yields-further-sparsification-or-a-pure-blockade</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-analytic-boundary-green-corrector-is-smooth</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-analytic-cauchy-data-reduce-to-zero-data-in-normal-form</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-analytic-constructible-sheaves-admit-coherent-six-operations</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-analytic-countable-operations-and-borel-inclusion</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-analytic-duhamel-cancellation-removes-the-generator-singularity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-analytic-exhaustion-of-plane-domains</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-analytic-noncharacteristic-hypersurfaces-flatten-to-a-coordinate-hyperplane</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-analytic-ordinary-differential-systems-by-coefficient-majorants</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-analytic-poisson-integrals-have-vanishing-negative-coefficients</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-analytic-quasiconformality-implies-modulus-distortion</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-analytic-quasiconformality-implies-quadrilateral-modulus-bounds</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-analytic-six-operation-support-and-trace-calculus</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-analytic-subsets-of-baire-space-have-tree-projections</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-anchored-box-summation-by-parts-hk-variation</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-anchored-irgnm-fixed-reference-error-and-residual</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-anchored-metric-graph-h1-space-is-hilbert</loc>
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<loc>https://alphabetamath.cc/item/lem-angular-fourier-orthogonality</loc>
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<loc>https://alphabetamath.cc/item/lem-annihilator-ideal-of-a-distribution-is-frame-independent</loc>
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<loc>https://alphabetamath.cc/item/lem-annihilator-of-a-cyclic-submodule</loc>
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<loc>https://alphabetamath.cc/item/lem-annihilator-reverses-inclusion-and-double-annihilator-closes</loc>
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<loc>https://alphabetamath.cc/item/lem-annihilators-are-closed-subspaces</loc>
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<loc>https://alphabetamath.cc/item/lem-annihilators-are-weak-and-weak-star-closed</loc>
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<loc>https://alphabetamath.cc/item/lem-annulus-far-field-estimates-for-the-maximal-function</loc>
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<loc>https://alphabetamath.cc/item/lem-anti-excedances-become-descents-under-foata-fundamental-transformation</loc>
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<loc>https://alphabetamath.cc/item/lem-antichains-well-order-linearly-ordered-sets</loc>
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<loc>https://alphabetamath.cc/item/lem-anticonnected-block-contraction-turns-an-upside-down-comb-into-a-pure-blockade</loc>
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<loc>https://alphabetamath.cc/item/lem-antipodal-circle-map-has-odd-lift-increment</loc>
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<loc>https://alphabetamath.cc/item/lem-antipodal-sphere-cover</loc>
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<loc>https://alphabetamath.cc/item/lem-antisymmetrizer-image-on-its-tabloid-module-is-one-dimensional</loc>
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<loc>https://alphabetamath.cc/item/lem-any-homology-theory-computes-relative-cell-groups-from-its-coefficient-group</loc>
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<loc>https://alphabetamath.cc/item/lem-any-two-points-in-a-connected-smooth-manifold-can-be-joined-by-a-piecewise-c-one-curve</loc>
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<loc>https://alphabetamath.cc/item/lem-anyonic-fusion-path-basis</loc>
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<loc>https://alphabetamath.cc/item/lem-anyonic-vacuum-f-symbol-frobenius-schur-normalization</loc>
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<loc>https://alphabetamath.cc/item/lem-aperiodic-minorization-times-are-cofinite</loc>
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<loc>https://alphabetamath.cc/item/lem-aperiodic-petite-set-with-accessible-small-set-is-small</loc>
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<loc>https://alphabetamath.cc/item/lem-aperiodic-return-times-are-eventually-positive</loc>
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<loc>https://alphabetamath.cc/item/lem-approximate-identities-in-schwartz-space-converge-in-tempered-distributions</loc>
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<loc>https://alphabetamath.cc/item/lem-arbitrarily-large-primes-congruent-to-two-modulo-three</loc>
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<loc>https://alphabetamath.cc/item/lem-arbitrary-hilbert-fredholm-determinant-from-separable-support</loc>
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<loc>https://alphabetamath.cc/item/lem-arcs-in-a-connected-submanifold-avoiding-finitely-many-double-points</loc>
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<url>
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<loc>https://alphabetamath.cc/item/lem-associated-prime-equivalent-cyclic-embedding</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-prime-localises-forward</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-prime-localises-reverse-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-primes-contained-in-support</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-primes-exact-sequence-left-inclusion</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-primes-exact-sequence-right-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-primes-from-a-minimal-primary-decomposition</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-primes-of-cohen-macaulay-module-have-full-dimension</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-sheaf-restriction-affine-open</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-sheaf-sections-basic-open</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-associated-sheaf-stalk-localization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-associates-characterisation</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-asymptotic-gromov-sequences-form-an-equivalence-relation</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-asymptotic-induction-identifies-leading-modular-simples</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-asymptotically-hyperbolic-half-line-operator-has-right-inverse</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-asymptoticity-is-an-equivalence-relation-on-gromov-sequences</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-atomic-forcing-relation-is-well-founded-and-definable</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-attaching-a-single-cell-kills-the-represented-homotopy-class</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-attaching-handles-along-isotopic-attaching-embeddings-preserves-the-diffeomorphism-type</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-augmentation-ideal-of-a-finite-p-group-algebra-is-nilpotent</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-augmenting-path-switching</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-auslander-buchsbaum-base-case-free-module</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-auslander-buchsbaum-first-syzygy-depth</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-auslander-buchsbaum-projective-dimension-one</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-auslander-buchsbaum-syzygy-projective-dimension</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-automizer-condition-gives-centralizer-transitivity</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-autonomous-periodic-orbit-has-neutral-floquet-multiplier</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-av7-classical-zmt-relative-integral-closure-neighbourhoods</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-av7-coprime-factorization-finite-component-neighbourhoods</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-av7-finite-morphism-projective-over-projective-base</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-av7-integral-closure-elementary-etale-base-change</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-av7-proper-quasi-finite-factor-is-finite</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-av7-relative-integral-closure-finite-affine-charts</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-av7-zero-dimensional-standard-smooth-local-tools</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-average-convergence-of-a-continuous-banach-valued-function</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-averages-over-probability-densities-attain-the-essential-supremum</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-averaging-makes-a-finite-dimensional-representation-unitary</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-averaging-operator-projects-onto-the-fixed-subspace</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-axiom-of-choice-implies-countable-choice</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-axiomatic-cellular-boundaries-are-integral-incidence-matrices-with-coefficients</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-axis-fellow-travelling-controls-the-centralizer</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-b-adic-anova-parseval</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-b-adic-step-functions-dense-in-l2-cube</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-b-spline-basis-refinement-under-single-knot-insertion</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-backdoor-criterion-implies-counterfactual-exchangeability</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-backward-euler-cq-principal-branch-generating-function</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-backward-euler-cq-weights-and-partial-sums</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-backward-gaussian-kernel-is-valid-under-full-smoothing-data</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-backward-uniqueness-for-the-heat-equation-on-a-bounded-interval</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-baer-sum-is-independent-of-extension-representatives</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-baer-sum-of-short-exact-sequence-classes-is-independent-of-representatives</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-baire-category-in-a-closed-interval</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-baire-diagonal-passage-from-finite-regularity-to-smooth-metrics</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-baire-property-sigma-algebra-and-borel-regularity</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balanced-convex-zero-neighborhood-refinement</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balanced-gauge-is-a-seminorm</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balanced-triple-linear-algebra-over-the-projective-line</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balancing-and-hopf-link-character-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ball-and-cube-maximal-functions-are-comparable</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ball-and-sphere-mean-radial-identity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ball-hardy-traces-and-evaluation-bound</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ball-mean-oscillation-potential-bound</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ball-poisson-kernel-is-positive-and-normalised</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balls-in-a-connected-locally-finite-graph-are-finite</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balogh-combinatorial-map</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balogh-countable-restriction-enumeration</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balogh-failure-of-countable-shrinking</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balogh-hereditary-normality</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-balogh-neighborhood-basis</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banach-gaussian-rkhs-unit-ball-is-compact</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banach-limit-properties</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banach-manifold-differentials-are-chart-independent</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banach-mazur-game-category-characterization</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banach-mean-value-estimate-on-a-convex-set</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banach-valued-cauchy-integral-vanishes</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banach-valued-cauchy-theorem-on-star-shaped-domains</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banach-valued-simple-integral-is-well-defined</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-banaschewski-prime-obstruction</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-band-exchanges-decompose-into-ordinary-markov-moves</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bandlimited-samples-are-fourier-coefficients-on-the-band-interval</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-baoab-one-step-error-moment-bounds</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-baoab-one-step-weak-expansion</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bar-differential-and-augmentation-form-a-complex</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bar-first-integral-homology-is-the-abelianization</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bar-transfer-is-a-chain-map-and-choice-independent-up-to-chain-homotopy</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bar-two-cocycles-classify-abelian-kernel-extensions</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-barycentric-coordinates-are-unique</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-barycentric-denominator-polynomial-nonzero</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-barycentric-face-chains-triangulate-a-geometric-simplex</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-barycentric-subdivision-removes-edge-inversions</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-b-expansion-cylinders-match-orbits-away-from-terminating-endpoints</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-base-change-affine-morphisms</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-change-composition</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-change-locally-finite-type-presentation</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-change-of-a-zero-dimensional-projective-quotient</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-change-of-intertwiner-spaces</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-change-open-closed-immersions</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-change-quasi-compact-morphisms</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-change-surjective-morphisms</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-base-extension-field-coordinate-ring</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<loc>https://alphabetamath.cc/item/lem-base-flat-syzygies-and-fibrewise-resolution-exactness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-based-and-free-homotopy-classes-of-sphere-maps-agree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-based-homotopies-transverse-to-the-zero-section-give-normal-cobordisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-based-sphere-maps-have-finite-affine-bubble-normal-forms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-bounding-and-dominating-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-bull-free-hole-with-a-complete-outside-vertex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-bull-free-hole-with-an-anticomplete-outside-vertex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-cohen-generic-reals-form-a-symmetric-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-cohen-model-schema-of-continuity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-cohen-search-and-shift-prime-ideal-construction</loc>
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<loc>https://alphabetamath.cc/item/lem-basic-cohen-symmetric-construction-is-uniformly-formalizable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-combinatorial-lemma-for-tableaux</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-conditional-complexity-inequalities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-ideal-cardinal-inequalities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-laws-of-inclusion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-opens-quasi-compact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-properties-of-characteristic-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-properties-of-the-holomorphic-hull</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-properties-of-total-variation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-pseudointersection-and-tower-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-weak-neighborhoods</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basic-weak-star-neighborhoods</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basis-change-and-direct-sum-formulas-for-chain-torsion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-basis-iff-maximal-independent-iff-minimal-spanning</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bdf2-root-locus-location</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-belt-sphere-complements-in-low-handle-levels-preserve-the-fundamental-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-exterior-energy-trace-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-far-panel-quadrature-residual</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-half-order-bessel-slobodeckij-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-helmholtz-double-layer-conormal-jump</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-lipschitz-graph-sobolev-and-green-interface</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-lipschitz-trace-and-lifting</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-lipschitz-transmission-kernel-representation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-newtonian-kernel-is-fundamental-solution</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-p0-negative-half-order-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-panel-pair-duffy-certificates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-plane-poisson-kernel-fourier-transform</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-polyhedral-edge-kernel-representation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-smooth-trace-and-helmholtz-layer-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bem-surface-fractional-norm-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bender-knuth-involutions-on-semistandard-tableaux</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-benjamini-hochberg-leave-one-out-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bergman-determinant-over-kernel-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bergman-evaluation-bound-on-compact-subsets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bergman-kernel-smoothness-and-positive-diagonal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bergman-mean-value-l2-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bergman-metric-determinants-of-ball-and-polydisc</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bernoulli-and-binomial-mean-and-variance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bernoulli-inequality</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bernoulli-root-laws-are-uniformly-weak-close</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bernstein-basis-moment-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bessel-casoratian-invariant-positive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bessel-integral-midpoint-error</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bessel-integral-representations-and-scaled-range</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bessel-j-zero-data-exclusion</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bessel-potential-norm-is-positive-definite</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bessel-potentials-shift-sobolev-order-isometrically</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-beta-density-normalization</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bezout-global-length-degree-product</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-bezout-no-common-component-finite-intersection</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bfgs-hessian-bounds-control-gradient-and-taylor-remainder</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bfgs-trace-determinant-potential-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bfgs-updates-preserve-secant-symmetry-and-spd</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bgg-euler-character-gives-the-weyl-numerator</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bh-prds-null-contribution-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bicosimplicial-derived-total-complex-agrees-with-diagonal-totalization</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-biduality-is-stable-under-products-closed-subgroups-and-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bigraded-string-type-contributions-to-bigraded-intersection-numbers</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bigradings-of-curves-exist-and-are-unique-up-to-the-deck-action</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-biholomorphic-invariance-of-plane-subharmonicity</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bilinear-right-exact-functors-are-determined-by-the-pair-of-regular-modules</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bimodule-tensor-associators-and-unitors-satisfy-bicategory-coherence</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bimodule-tensor-totalization-respects-differentials-and-homotopies</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binary-monotonicity-excludes-defiers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-binary-quadratic-form-substitution-is-a-right-action</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binary-quadratic-representation-via-hilbert-symbol</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binary-regression-l2-controls-local-likelihood-distances</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binary-resultant-scaling-specialization-and-dehomogenization</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binary-rounding-grid-and-ordered-two-sum</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binary-sequence-space-is-compact-without-tychonoff</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binary-trees-of-a-given-size-form-a-finite-set</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-binet-loggamma-right-halfplane-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binomial-coefficients-symmetric-and-unimodal</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binomial-count-law</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binomial-series-for-a-repeated-pole</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binomial-support-count-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-binomial-theorem-over-complex-numbers</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-birational-morphism-principal-open-isomorphism</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-birational-surface-morphism-factors-through-blowup-at-a-non-isomorphism-point</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bishop-phelps-support-cone-construction</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-bivariate-drift-minorization-coupling-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blass-paired-finite-modification-classes-form-a-russell-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blass-ultrafilter-free-model-is-finitely-formalizable</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-blichfeldt-lattice-point-principle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bloch-rescaling-at-an-almost-maximal-derivative</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-block-centre-locality-and-trace-ideal-sums</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-block-defect-is-an-intersection-of-two-sylow-subgroups</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-block-idempotents-are-fixed-by-normal-p-subgroup-brauer-projection</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-block-idempotents-lift-uniquely-from-kh-to-oh</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-block-induction-exists-under-centralizer-containment</loc>
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<loc>https://alphabetamath.cc/item/lem-block-induction-is-transitive</loc>
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<loc>https://alphabetamath.cc/item/lem-block-interchanges-transport-arbitrary-braid-boxes</loc>
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<loc>https://alphabetamath.cc/item/lem-block-principal-angle-squared-ritz-enclosure</loc>
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<loc>https://alphabetamath.cc/item/lem-block-projection-preserves-projectives</loc>
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<loc>https://alphabetamath.cc/item/lem-block-relative-trace-characterizes-diagonal-projectivity</loc>
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<loc>https://alphabetamath.cc/item/lem-block-triangular-basis-changes-diagonalize-an-invertible-differential-block</loc>
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<loc>https://alphabetamath.cc/item/lem-block-upper-triangular-pencil-determinant-factorizes</loc>
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<loc>https://alphabetamath.cc/item/lem-blockade-has-support-invariant-uniform-minor</loc>
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<loc>https://alphabetamath.cc/item/lem-blocks-from-different-mixed-block-classes-form-pure-pairs</loc>
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<loc>https://alphabetamath.cc/item/lem-blowing-up-a-regular-point-is-a-contraction</loc>
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<loc>https://alphabetamath.cc/item/lem-blowup-charts-of-the-quadric-cone</loc>
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<loc>https://alphabetamath.cc/item/lem-blowup-intersection-matrix-at-smooth-point</loc>
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<loc>https://alphabetamath.cc/item/lem-blowup-isomorphism-off-center</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blowup-local-on-base-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blowup-lowers-contact-order</loc>
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<loc>https://alphabetamath.cc/item/lem-blowup-multiplicity-euler-characteristic-drop</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blowup-of-closed-point-of-regular-surface-is-regular</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blowup-plane-origin-incidence-equations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blowup-point-pushforward-vanishing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blowup-power-of-ideal-same</loc>
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<loc>https://alphabetamath.cc/item/lem-blowup-reduced-integral-under-domain-rees</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blowup-separates-transverse-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blowups-of-projective-schemes-are-projective</loc>
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<loc>https://alphabetamath.cc/item/lem-blr-acceptance-fourier-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-blr-testing-supplies-nearby-linear-decoders</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bmo-averages-on-nested-cubes-grow-at-most-logarithmically</loc>
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<loc>https://alphabetamath.cc/item/lem-bmo-classes-are-determined-by-their-atom-pairings</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bmo-functions-pair-uniformly-with-hone-atoms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bmw-cubic-relation-and-hecke-quotient</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-boardman-approximate-cycle-obstruction-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bochner-density-defines-an-absolutely-continuous-vector-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bochner-functional-extends-and-has-a-radon-representing-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bochner-integral-norm-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bockstein-square-parity-recurrence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bohr-mollerup-factorial-squeeze</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bondy-chvatal-closure-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-boolean-circuits-reduce-to-quadratic-equation-systems-with-a-fixed-input-prefix</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-boolean-ultrafilter-extension-from-compact-products</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-boone-reduced-auxiliary-words-have-no-rule-pinches</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-boone-semigroup-histories-detect-halting</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bootstrap-particle-filter-weak-consistency</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bor-nonnegative-expansion-for-reduced-kronecker-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bordism-of-regular-preimages-produces-a-homotopy-of-sphere-maps</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-map-into-separable-banach-is-strongly-measurable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-meagre-sections-have-uniform-closed-covers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-moore-homology-of-compact-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-nevanlinna-growth-increment</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-null-sections-have-uniform-open-hulls</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-probability-sequences-on-compact-metric-spaces-have-integral-convergent-subsequences</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-product-of-second-countable-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-relations-admit-conull-borel-uniformizations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-representatives-make-the-convolution-integrand-borel-measurable</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-sigma-algebra-of-continuous-path-space-is-generated-by-coordinates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-borel-subgroup-is-the-stabilizer-of-a-maximal-flag</loc>
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<loc>https://alphabetamath.cc/item/lem-borel-subspaces-admit-polish-presentations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bott-samelson-bimodules-have-delta-and-nabla-support-filtrations</loc>
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<loc>https://alphabetamath.cc/item/lem-boundaries-and-cycles-in-a-free-complex-over-a-pid-are-free</loc>
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<loc>https://alphabetamath.cc/item/lem-boundary-fixed-disk-evaluation-has-continuous-local-point-motion-sections</loc>
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<loc>https://alphabetamath.cc/item/lem-boundary-horn-product-is-anodyne</loc>
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<loc>https://alphabetamath.cc/item/lem-boundary-label-of-a-van-kampen-diagram-is-null-in-the-presented-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-boundary-marked-five-bordisms-give-common-middle-two-handle-traces</loc>
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<loc>https://alphabetamath.cc/item/lem-boundary-point-whose-complementary-component-contains-another-point-is-regular</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-above-kac-moody-weight-modules-are-generated-by-primitive-vectors</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-borel-riemann-integrands-on-boxes-have-equal-lebesgue-integrals</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-centered-convergent-series-have-summable-variances</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-conjugates-give-finitely-many-integral-polynomials</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-coordinatewise-monotone-is-riemann-integrable</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-definitions-of-basic-set-operations</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-density-and-finite-vector-transitivity-for-c-star-representations</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-density-finite-second-moment-has-finite-differential-entropy</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-distance-is-an-equivalence-relation-compatible-with-composition</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-finite-length-complex-euler-identities</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-finite-projective-model-for-khovanov-seidel-modules</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-function-form-of-the-markov-property</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-functionals-on-finite-l-p-define-finite-signed-or-complex-measures</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-hierarchy-for-the-multiple-choice-argument</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-hilbert-operators-form-a-c-star-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-holomorphic-disc-functions-have-fatou-limits-under-countable-choice</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-independent-matrix-bernstein-via-trace-exponential</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-lipschitz-discrepancy-dominated-by-weighted-total-variation</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-lipschitz-metric-characterizes-weak-convergence-on-polish-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-lipschitz-profile-moments-control-uniform-distance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-local-displacement-on-a-geodesic-space-implies-coarse-lipschitz</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-minimising-sequence-has-a-weakly-convergent-subsequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-open-jordan-sets-have-compact-grid-exhaustions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-predictable-counting-integral-pathwise-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-punctured-slice-has-holomorphic-parameter-extension</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-quantifiers-preserve-primitive-recursiveness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-rate-reaction-generator-dynkin-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-rational-tree-limit-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-reachability-recursion-is-correct</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-reachability-uses-logarithmic-recursion-depth</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-real-c-zero-functional-is-a-difference-of-positive-functionals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-real-ultralimits-and-free-tail-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-remetrisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-restriction-and-cutoff-localisation-in-sobolev-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-sde-increment-moments</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-separate-rationality-is-rational</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-stage-capture-in-finite-support-iterations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-stopping-preserves-cadlag-square-integrable-martingales</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-support-makes-frechet-kolmogorov-tail-control-automatic</loc>
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<loc>https://alphabetamath.cc/item/lem-bounded-test-function-sets-have-common-compact-support</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounded-two-sided-projective-a-m-bimodule-complexes-act-on-c-m</loc>
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<url>
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<loc>https://alphabetamath.cc/item/lem-bounded-variation-gives-one-sided-dirichlet-integrability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bounding-projections-give-exact-upper-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-bowl-shaped-loss-has-centered-lipschitz-minorants</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-box-control-projection-is-pointwise-clipping</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-box-volume-is-additive-over-grid-subdivisions</loc>
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<loc>https://alphabetamath.cc/item/lem-boys-incomplete-gamma-large-t-tail-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-boys-positive-midpoint-enclosure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-boys-small-taylor-remainder</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-bracketing-zoom-finite-budget-checked-return</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-brahmagupta-fibonacci-two-square-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-braid-isotopic-closed-braids-are-conjugate</loc>
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<loc>https://alphabetamath.cc/item/lem-braid-like-moves-can-be-moved-to-height-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-braid-mapping-classes-lift-equivariantly-to-the-burau-cover</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-braided-tensor-product-of-separable-algebras-is-separable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-braids-lift-to-the-lkb-cover-and-act-lambda-linearly</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-branching-rule-for-specht-induction-and-coinvariants</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-brauer-and-partition-composition-is-associative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-brauer-and-partition-diagram-basis-ranks</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-brauer-character-is-independent-of-basis-and-splitting-field-realisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-brauer-homomorphism-is-conjugation-equivariant</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-broken-morse-trajectories-have-strictly-decreasing-critical-values-and-indices</loc>
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<url>
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<loc>https://alphabetamath.cc/item/lem-c-one-change-of-variables-for-nonnegative-borel-functions-via-radon-uniqueness</loc>
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<loc>https://alphabetamath.cc/item/lem-c-one-diffeomorphisms-map-lebesgue-measurable-sets-to-lebesgue-measurable-sets</loc>
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<loc>https://alphabetamath.cc/item/lem-c-one-diffeomorphisms-map-lebesgue-null-sets-to-null-sets</loc>
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<loc>https://alphabetamath.cc/item/lem-c-one-images-of-content-zero-compact-sets-have-content-zero</loc>
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<loc>https://alphabetamath.cc/item/lem-c-one-stokes-for-complex-euclidean-domains</loc>
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<loc>https://alphabetamath.cc/item/lem-c-prime-lambda-implies-c-lambda</loc>
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<loc>https://alphabetamath.cc/item/lem-c-prime-one-sixth-interior-faces-have-at-least-seven-arcs</loc>
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<loc>https://alphabetamath.cc/item/lem-c-soft-field-sheaves-are-compact-support-acyclic</loc>
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<loc>https://alphabetamath.cc/item/lem-c-star-algebras-and-closed-ideals-have-positive-contractive-approximate-units</loc>
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<loc>https://alphabetamath.cc/item/lem-c-star-positive-calculus-and-order-estimates</loc>
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<loc>https://alphabetamath.cc/item/lem-c-star-spectral-radius-equals-norm-for-normal-elements</loc>
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<loc>https://alphabetamath.cc/item/lem-c-star-state-gns-purity-and-polish-state-space</loc>
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<loc>https://alphabetamath.cc/item/lem-c-two-alpha-boundary-flattening-preserves-ellipticity-and-holder-norms</loc>
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<loc>https://alphabetamath.cc/item/lem-c-two-boundary-flattening-transforms-uniform-ellipticity</loc>
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<loc>https://alphabetamath.cc/item/lem-c-zero-is-a-closed-subspace-of-ell-infinity</loc>
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<loc>https://alphabetamath.cc/item/lem-c1-divided-difference-extends-continuously</loc>
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<loc>https://alphabetamath.cc/item/lem-c1-euclidean-maximal-flow-with-c2-upgrade</loc>
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<loc>https://alphabetamath.cc/item/lem-c1-foliated-atlas-preserves-plaque-equivalence-and-transverse-orientation</loc>
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<loc>https://alphabetamath.cc/item/lem-c1-germs-of-local-diffeomorphisms-form-a-group</loc>
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<loc>https://alphabetamath.cc/item/lem-c1-holonomy-is-a-well-defined-representation-into-transverse-germs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-c1-ode-flow-on-common-tube</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-c1-planar-fields-on-a-closed-disk-extend-to-a-neighborhood</loc>
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<loc>https://alphabetamath.cc/item/lem-c1-planar-hyperbolic-gradient-has-local-stable-and-unstable-curves</loc>
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<loc>https://alphabetamath.cc/item/lem-c2-density-with-bounded-hessian-is-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-c2-first-integral-period-annuli-have-c2-products</loc>
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<loc>https://alphabetamath.cc/item/lem-c2-inverses-and-scalar-return-roots</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-c2-leaf-intersection-with-a-box-transversal-is-countable</loc>
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<loc>https://alphabetamath.cc/item/lem-c2-saddle-function-has-c1-morse-coordinates</loc>
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<loc>https://alphabetamath.cc/item/lem-c2-spherical-leaf-stability-on-a-closed-manifold-needs-only-countable-choice</loc>
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<loc>https://alphabetamath.cc/item/lem-caccioppoli-inequality-for-truncated-subsolutions</loc>
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<loc>https://alphabetamath.cc/item/lem-calderon-reproducing-formula-for-the-hardy-decomposition</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-cartier-to-weil-injective-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cartier-to-weil-respects-principal-and-addition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-casimir-comparison-on-a-weight-vector</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-casimir-constrained-verma-character-expansion</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-casimir-element-of-a-rational-representation-is-an-endomorphism-of-g-modules</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-casimir-norm-excludes-nonzero-denominator-corrections</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-casimir-separates-comparable-dominant-primitive-weights</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-away-from-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-complete-and-archimedean-imply-mct</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-difference-quotient-exceptional-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-estimates-for-an-analytic-semigroup-give-generator-power-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-estimates-on-concentric-subdiscs</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-estimates-propagate-to-holomorphic-hulls</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-filter-with-a-cluster-point-converges</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-in-probability-sequences-have-a-measurable-limit</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-mean-value-quotient-form</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-product-of-absolutely-convergent-complex-series</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-product-of-real-power-series</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-reals-archimedean</loc>
<lastmod>2026-07-25T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-riemann-sums-give-rational-approximation</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-schwarz-for-finite-random-variables</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-sequence-bounded</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-transform-of-a-cycle-is-holomorphic-off-the-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-transform-with-smooth-parameters</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cauchy-with-convergent-subsequence</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cech-differential-squares-zero</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cech-h0-global-sections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cech-hypercohomology-computes-ext-of-the-cotangent-complex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cech-vanishing-on-a-cofinal-basis-implies-acyclicity</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ceiling-and-least-positive-integer-threshold</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cell-attachment-below-the-first-nonzero-homotopy-degree-preserves-the-required-connectivity</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cell-form-is-associative-and-its-radical-is-a-submodule</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cell-slides-and-stabilizations-realize-elementary-group-ring-matrices</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cell-trading-reduces-a-finite-relative-equivalence-to-two-high-cell-degrees</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cellular-attachments-with-finite-boundary-support-form-a-cw-complex</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cellular-boundary-coefficient-equals-the-morse-trajectory-count</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cellular-homology-of-the-one-polygon-surface-model</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cellular-mapping-cylinders-and-relative-cylinders-are-cw-complexes</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cellularity-is-well-defined</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cellwise-particle-quadrature-oscillation-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-center-frontier-selection-and-cancellation-search-has-a-finite-rank</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-center-is-normal</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-centered-chord-and-unequal-step-tangent-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-centered-difference-dirichlet-inverse-maxnorm</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-centered-difference-dirichlet-truncation-residual</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-centered-integrable-iid-random-walk-is-unbounded-above</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-centering-by-translation-and-modulation-preserves-the-variance-product</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-central-action-on-a-cyclic-highest-weight-module-is-scalar</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-actions-on-nilradical-cohomology-factor-through-harish-chandra</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-central-binomial-coefficient-bounds</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-binomial-coefficient-prime-valuation</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-character-cuts-of-a-typed-module-are-typed</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-diagonal-disintegration-has-factor-fibers</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-difference-has-fourth-order-remainder-under-bounded-fifth-derivative</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-elements-have-weight-zero</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-extension-linearizes-a-projective-representation</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-ga-subgroup-of-smooth-connected-unipotent-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-idempotent-decompositions-of-one-are-unique</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-kernel-descent-for-poincare-inductions</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-p-subgroups-lie-in-every-block-defect-group</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-product-absorption-of-the-exponent-p-squared-factor-for-odd-p</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-central-series-commutator-criterion</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-central-spectral-models-transport-and-intertwiners-disintegrate</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-centralizer-of-a-normal-subgroup-is-normal</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-centralizers-and-normalizers-are-subgroups</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-centre-central-characters-and-descent-along-central-isogenies</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-certified-exponential-step-action-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-certified-linear-solve-jacobian-and-pullback-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-certified-syntax-coding-operations-are-primitive-recursive</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cesaro-limit-of-truncated-means</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cg-affine-alcove-separation-and-facet-types</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-affine-diagram-enumeration</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cg-affine-generic-gallery-paths-and-disk-moves</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-affine-point-stabilizers-and-vertex-residues</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-affine-reflection-identities-and-local-finiteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-affine-slice-simplex-and-wall-reflections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-affine-type-crystallographic-alcove-diagrams</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-alexandrov-comparison-triangle-gluing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-artin-presentation-universal-properties-and-coxeter-surjection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-basic-degrees-independent-and-coinvariant-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-bounded-weak-order-join-construction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-bowditch-quantitative-short-loop-control</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-bruhat-chain-refinement-and-gradedness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-bruhat-increasing-chain-and-local-descent-replacement</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-bruhat-right-exchange-and-augmentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-canonical-cell-exposed-faces-and-normal-cones</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-classical-type-poincare-products</loc>
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<loc>https://alphabetamath.cc/item/lem-cg-comparison-product-perturbation-and-degenerate-limits</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-complete-cat-zero-circumcenters-and-convex-fixed-sets</loc>
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<loc>https://alphabetamath.cc/item/lem-cg-complexification-satisfies-reflection-invariant-hypotheses</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-convex-chains-consecutive-in-a-linear-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-convex-root-subcomplex-intersection-and-purity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cg-coxeter-elements-are-conjugate-via-source-sink-moves</loc>
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<url>
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<loc>https://alphabetamath.cc/item/lem-characteristic-strip-jacobian-at-the-initial-surface</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-characteristic-subgroup-of-a-normal-subgroup-is-normal</loc>
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<loc>https://alphabetamath.cc/item/lem-characteristic-subgroups-are-normal-and-characteristic-is-transitive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-characteristic-zero-scalar-extension-preserves-geometric-local-system-semisimplicity</loc>
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<loc>https://alphabetamath.cc/item/lem-characters-of-continuous-functions-are-evaluations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-characters-of-l1-of-an-abelian-lch-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-characters-on-a-commutative-c-star-algebra-preserve-star</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-charged-core-height-matrices-have-content-preserving-descent-and-minimal-switch-connectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-charpit-contact-compatibility-is-preserved</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-charpit-flow-preserves-the-pde-constraint</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-charpit-momentum-equation-from-differentiating-hamilton-jacobi</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chart-bump-at-a-point-with-prescribed-support</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chart-independence-of-c-r-smoothness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chart-supported-coefficients-have-well-defined-riemann-integrable-half-space-extensions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chebyshev-cardinal-polynomial-formulas</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chebyshev-constant-is-submultiplicative-root-limit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chebyshev-degree-leading-coefficients-and-extreme-values</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-chebyshev-functions-prime-power-comparison</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-chebyshev-lobatto-mode-aliasing</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-chebyshev-polynomials-orthogonal-in-arcsine-weight</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-chebyshev-psi-prime-power-expansion</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-chebyshev-rkc-bounds-and-endpoint-derivatives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cheeger-indicator-and-positive-part-energy</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cheeger-sweep-and-layer-cake</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cherednik-nilpotent-induced-connections-have-moderate-growth</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chern-character-and-todd-class-multiplicativity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chern-character-induces-the-rational-isomorphism-on-ahss-e-two</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-chern-class-naturality-additivity-and-splitting</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chernoff-bound-for-bernoulli-trials</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chernoff-bound-for-independent-bernoulli-trials</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chevalley-basis-and-real-structure-constants</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chinese-remainder-two-moduli</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chiral-dirac-is-fredholm-with-kernel-and-cokernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-choice-free-smooth-inverse-function-theorem-in-euclidean-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-choice-splits-essential-surjectivity-over-a-small-target</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chow-groups-of-projective-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chow-lemma-proper-noetherian</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chow-localization-and-vector-bundle-homotopy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-chow-ring-naturality-and-projection-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-christoffel-sampling-law-and-gram-mean</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cichon-cross-and-bounding-inequalities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cir-lamperti-transform-and-positive-root</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-circle-and-path-loop-models-for-eilenberg-maclane-induction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-circle-loops-of-equal-degree-are-path-homotopic</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-circle-maximal-weak-one-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-circle-neighbourhood-arc-contains-no-nontrivial-subgroup</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-circuit-satisfaction-is-linear-quadratic-consistency</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-circular-dilatation-quasisymmetry-and-analytic-quasiconformality</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-circumcision-meridian-pair-preserves-relative-three-manifold</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-clairaut-for-c2-potentials-by-rectangular-differences</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-clarkson-inequalities-for-real-and-complex-lp</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-affine-algebraic-set-finite-irreducible-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-affine-algebraic-set-product-coordinate-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-affine-closed-points-are-maximal-ideals</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-affine-morphisms-equal-on-dense-open</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-affine-variety-nonempty-opens-dense</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-derivatives-are-weak-derivatives</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-dominant-map-pulls-back-function-fields</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-dominant-rational-maps-compose</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-integral-affine-charts-have-canonical-common-function-field</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-irreducible-space-open-intersection-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-morphism-inverse-image-of-closed-is-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-morphisms-glue-on-open-cover</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-open-source-morphisms-equal-on-dense-open</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-parabolic-solution-at-time-zero-needs-the-compatibility-ax-plus-f-zero</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-point-cut-out-by-dimension-many-functions</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-points-inside-affine-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-principal-opens-form-affine-basis</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-rational-map-equivalence-transitive</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-regular-functions-locality-and-gluing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-regular-functions-on-open-embed-in-function-field</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-rk4-map-is-lipschitz-on-a-controlled-tube</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-solutions-satisfy-the-weak-formulation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-subharmonic-mean-value-inequalities</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-variety-noetherian-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-zero-locus-ideal-radical-invariance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-classical-zero-locus-vanishing-ideal-galois-connection</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-clean-block-sparse-gaussian-covariance-minimax-lower-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-clean-dense-gaussian-covariance-minimax-lower-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-clifford-centrioles-and-geodesic-tangent-condition</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-clifford-even-subalgebra-signature-identification</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-clifford-exterior-wedge-contraction-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-clifford-polarized-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-clifford-quotient-factorization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-clifford-quotient-has-canonical-z2-grading</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-clifford-zero-dimensional-algebra-is-base-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-clock-cutoffs-and-unions-preserve-nondeterministic-time-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-clocked-machine-construction</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-clopen-subset-gives-idempotent-decomposition</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-connected-one-manifolds-are-circles</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-form-and-size-bounds-for-the-dirichlet-kernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-gluing-of-two-projective-three-spaces-is-proper</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-ideal-quotient-is-a-banach-algebra</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-immersion-cohomology-pushforward</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-immersion-local-on-target</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-immersion-projection-formula-invertible</loc>
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<loc>https://alphabetamath.cc/item/lem-closed-immersion-proper</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-immersion-pushout-schemes</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-interval-compactness-from-completeness</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-l-two-subspaces-have-orthogonal-projections</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-lkb-basis-surfaces-have-the-three-required-topological-types-and-factors</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-null-fence-word-has-an-essential-lower-endpoint</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-open-and-cubic-covers-give-the-same-lebesgue-outer-measure</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-oriented-pid-manifolds-have-finitely-generated-homology</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-oriented-smooth-one-and-two-manifolds-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-payoffs-admit-unraveling-covers</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-closed-range-iff-quotient-estimate</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closed-subgroup-quotient-averaging-and-compact-lifts</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closed-subgroup-scheme-valued-point-criterion</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closed-subset-of-a-compact-space-is-compact</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closed-subsets-of-baire-space-are-tree-bodies</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closed-subspace-of-a-banach-space-is-banach</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closed-subspace-with-trivial-orthogonal-complement-fills-l-two</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closed-witness-codings-and-measured-projections</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closure-depends-only-on-the-braid-isotopy-class</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closure-in-an-ultrafilter-algebra-topology</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closure-of-a-point-is-its-vanishing-set</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-closure-points-on-regular-cardinals</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cloud-consistency-forces-near-constant-labels</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cloud-plurality-rounding</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-club-continuity-produces-strongly-increasing-subsequences</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-club-tree-coding-antichain-reflection</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cm-equidimensional-fibre-dimension-bound-regular-sequence</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cm-local-codimension-and-regular-quotient-ext-concentration</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cm-local-regular-sequence-dimension-drop</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cm-projective-curve-canonical-positive-twist-vanishing-generation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cm-quotient-of-regular-local-ring-ext-concentration</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-bird-free-complete-nonedge-pairs-are-pure-to-induced-e-graphs</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-bird-free-e-mixed-vertices-are-pure-on-terminal-edges</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-bird-free-edge-plus-isolate-witness-obstruction</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-bird-free-external-purity-survives-e-overlap-quotients</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-bird-free-path-plus-isolate-witness-obstruction</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-bird-free-separated-anticonnected-blocks-forbid-forward-mixing</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-e-free-complete-nonedge-pairs-are-pure-to-induced-h-five-graphs</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-e-free-external-purity-survives-h-five-overlap-quotients</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-co-e-free-mixed-vertices-on-an-induced-path-avoid-two-nonneighbours-and-three-neighbours</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coarse-triangle-minsize-is-bounded-by-square-root-area</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cobounded-proper-geodesic-actions-produce-finite-generating-sets</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cocompact-free-affine-plane-action-is-a-lattice</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coconnected-comodules-have-fixed-vectors</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cocountable-ultrafilter-on-uncountable-set</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cocycle-central-extension-is-a-group</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coderivation-extension-from-corestrictions</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-codifferent-is-a-fractional-ideal</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-codimension-one-maximal-order-components</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-comparison-on-finite-cw-pairs</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-field-maps-isomorphically-to-residue-field</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-field-purely-inseparable-complete-step</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-field-separable-adjunction-step</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-field-transcendental-adjunction-step</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-ideal-disjoint-centres</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-ideal-is-equivalent</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-ideal-restriction-support</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-ideal-under-smooth-morphisms</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coefficient-majorisation-is-preserved-by-sums-products-composition-and-differentiation</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coercive-form-operator-is-bounded-below</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coercive-sectorial-form-resolvents-define-a-closed-m-sectorial-operator</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coercivity-makes-a-small-form-step-a-contraction</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coercivity-makes-every-finite-level-minimising-sequence-bounded</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coercivity-of-the-adjoint-makes-the-form-operator-range-dense</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coercivity-of-the-principal-dirichlet-form</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coextension-of-scalars-carries-a-module-structure</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cofiber-of-a-based-cofibration-is-equivalent-to-the-quotient</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cofinal-aleph-product-cardinality</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cofinality-is-well-defined</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohen-macaulay-parameter-first-element-regular</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohen-macaulay-parameter-sequence-induction</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohen-presentation-surjective-by-completeness</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohen-presentation-surjective-mod-maximal-square</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coherent-devissage-one-generic-generator</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coherent-sheaf-finite-twisted-locally-free-resolution-projective-space</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coherent-shift-functors-and-transformations-form-hom-categories</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohomologous-two-cocycles-give-equivalent-extensions</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohomology-base-change-finite-free-criterion</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohomology-functoriality-sheaf-and-space</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohomology-of-a-finite-cw-complex-vanishes-above-its-dimension</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohomology-of-hypersurface-twists</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cohomology-ring-of-infinite-complex-projective-space</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coinduced-modules-are-injective</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collapse-after-regular-preimage-is-homotopic-to-the-original-map</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collapse-at-one-level-propagates</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collapse-fixes-transitive-parts-and-orders-ordinals</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collapse-map-is-continuous-and-smooth-away-from-the-basepoint</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collapse-map-is-independent-of-tubular-neighbourhood-and-radius-up-to-based-homotopy</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collapse-of-an-embedded-manifold-classifies-through-the-universal-thom-prespectrum</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collar-gluing-and-corner-smoothing-give-transitivity</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collared-gluing-has-relative-excision-and-evaluation-maps</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collectionwise-normal-moore-spaces-are-screenable</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collocation-polynomial-scaled-derivatives</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-collocation-quadrature-matrix-well-defined</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-colored-fr-surgery-and-coupon-cancellation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-colour-focussing-for-arithmetic-progressions</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-colouring-embeds-a-graph-in-a-balanced-blowup</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-column-antisymmetrizer-detects-dominance</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-column-collision-causes-antisymmetrizer-cancellation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-column-stochastic-l1-nonexpansive</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-common-domain-commutator-integrates-to-weyl-relations</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-common-law-forces-two-point-tail-loss-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-common-plaque-lifted-caps-admit-nested-source-disk-inclusions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-common-submeasure-and-bounded-radon-nikodym-density</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-common-submeasure-density-is-pointwise-minimum</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-common-support-likelihood-ratio-is-measurable</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-communication-is-an-equivalence-relation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-commutative-division-ring-is-a-field</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-commutator-identities-in-a-group-of-class-two</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-commutator-subgroup-is-normal</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-commuting-endomorphisms-preserve-eigenspaces</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-commuting-independent-vector-fields-give-a-coordinate-system</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-commuting-p-and-p-prime-parts-of-a-finite-group-element</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-c1-foliation-leaf-is-an-embedded-hypersurface</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-c1-leaf-has-finitely-generated-fundamental-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-c2-surfaces-admit-finite-cellulations-relative-to-a-finite-embedded-graph</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-closed-balls-in-a-locally-compact-metric-space</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-controlled-whitney-spaces-admit-commuting-radial-collars</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-convolution-operators-are-hilbert-schmidt</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-convolution-operators-commute-with-right-translations</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-convolution-operators-decompose-into-finite-dimensional-invariant-subspaces</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-curved-hypersurface-finite-graph-cover</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-cw-images-have-finite-cell-support-without-choice</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-distribution-convolution-preserves-schwartz-and-tempered-spaces</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-fibre-numerable-bundle-totals-are-paracompact-hausdorff-of-cw-type</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-generation-preserves-the-cylinder-and-closed-pushouts</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-gram-operator-is-positive-and-has-kernel</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-group-matrix-coefficients-separate-points</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-hausdorff-targets-embed-in-unit-cubes-under-dependent-choice</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-implies-closed-and-bounded-r</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-intertwiners-produce-finite-dimensional-invariant-subspaces</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-kernel-derivative-moment-identities</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-leaf-control-and-compact-ambientness-give-the-required-closedness</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-lie-groups-admit-central-continuous-approximate-identities</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-local-homeomorphism-surjective-with-finite-fibres</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-metric-space-has-a-countable-dense-subset</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-morse-critical-points-have-uniform-hessian-gaps</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-null-iff-content-zero-in-rn</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-open-and-pointwise-topologies-agree-on-an-equicontinuous-family</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-open-character-group-operations-are-continuous</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-open-subgroups-in-totally-disconnected-lca-groups</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-open-topology-on-a-discrete-domain-is-pointwise</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-oriented-boundary-manifolds-have-finite-dimensional-cohomology</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-polar-sets-and-subharmonic-minus-infinity-loci</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-self-adjoint-residual-controls-invariant-subspace-gap</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-semialgebraic-families-admit-compatible-finite-triangulations</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-set-has-a-jordan-neighborhood-inside-an-open-set</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-set-in-open-neighborhood-has-uniform-radius</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-smooth-manifolds-have-finite-cw-models-under-countable-choice</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-spectral-multiplier-is-well-defined</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-stable-leaves-form-an-open-saturated-set</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-subsets-of-a-bernstein-set-are-countable</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-subsets-of-an-arbitrary-simplicial-realization-meet-finitely-many-open-simplices</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-support-calculus-of-extension-by-zero-and-closed-pushforward</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-support-continuous-primitive-representation</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-support-gives-an-entire-fourier-laplace-transform</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-support-zero-extension-in-wkp</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-surface-admits-a-finite-triangulation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-test-exponential-law-and-products-of-quotients</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-transverse-complementary-intersections-are-finite</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-uniform-lan-posterior-approximation</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-uniform-spaces-are-complete</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-uniform-spaces-are-totally-bounded</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compact-wavelet-projection-kernel-and-commutator</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactified-unstable-manifolds-give-a-cw-decomposition</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactly-generated-lca-group-with-no-open-subgroup-of-infinite-index-splits-as-compact-times-euclidean</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactly-supported-continuous-functions-are-translation-continuous-in-l-p</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactly-supported-covariant-generators-are-dense</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactly-supported-distributions-extend-to-smooth-functions</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactly-supported-h1-belongs-to-h-zero</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactly-supported-kernels-admit-commuting-radon-integrals</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactly-supported-riemann-integral-is-well-defined</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactly-supported-top-cohomology-propagates-across-overlapping-oriented-coordinate-balls</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactness-allows-a-cutoff-to-produce-a-compactly-supported-time-dependent-field</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactness-is-intrinsic</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compactness-of-a-subspace-is-ambient</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-companion-powers-bounded-under-root-condition</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-comparison-map-from-an-exact-complex-into-an-injective-resolution</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-comparison-maps-between-homology-theories-extend-over-one-skeleton-stage</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compatible-arbitrary-pi-fence-reduction</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compatible-connections-exist-on-smooth-hermitian-and-euclidean-bundles</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compatible-local-orientation-classes-exist-over-compact-subsets</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compatible-refinement-for-tuple-indexed-coverings</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compatible-signs-exist-on-the-bruhat-graph</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compatible-smooth-simplex-faces-have-a-neighbourhood-extension</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compatible-tuples-form-a-subgroup</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compatible-well-founded-recursion-attempts</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-compensated-band-kinks-decompose-into-ordinary-markov-moves</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-competing-exponential-race-for-reaction-channels</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-complement-commutes-with-induced-subgraphs</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-complement-swaps-cliques-and-stable-sets</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-complementation-preserves-disjoint-regular-pairs</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-complete-coderivations-form-a-filtered-differential-graded-lie-algebra</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-complete-connected-scheme-to-affine-scheme-morphism-is-constant</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-complete-connection-of-perfect-graphs-is-perfect</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-complete-henkin-theory-truth-rules</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-homogeneous-expansion-in-power-sums</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-intersection-hilbert-series-two-plane-forms</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-linear-blowup-reductions-compose</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-local-finite-etale-algebra-lifting</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-local-hecke-modular-systems-and-idempotent-lifting</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-normal-surface-regular-resolution-converts-to-normalized-point-blowups</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-ordered-field-is-archimedean</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-reducibility-reduces-to-codimension-one-simple-submodules</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-regular-surface-degree-p-extension-has-bounded-h1</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-regularity-is-hereditary</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-remetrisation</loc>
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<loc>https://alphabetamath.cc/item/lem-complete-subspace-is-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-completed-fourfold-graded-cohomology-ring-laws-and-naturality</loc>
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<loc>https://alphabetamath.cc/item/lem-completed-measure-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-completely-regular-topologies-come-from-continuous-pseudometrics</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-completion-automorphisms-for-tangent-directions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-completion-domain-is-a-sigma-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-completion-operations-are-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-completion-preserves-embedding-dimension</loc>
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<loc>https://alphabetamath.cc/item/lem-completion-preserves-regular-sequences</loc>
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<loc>https://alphabetamath.cc/item/lem-completion-reflects-depth</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-affine-group-comodule-local-finiteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-algebraic-boundary-points-admit-normalized-curve-arcs</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-algebraic-groups-are-smooth</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-algebraic-morphisms-admit-compatible-finite-smooth-stratifications</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-algebraic-stratifications-have-finite-conical-cochain-models</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-circle-measures-have-finite-total-variation-under-countable-choice</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-conjugation-and-modulus-laws</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-coordinate-l1-is-a-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-exponential-series-converges-everywhere</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-flag-splitting-over-smooth-bases-with-injective-real-pullback</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-gaussian-interference-entropy-estimates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-haar-l1-and-l2-are-complete-and-cc-dense</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-hermitian-eigenvalue-perturbation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-hermitian-eigenvalues-lipschitz</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-hermitian-realification-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-hermitian-toeplitz-reflection-recursion</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-hessian-domination-at-a-common-minimum</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-infinity-matrix-norm-submultiplicative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-infinity-neumann-inverse-norm-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-integration-by-parts-on-intervals-and-decaying-lines</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-l-one-functionals-on-finite-measure-spaces-have-bounded-densities</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-linear-real-differential-criterion</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-lp-completeness-density-and-inner-product</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-lp-duality-from-real-lp-duality</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-lq-norm-from-finite-simple-dual-tests</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-modulus-of-real-embedding-equals-real-absolute-value</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-multinomial-theorem</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-norm-realification-is-a-real-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-normed-subspace-realifies-to-real-normed-subspace</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-orientation-of-underlying-real-bundles</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-oriented-diagonal-thom-class-realizes-the-six-functor-exchange-on-supports</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-polynomial-growth-and-minimum-modulus</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-power-series-reexpansion-double-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-projector-tangent-commutator-curves</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-scalar-gaussian-maximum-differential-entropy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-scaled-householder-step-termination-and-status</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-specht-modules-are-self-dual</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complex-stratified-morse-data-have-tangential-normal-product-and-link-description</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-tautological-euler-class-restricts-to-the-projective-fiber-generator</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-time-heat-kernel-is-lone-differentiable-in-its-parameter</loc>
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<loc>https://alphabetamath.cc/item/lem-complex-translation-and-approximate-identity-interfaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-complexified-tautological-line-resolves-real-projective-k-theory-extensions</loc>
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<loc>https://alphabetamath.cc/item/lem-components-of-the-frame-bundle-of-a-connected-manifold</loc>
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<loc>https://alphabetamath.cc/item/lem-composite-midpoint-panel-error-kernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-composites-of-coarse-lipschitz-maps-and-of-quasi-isometric-embeddings</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-composition-of-homotopy-classes-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-composition-of-quotient-integrals-for-subgroup-chains</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-composition-of-roofs-is-well-defined</loc>
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<loc>https://alphabetamath.cc/item/lem-composition-operator-norm-inequality</loc>
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<loc>https://alphabetamath.cc/item/lem-compositions-with-a-compact-operator-are-compact</loc>
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<loc>https://alphabetamath.cc/item/lem-compressible-ideal-gas-entropy-pair-and-variables</loc>
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<loc>https://alphabetamath.cc/item/lem-computed-augmented-tikhonov-solve-residual-and-output-error</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-conditional-expectation-constructs-the-inner-code-in-polynomial-time</loc>
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<loc>https://alphabetamath.cc/item/lem-conditional-independence-splicing-over-a-standard-borel-variable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conditional-intensity-interevent-survival-and-density</loc>
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<loc>https://alphabetamath.cc/item/lem-conditional-kernel-tail-and-atom-evaluations-are-measurable</loc>
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<loc>https://alphabetamath.cc/item/lem-conditional-subgaussian-exponential-process</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conditional-treatment-indicator-factorization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conditional-variance-is-well-defined-and-has-the-second-moment-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conditioning-a-known-state-and-independent-noise</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conditioning-a-known-variable-and-an-independent-variable</loc>
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<loc>https://alphabetamath.cc/item/lem-conductor-ideal-common-ideal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cone-sites-admit-stable-polynomial-norming-stencils</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cone-triangles-satisfy-the-octahedral-axiom</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cone-triangles-satisfy-tr-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cone-triangles-satisfy-tr-three</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cone-triangles-satisfy-tr-two-with-the-declared-rotation-sign</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-configuration-loops-admit-smooth-separated-point-motion-representatives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conformal-removability-is-quasiconformally-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conforming-energy-projection-is-best-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conforming-galerkin-ritz-matrix-error-is-quadratic-in-gap</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-congruence-is-an-equivalence-relation</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-congruence-respects-integer-arithmetic</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugacy-class-splitting-over-an-index-two-normal-subgroup</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugacy-of-cyclically-britton-reduced-hnn-words-reduces-to-associated-subgroup-conjugacy</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugate-dirichlet-kernel-and-principal-value-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugate-specht-sign-duality-over-fields</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugate-transpose-kernels-give-adjoints</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugates-of-an-average-of-roots-of-unity-are-averages-of-roots-of-unity</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugating-a-cycle-relabels-its-entries</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugation-by-delta-reverses-artin-generators</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugation-orbits-of-finite-rank-operators-are-norm-continuous</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conjugation-reverses-dominance</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-connected-cover-of-punctured-disc-for-irreducible-plane-curve</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-connected-covers-of-smooth-manifolds-have-a-canonical-smooth-structure</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-connected-graded-bialgebra-has-a-recursive-antipode</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-connected-groups-of-rank-zero-are-unipotent</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-connected-spherical-complement-implies-null-homology</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-connected-subsets-and-separated-sets</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-connected-sum-of-oriented-homotopy-spheres-is-a-homotopy-sphere</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-conservative-fv-face-fluxes-converge-in-l1loc</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-consistency-of-brownian-finite-dimensional-laws</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-consistent-sentence-decision</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constant-rank-source-coordinate-map-is-locally-invertible</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constant-rank-tail-components-ignore-kernel-coordinates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-constant-scale-restricted-generalized-niceness-yields-an-x-scale-restricted-subgraph-a-polynomial-clique-or-stable-set-or-a-blockade</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constant-scale-restricted-property-star-yields-a-restricted-subgraph-a-polynomial-clique-or-stable-set-or-two-blockade-alternatives</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constant-sheaf-is-the-sheaf-of-locally-constant-functions</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constant-sheaf-on-irreducible-space-is-flasque</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constant-vector-is-a-top-eigenvector</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constituent-multiplicities-under-a-semisimple-endomorphism-algebra</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constraint-expander-overlay</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constructible-boolean-operations</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-constructible-dense-contains-open</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-constructible-stable-generalisation-open</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-contact-equivalence-is-chart-independent-and-an-equivalence-relation</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-content-divisibility-characterisation</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-content-zero-implies-null</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-contiguous-simplicial-maps-have-homotopic-realizations</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuation-energy-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuation-map-of-constant-data-is-the-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuation-solutions-have-critical-limits</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continued-fraction-complete-quotient-formula</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-continued-fraction-convergent-recurrence</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continued-fraction-determinant-identity</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continued-fraction-error-bound</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-continuity-criteria-for-unitary-representations</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-continuity-is-local-and-pastes</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-continuous-adapted-process-at-bounded-stopping-time</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-characters-of-the-real-line-are-exponentials</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-characters-separate-points-of-an-lca-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-coagulation-fragmentation-local-positive-wellposedness</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-coagulation-fragmentation-vector-field-locally-lipschitz</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-coagulation-operator-weighted-total-variation-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-compactly-supported-functions-differentiate-by-ball-averages</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-convolution-operators-are-hilbert-schmidt-and-compact</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-finite-dimensional-representations-of-a-product-of-finite-groups-factor-through-a-finite-subproduct</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-finite-dimensional-representations-of-profinite-groups-factor-through-finite-quotients</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-finite-variation-martingale-is-zero</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-fractional-integral-is-holder</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-fragmentation-operator-weighted-total-variation-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-function-holomorphic-off-a-point-is-holomorphic</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-functional-calculus-produces-a-regular-pvm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-functions-determine-borel-probabilities-on-compact-metric-spaces</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-functions-on-a-compact-metric-space-have-a-countable-dense-family</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-functions-on-omega-one-plus-one-are-eventually-constant</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-functions-riemann-integrable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-gauge-of-an-open-convex-zero-neighborhood</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-images-of-universal-nets-are-universal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-kernel-integral-operator-is-compact-on-c</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-one-handle-surgery-replacement-gives-relative-kirby-moves</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-path-space-is-polish</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-periodic-functions-are-dense-in-l-p-of-finite-tori</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-predictable-bracket-uniqueness</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuous-riemann-lebesgue-agreement</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-continuum-sized-almost-disjoint-family-on-omega</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-contour-definition-of-an-analytic-semigroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-contour-integral-commutes-with-bounded-linear-maps</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-contour-subdivision-into-discs-missing-a-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-contracted-curve-count-decreases-under-a-point-blowup-factorization</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-contractibility-implies-trivial-fundamental-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-contractible-cosimplicial-evaluation-computes-derived-colimit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-contraction-is-independent-of-the-basis-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-contraction-recovers-primary-component-after-localising-away-from-radical</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-contraction-torsion-is-independent-of-the-contracting-homotopy</loc>
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<loc>https://alphabetamath.cc/item/lem-controlled-nested-horn-construction-embeds-a-closed-three-ball</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-controlled-stratified-submersions-have-continuous-local-trivializations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-controlled-transform-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convergence-in-the-pointwise-topology</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convergent-filters-are-cauchy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convergent-implies-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convergent-implies-cauchy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convergent-power-series-termwise-differentiation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-entropy-condition-for-a-shock-is-the-flux-chord-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-function-bound-on-an-interior-cube</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-functions-have-countable-supporting-line-representations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-generator-boundary-limits-exist</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-mixture-of-probability-laws</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-norm-lower-semicontinuous-functionals-are-weakly-lower-semicontinuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-perspective-is-subadditive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-set-and-closure-have-same-interior-and-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-smooth-component-gradient-cocoercivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convex-windows-admit-rectangle-approximations-and-are-folner</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convolution-is-independent-of-the-chosen-borel-representatives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convolution-of-distributions-is-well-defined-under-the-support-hypothesis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-convolution-preserves-cc-and-is-associative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cook-levin-can-be-made-parsimonious</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cook-levin-formula-is-satisfiable-iff-acceptance-occurs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cook-levin-map-is-polynomial-time</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-ball-classes-identify-local-homology-stalks</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-balls-form-a-basis-of-a-topological-manifold</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-block-smoothness-descent-model</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-change-congruence-for-the-critical-hessian</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-derivations-are-well-defined-derivations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-direction-form-of-the-slobodeckij-seminorm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-lasso-soft-threshold-update</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-maps-and-permutations-are-measurable-on-finite-products</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-ring-of-affine-group-scheme-is-a-hopf-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-scalings-and-permutations-scale-the-unit-cube-by-the-absolute-determinant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-separable-penalty-is-proper-closed-convex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinate-telescoping-on-a-euclidean-ball</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinatewise-addition-and-negation-make-zp-a-topological-abelian-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coordinatewise-minimum-implies-composite-stationarity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-copower-presentation-construction-is-left-adjoint-to-generator-hom</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-cyclic-pid-quotients-split</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-discriminant-compositum-integral-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-divides-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-factor-bezout-lift</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-kernel-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-plane-forms-form-a-homogeneous-regular-sequence</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-polynomial-factorization-lifts-etale-locally</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-coprime-primitive-two-square-products-remain-primitive</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-coproduct-preserves-the-positive-and-negative-quantum-serre-ideals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-core-is-largest-normal-subgroup-contained</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-corestriction-after-bar-transfer-is-index-multiplication-on-homology</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-corestriction-is-independent-of-the-coset-representatives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-corner-adapted-strong-approximations-remain-in-the-same-orthant</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-corson-ordered-urysohn-automorphism-group-is-extremely-amenable</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-corson-rational-metric-not-metacompact</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-corson-stone-obstruction-is-ordinal-boundable</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-coset-equinumerous-with-subgroup</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-coset-membership-and-equality</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-coset-partition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cost-constrained-dmc-achievability</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cost-constrained-dmc-information-capacity-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cost-constrained-dmc-mutual-information-under-average-cost</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cost-pruned-random-code</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cotangent-complex-h0-and-polynomial-case</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cotangent-complex-resolution-independence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cotangent-complex-truncation-and-smooth-case</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cotangent-coordinate-changes-use-the-inverse-transpose-jacobian</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cotangent-localization-at-rational-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cotlar-inequality-for-maximal-truncations</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-boolean-algebra-prime-ideal-compactness-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-borel-hierarchy-exhaustion-and-pullbacks</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-boundary-coordinate-cover-has-locally-finite-shrinking</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-boundary-null-partitions-of-a-separable-metric-space</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-choice-sequence-and-product-formulations-are-equivalent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-compactly-supported-tests-determine-euclidean-weak-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-discrete-space-is-standard-borel</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-generators-yield-countable-set-algebras</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-henkin-syntax-coding</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-iff-surjection-from-n</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-iid-baseb-digits-from-one-uniform</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-intersection-of-completely-metrizable-subspaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-intersections-of-club-subsets-of-omega-one-are-club</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-local-bases-can-be-open-and-decreasing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-mode-car-fock-representation-is-irreducible</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-mode-car-particle-hole-automorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-normal-tree-cofinal-branch</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-norming-family-determines-borel-laws</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-product-cylinder-premeasure-is-countably-additive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-sequence-groups-and-tail-filtrations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-sets-are-null</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-tower-completion-obstruction-exact-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-tower-six-term-limit-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-tree-antichain-sealing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-tree-ranks-and-rank-monotonicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-uniform-base-normalisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-uniformly-dense-tests-on-a-compact-metric-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countable-union-of-compact-content-zero-sets-is-null-in-zf</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countably-compact-paracompact-hausdorff-is-compact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countably-generated-kernel-lebesgue-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-countably-generated-kernel-stable-sub-sigma-field</loc>
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<loc>https://alphabetamath.cc/item/lem-counter-based-keyed-stream-no-reuse</loc>
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<loc>https://alphabetamath.cc/item/lem-counting-circuits-of-bounded-size</loc>
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<loc>https://alphabetamath.cc/item/lem-counting-elements-of-order-dividing-two-in-a-central-product-of-extraspecial-two-groups</loc>
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<loc>https://alphabetamath.cc/item/lem-counting-measure-on-a-discrete-group</loc>
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<loc>https://alphabetamath.cc/item/lem-covariance-median-pilot-exact-block-budget</loc>
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<loc>https://alphabetamath.cc/item/lem-covariant-derivatives-commute-up-to-curvature-in-a-two-parameter-variation</loc>
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<loc>https://alphabetamath.cc/item/lem-covering-basepoint-change-conjugates-subgroup</loc>
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<loc>https://alphabetamath.cc/item/lem-covering-homotopies-lift-by-finite-local-strips</loc>
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<loc>https://alphabetamath.cc/item/lem-cox-partial-likelihood-hessian-convergence</loc>
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<loc>https://alphabetamath.cc/item/lem-cox-score-martingale-replacement</loc>
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<loc>https://alphabetamath.cc/item/lem-cox-uniform-risk-set-convergence</loc>
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<loc>https://alphabetamath.cc/item/lem-cq-quadratic-generating-coefficient-estimate</loc>
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<loc>https://alphabetamath.cc/item/lem-created-canonical-presentations-give-a-quasi-inverse-to-the-comparison-functor</loc>
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<loc>https://alphabetamath.cc/item/lem-critical-hessian-agrees-with-the-levi-civita-hessian</loc>
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<loc>https://alphabetamath.cc/item/lem-critical-images-of-proper-local-fredholm-restrictions-are-nowhere-dense</loc>
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<loc>https://alphabetamath.cc/item/lem-critical-locus-image-dimension-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-critical-values-of-disjoint-trajectory-closures-can-be-interchanged</loc>
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<loc>https://alphabetamath.cc/item/lem-cross-ito-isometry</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cross-product-is-bilinear-alternating-and-orthogonal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-crossed-homomorphisms-with-abelian-coefficients-form-an-abelian-group</loc>
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<loc>https://alphabetamath.cc/item/lem-crouzeix-raviart-broken-gradient-is-a-norm</loc>
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<loc>https://alphabetamath.cc/item/lem-crouzeix-raviart-comparison-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-crouzeix-raviart-conforming-companion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-crouzeix-raviart-consistency-defect</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-crouzeix-raviart-continuous-poincare</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-crouzeix-raviart-face-jump-estimate</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-crouzeix-raviart-simplex-traces-and-green-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-crystal-lattice-polarizations-are-perfect-at-q-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-crystal-operators-commute-with-highest-weight-projection-modulo-q</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-crystal-tensor-product-weight-epsilon-and-phi-formulas</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ctrl1-compact-convex-control-cell-averages-form-a-recovery-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ctrl1-control-box-is-weakly-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ctrl1-lqr-adjoint-exists-uniquely</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ctrl1-lqr-adjoint-identity-and-gradient</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ctrl1-lqr-cost-is-weakly-lower-semicontinuous</loc>
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<loc>https://alphabetamath.cc/item/lem-ctrl1-lqr-transcription-is-a-convex-quadratic-program</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ctrl1-single-and-multiple-shooting-nlps-are-equivalent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ctrl1-weak-control-convergence-implies-uniform-state-convergence</loc>
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<loc>https://alphabetamath.cc/item/lem-cubical-pinch-is-additive-on-relative-homology</loc>
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<loc>https://alphabetamath.cc/item/lem-curl-is-the-antisymmetric-part-of-the-total-derivative</loc>
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<loc>https://alphabetamath.cc/item/lem-curvature-count-for-reduced-c-prime-one-sixth-diagrams</loc>
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<loc>https://alphabetamath.cc/item/lem-curvature-is-c-infinity-linear-in-all-three-vector-fields</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-curvature-of-an-extending-bott-connection-lies-in-the-transverse-differential-ideal</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-curve-different-local-support-and-index-bound</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-curvilinear-triangulation-induces-a-finite-cw-structure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cut-surface-and-boundary-jumps-of-primitives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cutoff-commutator-for-local-w-two-p-estimates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cutoff-overflow-return-error-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cw-homotopy-equivalence-inclusions-are-strong-deformation-retracts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cw-quotient-induces-relative-singular-homology-isomorphisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cw-quotients-and-collapse-of-a-contractible-subcomplex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cy-restricted-generalized-niceness-yields-three-outcomes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cycle-boundary-short-exact-sequences-for-a-free-complex-over-a-pid</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclic-coordinate-permutations-preserve-integrals-in-r3</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclic-p-fold-power-construction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclic-permutations-of-a-cyclically-britton-reduced-hnn-word-are-conjugate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclic-rotation-fixed-tuples-are-periodic</loc>
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<loc>https://alphabetamath.cc/item/lem-cyclic-shift-positivity-is-a-strict-right-minimum-of-the-partial-sums</loc>
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<loc>https://alphabetamath.cc/item/lem-cyclotomic-klr-coherent-graded-biadjunction-and-crossing-mates</loc>
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<loc>https://alphabetamath.cc/item/lem-cyclotomic-klr-induction-restriction-bimodules-have-compatible-frobenius-dual-bases</loc>
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<loc>https://alphabetamath.cc/item/lem-cyclotomic-klr-partial-frobenius-caps-satisfy-two-color-terminal-contractions</loc>
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<loc>https://alphabetamath.cc/item/lem-cyclotomic-klr-terminal-dot-caps-have-the-prefix-residue-formula</loc>
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<loc>https://alphabetamath.cc/item/lem-cyclotomic-klr-word-traces-assemble-a-perfect-symmetric-form</loc>
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<loc>https://alphabetamath.cc/item/lem-cyclotomic-normalized-functors-give-an-integrable-quantum-action</loc>
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<loc>https://alphabetamath.cc/item/lem-cyclotomic-polynomial-flag-comparison-has-the-prescribed-second-mate-inverse</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclotomic-projective-covers-and-dualities-descend-through-the-quotient</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclotomic-schur-generic-deformation-standards-have-nondegenerate-forms</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclotomic-schur-weight-gram-determinants-are-products-of-monic-semistandard-norms</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclotomic-schur-weight-gram-valuations-equal-signed-rim-hook-kostka-sums</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclotomic-semistandard-row-type-sums-give-permutation-module-bases</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-cyclotomic-semistandard-sums-give-schur-endomorphism-basis</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cyk-table-invariant</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cylinder-premeasure-from-consistent-finite-dimensional-laws-is-well-defined</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cylinder-sigma-events-depend-on-countably-many-coordinates</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cylinders-give-reflexivity-of-cobordism</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cz-bad-part-is-integrable-away-from-expanded-cubes</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-cz-good-part-has-controlled-ltwo-image</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-d-separation-ancestral-moral-separation</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-daha-a1-affine-normal-words-span</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-daha-a1-bernstein-quotients-are-laurent</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-daha-a1-macdonald-operator-preserves-orbit-sums</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-daha-a1-polynomial-operators-satisfy-presentation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-daha-a1-q-affine-automorphisms-linearly-independent</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-daha-a1-y-sum-restricts-to-macdonald-operator</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dalembert-formula-attains-both-initial-data</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dalembert-minimum-modulus-descent</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dbar-adjoint-and-dolbeault-laplacian-local-formulas</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dbar-solvability-criterion-for-a-smooth-zero-one-form</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-de-giorgi-oscillation-reduction</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-de-rham-and-singular-cohomology-respect-countable-disjoint-unions</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-de-rham-integration-respects-wedge-and-cup-in-cohomology</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-de-rham-mayer-vietoris-with-boundary-and-an-explicit-partition-lift</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-de-rham-top-integral-is-fundamental-class-evaluation</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-deck-group-of-the-holonomy-cover-is-the-holonomy-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-deck-transformations-correspond-to-normalizer-cosets</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-decomposition-numbers-are-nonnegative-integers</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-decorated-graphs-lift-through-relative-surgery-calculus</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dedekind-localisation-at-nonzero-prime-is-dvr</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dedekind-modular-law-for-subgroups</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-def-operation-is-absolute</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-definable-subsets-of-constructible-levels-are-small</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-definite-quadratic-forms-have-a-uniform-sphere-bound</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degenerate-affine-hecke-ordered-monomials-form-a-basis</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degenerate-bar-chains-form-a-contractible-subcomplex</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degenerate-cyclotomic-hecke-center-is-the-symmetric-polynomial-image</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-and-codegree-of-standard-tableaux</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-effective-divisor-nonnegative</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-four-characteristic-numbers-add-under-clutching-product</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-is-well-defined-and-independent-of-the-normalized-top-form</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-of-a-compositum-with-a-galois-extension</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-one-holomorphic-map-of-compact-riemann-surfaces-is-an-isomorphism</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-one-maps-and-quotient-action-are-well-defined</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-order-is-representative-independent</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-p-inseparable-differential-trace-extends-on-normal-surfaces</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-pullback-divisor-finite-morphism-curves</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-under-arithmetized-quantifiers</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-zero-effective-divisor-empty</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-zero-horseshoe-lift</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-degree-zero-unit-vector-field-on-a-sphere-extends-over-the-ball</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dehn-replacement-strictly-shortens-a-word</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-delay-history-space-is-banach</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-deleted-row-minors-of-a-matrix-with-zero-column-sums</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-deleted-tychonoff-plank-is-regular-and-nonnormal</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-deletion-of-one-point-is-measurable</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-deligne-splitting-of-a-mixed-hodge-structure</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-delta-is-the-lcm-of-the-artin-atoms-and-has-the-same-left-and-right-divisors</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-denotation-is-structurally-well-defined</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dense-forcing-name-translations-preserve-forcing</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-density-bridge-norm-cdfs-are-continuous-and-strict</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-density-channel-threshold-random-coding-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-density-gaussian-bridge-is-borel-on-m0w</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-density-is-well-defined</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-density-mixing-preserves-domain-but-not-projectors</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-density-nonempty-open-affine-variety</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-density-normal-laws-and-square-summable-gaussian-series</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dentable-average-ranges-give-vector-measure-densities</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dependent-choice-along-a-sequence-of-relations</loc>
<lastmod>2026-08-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dependent-choice-implies-countable-choice</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dependent-choice-riesz-separated-unit-sequence</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dependent-iff-a-vector-lies-in-the-span-of-the-others</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-acyclicity-highest-homology</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-at-a-prime-bounded-by-local-dimension</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-bounded-by-associated-prime-quotient-dimension</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-infinity-when-ideal-acts-surjectively</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-lemma-lower-bound-left</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-lemma-lower-bound-middle</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-lemma-lower-bound-right</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-localisation-inequality</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-quotient-by-regular-element</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-radical-invariance-via-ext</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-two-excludes-finite-punctured-extension</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-depth-zero-exact-free-complex-splits</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivation-finite-support-and-concatenation</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivative-algebra-and-chain-rules</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivative-estimate-proof-of-one-sided-harmonic-liouville</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivative-ideals-have-the-same-support</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivative-ideals-under-etale-morphisms</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivative-of-a-power</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivative-of-an-integral-with-moving-endpoints</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivative-of-det-i-minus-xa</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivatives-along-a-line-have-the-multinomial-expansion</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivatives-commute-with-controlled-transform</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-derivatives-of-a-multiple-test-blowup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derivatives-of-harmonic-functions-are-harmonic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derivatives-of-maximal-order-ideals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derivatives-under-field-isomorphisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-and-integrated-power-series-have-the-same-radius</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-colimit-coefficient-and-category-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-complex-power-series-has-the-same-radius</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-hall-associativity-squares</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-hall-moduli-spaces-and-convolution-are-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-hall-stabilizer-homotopy-sequence</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-series-terms-are-characteristic-ideals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-subgroup-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-derived-tensor-product-of-abelian-sheaves</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-detailed-balance-implies-invariance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-determinacy-measure-game-inner-outer-comparison</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-determinant-base-height-identity-in-r2</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-determinant-classifies-loops-in-complex-general-linear-groups</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-determinant-independence-criterion</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-determinant-rank-one-update-over-a-commutative-ring</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-determinant-trick-for-nakayama</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-determinantal-grade-necessary-exact-free-complex</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-determinantal-grade-sufficient-exact-free-complex</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-deterministic-nonhalting-configurations-have-unique-successors</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dfa-states-refine-nerode-classes</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dft-squares-to-reflection-and-has-fourth-power-identity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-adagrad-one-step-regret-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-adagrad-subproblem-well-defined</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-affine-variety-cut-out-by-coordinate-differences</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-bar-coinvariants-compute-group-homology</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-base-change-identification</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-class-expansion-gives-the-alternating-trace</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-covariance-minimax-lower-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-heat-semigroup-generator-domain</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-independence-criterion</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-is-immersion</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-multipliers-form-a-von-neumann-algebra</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-pade-remainder-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-quasi-compact-iff-quasi-separated</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-self-application-machine</loc>
<lastmod>2026-09-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-set-at-each-level</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-trace-class-operator-on-ell-two</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonal-unitary-coefficients-have-positive-type</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diagonalizable-character-antiequivalence</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dieudonne-measure-and-top-dirac-agree-on-continuous-functions</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-difference-quotient-integration-by-parts</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differences-of-overlapping-modules-are-modules</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differential-of-morphism-via-cotangent-map</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differential-of-the-moment-map-and-orbit-orthogonal-identity</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differentials-base-change</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differentials-commute-base-change-schemes</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differentials-diagonal-ideal-square</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differentials-generating-a-free-direct-summand-are-nonzerodivisors</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-differentials-localization</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differentials-polynomial-algebra-free</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differentiating-cauchy-integrals</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differentiation-of-an-integral-functional</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-differentiation-of-l-one-functions-for-a-doubling-weight</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-diffuse-finite-window-poisson-process-is-simple</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-digital-shift-marginals-and-net-preservation</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dilworth-induction-step</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dilworth-maximal-antichain-decomposition</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimension-finite-union-components</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimension-local-ring-codimension-closure</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimension-nonempty-open-subset</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimension-of-holomorphic-germ-ring</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimension-of-the-kernel-modulo-n-minus-equals-the-next-term</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimension-one-smooth-connected-group-is-ga-or-gm</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimension-shift-for-a-cohomological-delta-functor-effaced-in-the-middle</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimension-shift-for-a-homological-delta-functor-effaced-in-the-middle</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dimer-central-force-hessian-vector-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dipole-green-function-on-riemann-surface</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirac-comb-of-a-full-rank-lattice-transforms-to-the-dual-comb</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirac-condition-implies-ore-condition</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirac-heat-parametrix-has-graph-norm-remainder</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirac-heat-trace-and-mckeen-singer-index</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirac-integral-evaluation</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirac-maximal-domain-is-h1</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-direct-image-is-sheaf</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-direct-integrals-transport-along-bimeasurable-base-isomorphisms</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-direct-product-of-finite-cyclic-groups-is-cyclic-iff-orders-are-coprime</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-direct-search-finite-budget-returns-status</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-direct-search-local-descent-inequality</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-direct-sum-criterion</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-direct-sum-factor-swap-scales-oriented-bases-by-a-sign</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-direct-summands-of-verma-filtered-objects-are-verma-filtered</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-direct-sums-and-tensor-products-of-finite-dimensional-unitary-representations</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-directed-dyadic-rounding-enclosure-and-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-directed-progressive-products-have-club-continuous-chains</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-directed-union-of-amenable-subgroups-is-amenable</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-directional-tail-implies-subgaussian-mgf</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-directional-tail-products-are-subexponential</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-aggregation-under-coarsening</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-character-arithmetic-function-characterization</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-character-chebyshev-laplace-transform</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-character-extension-well-defined</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-character-values</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-forcing-coefficients-exceed-the-generator-domain</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-green-function-is-unique-and-positive</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-grid-poincare-inequality</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-grid-summation-by-parts</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-normal-mixture-countable-band-entropy-sum</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-normal-mixture-density-well-defined</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-normal-mixture-finite-support-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-normal-mixture-interval-mass-local-prior-mass</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-normal-mixture-local-prior-mass</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-normal-mixture-posterior-sieve-tail</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-normal-mixture-sieve-entropy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dirichlet-process-simplex-small-ball</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-disc-hardy-traces-and-szego-reproducing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-families-are-locally-finite</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-form-perturbation-preserves-coercivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-memoryless-channel-average-to-maximal-expurgation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-memoryless-channel-block-kernels-are-stochastic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-memoryless-channel-capacity-achieving-output-divergence-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-memoryless-channel-capacity-is-attained</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-memoryless-channel-iid-information-density-converges</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-memoryless-channel-information-density-concentration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-memoryless-channel-n-letter-information-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-one-step-error-recurrence-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-sequence-spaces-are-complete-in-zf</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-subgroups-of-real-vector-spaces-are-lattices</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-discrete-summation-by-parts-poincare-and-inverse-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discriminant-change-of-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-discriminant-detects-etaleness-of-finite-free-algebra</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-discriminant-is-a-nonvanishing-cusp-form</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-disjoint-coordinate-neighborhoods-evenly-cover-unordered-configurations</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-disjoint-cycles-commute</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-disjoint-modules-are-a-pure-pair</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-disjoint-union-of-framed-cobordisms-is-a-framed-cobordism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-disjoint-union-of-perfect-graphs-is-perfect</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-disjointification-of-an-algebra-cover</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-disk-bundle-intersection-form-and-signature-for-xi-h-j</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-disk-pair-cohomology-over-an-arbitrary-commutative-ring</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-displacement-generator-update-under-scalar-schur-elimination</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distance-to-set-is-lipschitz</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-distant-soergel-generators-commute</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distinct-characters-are-linearly-independent</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distinct-components-commute</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-distinct-cyclotomic-shears-give-integrable-based-sl-two-chains</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-distinct-minimal-normal-subgroups-centralize-one-another</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distinct-normal-sylow-subgroups-commute</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distinct-verma-weight-spaces-are-shapovalov-orthogonal</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distinguished-open-refinement-at-a-point</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distinguished-opens-cover-every-open</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-distinguished-subset-cover-detects-radical</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distinguished-subset-identities</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-distributed-delay-midpoint-error-split</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-distribution-pairing-with-smooth-parameter-families</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distributional-derivatives-commute-with-convolution-against-test-functions</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-distributional-laplacian-commutes-with-mollification</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-divergence-and-curl-are-linear-and-obey-the-scalar-product-rules</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-divergence-form-identity</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divided-difference-lagrange-formula-and-symmetry</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divided-difference-repeated-rolle-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divided-power-and-toral-quantum-binomial-reordering-identities</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divided-power-half-has-integral-skew-string-coefficients</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-divisibility-basic</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divisibility-poset-is-lower-finite-and-factorises</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divisibility-via-valuations</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divisor-bound</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divisor-decomposition-positive-negative-points</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-divisor-order-monotonicity-sections</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dixmiers-lemma-for-countable-dimensional-algebras</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dixon-entire-gluing</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dj-bridge-integral-murphy-and-polytabloid-straightening</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dj-bridge-murphy-cellular-basis-and-cell-form</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dj-bridge-parabolic-double-coset-annihilation</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dj-bridge-permutation-form-invariance-and-restriction</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dj-bridge-row-permutation-module-standard-action</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dj-bridge-sign-automorphism-and-star-dual</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dj-bridge-theta-transport-of-the-cellular-structure</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dobrushin-contraction-from-density-ratios</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dobrushin-zero-sum-l1-coefficient</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dolbeault-green-operator-is-compact-on-the-orthogonal-complement-of-the-kernel</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-domain-cancellation</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dominance-is-necessary-for-an-integrable-highest-weight-module</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dominant-affine-image-contains-principal-open</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dominant-affine-map-normalization-over-open</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dominant-characters-arise-as-primitive-weights-for-split-reductive-groups</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dominant-characters-of-products-of-tori-and-split-semisimple-groups-arise-as-primitive-weights</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-dominant-characters-of-split-semisimple-groups-arise-as-primitive-weights</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dominant-integral-dot-translates-embed-in-the-verma-module</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dominant-map-generic-differential-surjectivity-char-zero</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dominant-map-pullback-function-fields</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dominant-norm-distance-comparison</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-dominant-weights-are-maxima-of-their-weyl-orbits</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dominated-positive-type-functions-give-positive-commutant-contractions</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-doob-martingale-differences-inherit-coordinate-oscillations</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-doob-upcrossing-inequality</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-double-bar-comparison-for-cyclic-bimodule-tensor-products</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-double-cover-branched-over-a-slice-disk-is-a-rational-homology-ball</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-double-exponential-truncated-tail-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-double-plus-simple-cubic-rational-surface-branch-terminates</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-double-point-locus-has-expected-dimension-two-m-minus-n</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-doubling-variables-maximum-localisation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-douglas-rachford-map-is-firmly-nonexpansive</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-dovetailing-reaches-every-finite-stage</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-dpdas-have-unique-computations</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-drift-sublevel-union-is-petite</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-dual-ball-as-a-closed-subset-of-a-product</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-dual-compact-sets-give-a-neighbourhood-basis-on-the-original-lca-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dual-homomorphisms-are-continuous-and-functorial</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dual-identity-neighbourhood-is-compact</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-dual-knuth-star-operations-give-antiparallel-kazhdan-lusztig-graph-edges</loc>
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<loc>https://alphabetamath.cc/item/lem-dual-locally-free-and-base-change</loc>
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<loc>https://alphabetamath.cc/item/lem-dual-of-zd-is-torus</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dual-pairing-between-opposite-principal-series-parameters</loc>
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<loc>https://alphabetamath.cc/item/lem-duality-eliminates-top-and-cotop-handles</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-duality-extends-from-two-open-sets-to-finite-unions-of-coordinate-balls</loc>
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<loc>https://alphabetamath.cc/item/lem-duals-of-finite-products-and-discrete-direct-sums</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-duffy-reference-map-jacobian-and-image</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dunford-contour-construction-satisfies-the-semigroup-law</loc>
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<loc>https://alphabetamath.cc/item/lem-dvoretzky-rogers-finite-block-estimate</loc>
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<loc>https://alphabetamath.cc/item/lem-dvr-cellular-jantzen-filtration-and-gram-valuation</loc>
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<loc>https://alphabetamath.cc/item/lem-dyadic-cell-average-projections-converge-in-l2</loc>
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<loc>https://alphabetamath.cc/item/lem-dyadic-coding-coin-measure-and-lebesgue-transfer</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyadic-cube-values-are-forced-by-translation-invariance-and-normalisation</loc>
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<loc>https://alphabetamath.cc/item/lem-dyadic-cubes-all-generations-partition-and-nesting</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyadic-cubes-of-one-generation-partition-rn</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyadic-determinant-integer-clearance-preserves-sign</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyadic-fourier-coefficient-square-sum-bound-for-holder-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyadic-level-set-summability-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyadic-mihlin-kernels-have-uniform-integral-hormander-control</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyadic-pieces-are-uniform-mihlin-multipliers-and-lp-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyadic-pieces-have-annular-support-and-uniform-kernel-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dyck-paths-of-a-given-semilength-form-a-finite-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-dynkin-diagrams-of-irreducible-finite-root-systems-are-trees-with-controlled-branching</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-e-ideals-and-commutator-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-e-overlap-classes-form-an-anticonnected-partition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-e-overlap-quotient-iteration-terminates-at-a-pure-blockade</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-e2-transformation-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-each-artin-atom-divides-delta-on-both-sides</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-each-combing-factor-reduces-to-a-lower-rank-letter-or-an-x-letter</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-each-feferman-levy-real-layer-is-countable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-each-kostant-extremal-harmonic-space-is-one-dimensional</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-each-oriented-reidemeister-move-is-realized-by-ambient-isotopy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-each-round-has-polynomial-communication</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-easton-class-forcing-truth-and-set-names</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-easton-class-generic-model-satisfies-zfc</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-easton-class-separation-and-power-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-easton-class-tail-head-decision</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-easton-head-cardinality-and-name-count</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-easton-head-cc-and-tail-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-easton-head-tail-no-new-short-sequences</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-eberlein-smulian-countable-compactness-closes-in-the-bidual</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-eberlein-smulian-metrization-on-the-relevant-dual-ball</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-eberlein-smulian-separable-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-edge-addition-to-a-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-edge-connectivity-at-most-minimum-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-edge-deletion-in-a-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-edge-homomorphisms-are-natural</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-edge-is-a-bridge-iff-it-lies-on-no-cycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-edge-maps-of-a-bounded-skeletal-ahss</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-edge-maximal-kuratowski-free-is-three-connected</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-effective-cartier-divisor-exact-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-effective-cartier-divisor-has-no-embedded-associated-primes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-effective-divisors-sections-mod-scalars</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-effective-enumeration-of-clocked-machines</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-effective-fppf-descent-separated-locally-quasi-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-efficient-prime-field-for-a-polynomial-soundness-budget</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-eigenbasis-expansion-in-the-form-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-eigenspaces-of-a-self-adjoint-operator-are-orthogonal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-eilenberg-maclane-spaces-of-torsion-abelian-groups-are-rationally-acyclic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-abelian-p-groups-are-canonical-fp-vector-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-and-hyperelementary-subgroups-are-subgroup-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-basis-changes-orientations-and-deck-lift-changes-die-in-the-whitehead-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-counting-integral-preserves-martingales</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-counting-process-integral-isometry</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-detection-at-a-fixed-element</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-diagram-embedding</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-divisors-regroup-into-invariant-factors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-duality-formula-for-nonnegative-l-p-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-etale-neighbourhood-finite-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-hnn-reductions-preserve-the-represented-element</loc>
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<loc>https://alphabetamath.cc/item/lem-elementary-ideals-are-independent-of-the-presentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-ito-integral-is-independent-of-the-step-representation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-kernel-range-annihilator-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-power-series-converge-uniformly-on-bounded-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-row-operations-are-reversible</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-sets-admit-compact-inner-and-open-outer-approximations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-elementary-sets-are-finite-disjoint-unions-of-half-open-boxes</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-elimination-tree-reach-contains-each-filled-neighbor</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ell-divisibility-amplifies-through-a-blockade</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-elliptic-fredholm-range-condition-translates-to-adjoint-kernel-orthogonality</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-ellp-sums-of-hp-atoms-converge-in-tempered-distributions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-empirical-bayes-radius-bias-and-noise-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-empirical-process-asymptotic-equicontinuity-from-bracketing-entropy</loc>
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<url>
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<loc>https://alphabetamath.cc/item/lem-endpoint-interpolation-simple-analytic-families</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-endpoints-in-a-short-exact-sequence</loc>
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<loc>https://alphabetamath.cc/item/lem-energy-boost-for-an-irregular-pair</loc>
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<loc>https://alphabetamath.cc/item/lem-energy-controls-density-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-energy-identity-on-a-truncated-wave-cone</loc>
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<loc>https://alphabetamath.cc/item/lem-energy-increment-for-an-irregular-partition</loc>
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<loc>https://alphabetamath.cc/item/lem-energy-is-monotone-under-refinement</loc>
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<loc>https://alphabetamath.cc/item/lem-enflo-quantitative-trace-obstruction-to-the-approximation-property</loc>
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<loc>https://alphabetamath.cc/item/lem-enflo-symmetry-averaging-and-block-assembly</loc>
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<loc>https://alphabetamath.cc/item/lem-enflo-walsh-block-estimates</loc>
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<loc>https://alphabetamath.cc/item/lem-engel-common-zero-vector</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ensemble-kalman-update-preserves-joint-exchangeability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-entourage-and-uniform-cover-dictionary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-entourages-on-minimal-cauchy-filters-form-a-separated-uniformity</loc>
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<loc>https://alphabetamath.cc/item/lem-envelope-stationarity-implies-the-hamilton-jacobi-equation</loc>
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<loc>https://alphabetamath.cc/item/lem-envelopes-are-the-least-semicontinuous-majorants</loc>
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<loc>https://alphabetamath.cc/item/lem-enveloping-algebra-is-left-and-right-noetherian</loc>
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<loc>https://alphabetamath.cc/item/lem-enveloping-algebra-of-the-negative-nilpotent-lie-algebra-is-a-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-enveloping-quotient-kernels-and-augmentation-intersections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-epsilon-closure-is-a-closure-operator</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-epsilon-net-controls-symmetric-operator-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-epsilon-net-of-unit-sphere-has-cardinality-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equal-coordinate-rank-one-principal-series-of-gl2-fq</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equal-framing-sign-points-do-not-cancel-in-oriented-zero-bordism</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equal-images-iff-same-kernel-coset</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equal-plane-face-boundaries-force-a-cycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equality-case-for-a-finite-sum-of-unit-complex-numbers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equality-in-a-filtered-colimit-of-sets-is-eventual</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equality-near-a-point-is-an-equivalence-relation-on-local-smooth-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equi-lipschitz-curves-in-compact-euclidean-set-have-uniformly-convergent-subsequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equicharacteristic-fixed-coordinate-blowup-chain-defines-formal-arc</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equicharacteristic-prime-field-lifts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equicontinuity-and-pointwise-boundedness-give-uniform-boundedness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equicontinuity-on-a-compact-domain-is-uniform</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equicontinuous-bounded-rn-valued-curves-have-a-uniformly-convergent-subsequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equicontinuous-families-have-finite-sup-nets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalence-classes-partition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalence-of-powers-of-a-marked-ideal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalences-preserve-progenerators</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalent-definitions-of-the-hilbert-symbol</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalent-event-tests-for-a-discrete-stopping-time</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalent-extensions-have-the-same-ext-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalent-folner-boundary-formulations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalent-hnn-presentation-with-associated-subgroups</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivalent-radon-measures-on-a-homogeneous-space-have-local-densities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-equivariant-p-fold-external-power-and-diagonal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-erdos-hajnal-constants-are-downward-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-erdos-rado-pattern-closure-and-end-homogeneity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-erf-series-geometric-tail</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-erfcx-asymptotic-remainder</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-erfcx-continued-fraction-enclosure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-erfcx-moment-recurrence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ergodic-averages-converge-in-l-p-on-finite-measure-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ergodic-imprimitivity-systems-with-regular-orbits-concentrate-on-one-orbit</loc>
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<loc>https://alphabetamath.cc/item/lem-error-contrast-matrix-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-eta-wedge-d-eta-is-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-commutativity-of-companion-step</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-commutativity-of-maximal-order-case</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-equivalence-relation-restriction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-formal-local-isomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-morphism-extends-to-ambient-neighbourhoods</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-neighbourhood-isolated-fibre-point-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-radicial-morphism-open-immersion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-residue-extensions-finite-separable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-specialization-geometric-basepoint-interface</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-specialization-proper-geometric-finite-etale-invariance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-specialization-trait-through-a-specialization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etale-stable-base-change-composition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-etd2-local-defect</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-balls-are-bounded-c-one-domains</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-balls-have-positive-finite-lebesgue-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-bump-for-a-compact-set-inside-an-open-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-chart-measure-agrees-with-polar-surface-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-cube-bounds-for-hausdorff-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-gaussian-fourier-transform-with-two-pi-normalization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-linear-maps-have-matrices-and-are-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-polygonal-paths-are-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-spin-sphere-bundle-local-sections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euclidean-stokes-for-a-compactly-supported-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-acoustic-wave-pressure-response</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-and-first-pontryagin-classes-of-xi-h-j</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-backward-characteristic-foot-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-characteristic-additive-short-exact</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-characteristic-finite-support-twist-invariance</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-characteristic-is-unchanged-by-edge-and-face-subdivision</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-characteristic-twist-integral-proper-curve</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-class-of-a-bounded-projective-complex-is-homotopy-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-class-of-a-rouquier-complex-is-homotopy-invariant-and-multiplicative</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-count-for-planar-triangulation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-curvature-identity-for-an-arc-reduced-disc-diagram</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-double-tree-shortcutting-does-not-increase-cost</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-four-square-product-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-maruyama-autonomous-interpolation-increment-moments</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-number-is-the-clutching-degree</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-poisson-darboux-equation-for-spherical-means</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-polygonal-approximations-are-uniformly-bounded-and-equicontinuous</loc>
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<loc>https://alphabetamath.cc/item/lem-euler-pressure-solver-bracket-and-termination</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-twisted-hall-product-is-associative-and-unital</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-euler-twisted-hall-product-is-well-defined</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-evaluation-ideal-is-maximal</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-evaluation-map-of-separating-family-is-an-embedding</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-evaluation-on-a-regular-level-identifies-unparametrized-trajectories</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-evaluation-on-an-unordered-marked-set-is-a-numerable-bundle-and-fibration</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-evaluation-on-the-regular-module-has-a-commuting-right-action</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-even-row-tableau-generating-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-event-weighted-ito-isometry</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-eventual-flatness-noetherian-local-approximation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-eventual-global-generation-coherent-twists</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-eventual-hilbert-function-equals-zero-dimensional-projective-length</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-eventual-products-below-aleph-omega-have-a-continuous-long-chain</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-abelian-group-embeds-in-a-divisible-group</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-central-character-of-the-enveloping-algebra-arises-from-a-weight</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-conjugacy-class-contains-a-cyclically-britton-reduced-word</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-ext-one-class-is-represented-by-an-extension</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-finite-dimensional-irreducible-representation-has-a-highest-weight-vector</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-finite-group-is-finitely-presented</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-finite-singular-chain-becomes-cover-small-after-enough-subdivision</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-geometric-braid-is-a-word-in-half-twists</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-geometric-braid-is-braid-isotopic-to-a-smooth-braid</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-graph-walk-contains-a-path-between-its-endpoints</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-integer-above-one-has-a-prime-divisor</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-integer-degree-is-realized-by-a-map-to-the-sphere</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-line-in-a-finite-projective-plane-has-the-same-number-of-points</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-manifold-has-a-compact-exhaustion</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-net-has-a-universal-subnet</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-nonzero-verma-submodule-contains-a-singular-vector</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-norm-on-rn-is-continuous-for-the-euclidean-metric</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-open-cover-of-a-manifold-has-a-countable-cover-by-relatively-compact-coordinate-balls-subordinate-to-it</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-oriented-link-admits-a-regular-projection</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-polynomial-agrees-on-the-cube-with-its-multilinear-reduction</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-positive-braid-divides-a-power-of-delta-on-both-sides</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-trivial-braid-word-combs-as-w-one-w-two</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-unoriented-and-oriented-bordism-class-is-realized-by-an-embedded-collapse</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-vector-in-a-fibre-extends-to-a-compactly-supported-smooth-section</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-verma-module-contains-a-simple-verma-submodule</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-vertex-lies-in-a-unique-maximal-proper-module</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-walk-in-a-simple-graph-contains-a-path-with-the-same-endpoints</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-whitehead-class-is-realized-by-a-finite-cw-homotopy-equivalence</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-every-zariski-closed-set-has-a-radical-defining-ideal</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ewald-certified-particle-mesh-evaluator-terminates</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ewald-gaussian-poisson-periodization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ewald-lattice-shell-gaussian-tail-controllers</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ewald-pme-derivative-window-alias-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ewald-pme-spline-alias-and-dft-normalization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ewald-screened-coulomb-kernel-and-self-limit</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ewald-smooth-torus-fourier-pairing</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exact-dyadic-determinant-sign-correct-and-terminates</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exact-francis-step-termination-and-similarity</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exact-free-complex-reduction-nonzerodivisor</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exact-householder-bidiagonal-reduction</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exact-ornstein-uhlenbeck-momentum-substep</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exact-rational-two-by-two-discriminant-sign</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exact-sequence-dimension-inequality</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exactly-one-symbol-constraints-have-polynomial-size</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exactness-at-the-homology-of-the-left-complex</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exactness-at-the-homology-of-the-middle-complex</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exactness-at-the-homology-of-the-right-complex</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exactness-at-the-target-of-the-connecting-map</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exceptional-curve-normal-bundle-minus-one</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exceptional-fiber-line-bundle-euler-characteristic</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-existence-of-a-fibre-cutter</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-existence-of-a-smooth-inhomogeneous-dyadic-frequency-partition</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-existence-of-schwartz-functions-with-flat-fourier-transform-at-the-origin</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-expander-size-adjustment-and-laziness</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-expander-walk-bad-edge-return</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-expander-walk-contraction</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-expander-walk-restricted-operator</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-expander-walk-violated-edge-collision-bound</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-expectation-by-distribution</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-expectation-is-independent-of-the-ae-representative</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-explicit-euler-constant-enclosure</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-explicit-rk-differentiated-stages-give-local-c1-order</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-base-assignment-tester-from-quadratic-oracles</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-decay-dominates-every-inverse-power</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-dominates-one-plus-x</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-euler-local-defect</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-factorial-tail-bound</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-integrator-interaction-picture-stability</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-phi-integral-representations</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-series-has-infinite-radius</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-series-of-a-bounded-operator</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-exponential-test-posterior-splitting-at-kl-projection</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ext-depth-shift-across-a-regular-element</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ext-depth-zero-identifies-annihilated-elements</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ext-of-locally-free-sheaf-via-cohomology</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ext-one-of-z-mod-n-by-z-is-z-mod-n</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extend-a-degree-zero-transformation-through-one-dimension-shift</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extend-a-partial-comparison-homotopy-by-one-degree</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extend-a-partial-comparison-map-by-one-degree</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extend-sections-from-nonvanishing-open</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extended-dfa-transition-respects-concatenation</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extended-hall-torus-action-is-well-defined</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extended-reals-complete</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extending-a-map-over-one-cell-is-equivalent-to-nullhomotoping-its-attaching-sphere</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extension-by-zero-short-exact-sequence</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-extension-by-zero-vanishing-reduces-to-all-sheaves</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-extension-from-subobjects-of-a-generator-detects-injectivity</loc>
<lastmod>2026-09-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-extensional-collapse-is-injective</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-extensions-between-distinct-o-linkage-classes-split</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-exterior-algebra-basis-monomials</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-exterior-and-cartan-calculus-extend-to-manifolds-with-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-exterior-multiplication-koszul-sign-rule</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-exterior-square-has-the-alternating-universal-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-external-evaluation-detects-tensor-square-operations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-extremal-comparability</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-extremal-cut-closed-under-f</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-extremal-cut-closed-under-sups</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-extremal-fork-noodle-terms-have-one-sign-and-cannot-cancel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-extremal-weight-cochain-for-a-weyl-element-is-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-extremal-word-characters-detect-normalized-cyclotomic-simple-labels</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-extreme-points-of-the-dual-ball-of-c-of-k</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-extreme-value-theorem-from-compactness</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-face-containment-under-plane-subgraphs</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-facet-tensor-weight-exclusion</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-factor-elements-act-on-amalgamated-normal-words</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-factor-elements-act-on-reduced-syllable-words</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-factor-set-is-a-normalized-two-cocycle</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-factor-set-of-a-section-is-a-normalized-two-cocycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-factorial-beats-geometric</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fair-coin-cylinder-content-is-a-premeasure</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fair-coin-open-content-is-countably-subadditive</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-faithful-essential-pure-state-orbits-obstruct-countable-separation</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-faithful-irrep-with-a-noncentral-abelian-normal-subgroup-is-properly-induced</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-faithfully-flat-effective-descent-of-modules-and-algebras</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-family-signature-constancy-and-the-weak-lefschetz-substitute</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fas-coarse-branch-derivative</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fas-fine-root-fixed-point</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fas-inexact-coarse-solve-residual-defect</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fas-linear-vw-cycle-translation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fas-second-derivative-of-composed-cycle-map</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fas-vw-cycle-work-and-status</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-feferman-levy-bounded-layer-support</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-feferman-levy-fixed-boolean-values-come-from-initial-layers</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-feferman-levy-real-layer-ground-cardinality-bound</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-feferman-levy-symmetric-collapse-is-finitely-formalizable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-feferman-tail-complement-automorphism</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-feferman-tail-flip-model-is-finitely-formalizable</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fehmm-micro-cell-solves-wellposedness</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fehmm-micro-tensor-approximation-error</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fehmm-one-dimensional-nonaligned-resonance-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fehmm-period-aligned-sampling-has-zero-resonance</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fejer-kernel-is-a-positive-approximate-identity</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fekete-diameters-decrease</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fell-closure-is-characterized-by-weak-containment</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fell-closure-of-a-single-representation-is-its-weak-containment-closure</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fell-continuity-in-the-parameter-of-the-unitary-principal-series</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fell-neighbourhoods-of-an-irreducible-representation-are-saturated-under-weak-equivalence</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fem-control-gradient-residual-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fenchel-conjugate-is-proper-closed-convex</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fenchel-young-equality-characterizes-subgradients</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-few-induced-copies-exclude-a-fixed-labelled-blowup</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-few-induced-copies-is-inherited-by-large-induced-subgraphs</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-feynman-kac-path-measures-satisfy-forward-recursion</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fi-coinvariant-functors-detect-vanishing-in-bounded-weight</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fiber-and-limit-isomorphisms-force-the-base-axis-isomorphism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fiber-transport-homology-and-cohomology-form-the-serre-local-systems</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-fiber-transport-makes-homology-into-a-functor-on-the-base-fundamental-groupoid</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fibonacci-positive-spherical-pivotal-structure</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-after-base-change</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-as-base-change-to-point-classical</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-components-of-a-proper-birational-morphism-of-regular-surfaces</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-degree-sum-ramification-residue</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-dimension-upper-semicont-proper</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-injective-map-flat-cokernel-noetherian-target</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-product-associativity-and-symmetry</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-product-open-restriction</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-product-unique-canonical-isomorphism</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-products-glue-over-open-covers</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibre-regular-sequence-locus-open-cm-equidimensional</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fibrewise-exact-flat-complex-lifts-noetherian-target</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-fibrewise-exact-free-complex-locus-open-cm-flat-family</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-field-antisymmetrizer-image-and-dominance</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-field-integrality-criterion</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-field-is-a-commutative-ring</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-field-is-noetherian</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-field-module-sheaves-have-injective-derived-models</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-field-valued-points-of-schemes</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-filled-edge-path-characterisation</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-filter-base-generates</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-filter-derived-net-preserves-convergence-and-cluster-points</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-filtered-colimit-flat-fp-sheaf-stage</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-filtered-colimit-fp-scheme-stage</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-filtered-colimit-fp-sheaf-stage</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-filtered-colimit-proper-fp-stage</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-filtered-colimits-commute-with-sheaf-cohomology-on-noetherian-spaces</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-filtered-colimits-of-abelian-groups-are-exact</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-filtered-freeness-lifts-from-associated-graded-algebras</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-filtered-graded-lie-algebra-defines-a-shifted-l-infinity-algebra</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-filtered-l-infinity-taylor-map-extends-to-completed-coalgebra</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-filtered-maurer-cartan-gauge-equation-has-unique-complete-polynomial-flow</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-filtered-projectives-prove-canonical-basic-set-reciprocity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finitary-monad-algebras-have-coequalizers-under-dependent-choice</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-acyclic-quiver-hall-category-is-hereditary-finitary</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-acyclic-quiver-representations-are-finitary-hereditary-with-euler-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-affine-bubbles-represent-signed-cubical-sums</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-alphabet-iid-information-aep</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-alphabet-past-information-convergence</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-ambient-partitions-for-euclidean-boundary-integration</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-analytic-chart-triangulation-compact-riemann-surface</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-and-complete-filtered-isomorphism-lifting</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-arithmetic-schedule-termination-and-count</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-atomic-sums-are-dense-in-hone</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-b-stable-generators-and-weight-flags-in-category-o</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-bessel-inequality</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-binary-digit-changes-do-not-alter-zero-one-measure</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-biproducts-of-injective-objects-are-injective</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-birational-algebra-descends-from-a-flat-completion-neighbourhood</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-birational-to-normal-is-isomorphism</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-block-entropy-chain-rule</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-boolean-algebras-are-powersets-of-atoms</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-bootstrap-cdf-supremum-is-measurable</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-boundary-and-interior-partition-glues-local-h-two-estimates</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-budget-adaptive-em-status</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-budget-fixed-point-iteration-work</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-budget-newton-work-and-status</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-budget-scf-iteration-work</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-budget-stopped-normalizer</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-c2-surface-carriers-have-smooth-normal-forms-and-relative-cap-approximations</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-caratheodory-splitting</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-cell-local-system-cohomology-is-finite-and-commutes-with-field-extension</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-cellular-cyclic-squares-agree-with-singular-cup-i-squares</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-cellular-cyclic-squares-cartan-and-basis-action</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-cellular-nonzero-form-heads-purity-and-shared-factor-linkage</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-chart-localization-defines-choice-free-integration-and-compact-stokes</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-chart-localization-for-compactly-supported-forms-on-manifolds-with-boundary</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-chart-surface-normal-forms-supply-jordan-disks-and-torsion-free-groups</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-choice</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-circle-wedge-open-cover</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-closed-immersion-derived-coinduction-adjunction</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-coagulation-fragmentation-event-moments</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-coefficient-vector-has-polynomial-representative</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-complex-circle-measures-are-determined-by-fourier-coefficients</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-conditional-channel-mutual-information-concave-input-law</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-conditional-codebook-covering</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-conditional-typicality-packing</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-configuration-product-measurable</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-convex-cell-complexes-admit-compatible-triangulations</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-coordinate-cylinder-sets-form-an-algebra</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-coordinate-cylinders-form-a-pi-system</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-coordinate-posterior-total-variation-limit</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-coset-partition</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-covariance-matrix-basic-properties</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-cover-transfer-with-inverted-degree-and-sign-anti-invariants</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-cube-covers-admit-grid-control</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-cw-basepoints-have-explicit-homotopy-extension</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-cw-complexes-are-euclidean-neighborhood-retracts</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-cw-pairs-admit-finite-simplicial-homotopy-models</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-cw-relative-ko-triples-and-homotopy-invariance</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dependent-vector-clt</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-diagonal-cohomological-double-complex-spectral-sequences</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-algebras-admit-primitive-idempotent-decompositions</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-auerbach-basis</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-axiomatic-homology-has-finite-subcomplex-support</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-commutative-algebras-decompose-into-local-factors</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-functional-convolution-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-galerkin-minmax</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-golden-thompson-trace-inequality</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-graded-algebras-have-graded-projective-covers</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-integral-jensen-for-convex-loss</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-projection-is-linear-and-contractive</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-separation-of-a-compact-convex-set-and-a-point</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-skeletal-exactness-computes-axiomatic-homology</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-space-over-an-infinite-field-is-not-a-finite-union-of-proper-subspaces</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-subcomodules-contain-elements</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-subspace-admits-a-linear-projection-without-choice</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-tensors-reach-every-block-simple</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dimensional-unit-spheres-are-sequentially-compact</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-directed-information-feedback-decomposition</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dirichlet-gamma-representation-and-bernstein-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-domination-of-surface-modifications-via-relative-hilbert-scheme</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dot-orbit-weight-spaces-detect-o-subquotients</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-double-sum-interchange</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dynkin-hall-algebra-is-simple-generated</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-dynkin-quiver-reflection-classification</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-eilenberg-watts-kernel-end-and-coend-exist-with-explicit-universal-maps</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-elementary-abelian-p-groups-have-bases-and-basis-extension</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-empirical-measure-is-a-probability-law</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-etale-algebra-module-presentation-and-rank</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-etale-galois-refinements-and-quotients</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-etale-lifting-over-complete-dvr</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-etale-separability-and-hochschild-contraction</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-euclidean-space-is-standard-borel</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-evaluations-separate-from-a-dual-subspace</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-event-conditional-expectation-formula</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-extension-with-finitely-many-intermediate-fields-is-simple</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-factor-projection-comparison-and-normalized-trace</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-fibre-dimension-gives-bounded-fibrewise-soft-resolutions</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-field-quadratic-isotropy-in-dimension-at-least-three</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-field-quiver-semistable-stack-points-are-hall-groupoids</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-field-schur-descent-and-restriction</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-field-stack-groupoid-cardinality-respects-motivic-relations</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-filtration-of-generated-subsheaves-of-the-constant-integer-sheaf</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-flat-curve-fibre-degree</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-formula-witness-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-formula-witness-rank-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-fourier-transform-converts-cyclic-convolution-to-scaled-product</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-fragment-l-interpretation-with-gch</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-frameable-decomposition-of-a-regular-disk-region</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-frobenius-functional-determines-coproduct</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-galois-descent-for-multiplicative-hopf-algebras</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-generating-subset-of-a-generating-set</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-gibbs-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-graded-projective-a-m-modules-are-sums-of-shifted-vertex-projectives</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-graded-projective-resolutions-are-extension-stable</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-grid-interval-discrepancy</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-group-induction-is-coinduction-and-thus-biadjoint</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-groups-acting-on-trees-have-a-global-fixed-vertex-after-subdivision</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-haar-volume-compactness-criterion</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-hardykrause-variation-implies-riemann-integrability</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-harnack-chain-on-a-compact-connected-subset</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-hermite-interpolation-for-jordan-data</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-hmm-joint-law-normalizes</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-holonomy-acts-on-a-small-transverse-disk</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-horizon-girsanov-and-relative-entropy-for-lipschitz-drifts</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-horizon-test-supermartingale-crossing-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-iid-log-likelihood-concentrates</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-independent-gaussian-vectors-form-joint-multivariate-normal</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-index-bootstrap-sample-is-conditionally-iid</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-index-bounded-vector-pull-down</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-intensity-mecke-identity</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-interior-ball-chain-propagates-weak-harnack-bounds</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-interval-cover-total-length</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-irreducible-chain-hitting-time-geometric-tail</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-join-models-for-circle-and-two-point-groups</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-joint-iid-strong-typicality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-jordan-cover-sum-bounds</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-kl-generator-is-admissible</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-kl-nonnegative-choice-free</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-knaster-poset-products</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-lacunary-fourier-sums-have-their-coefficient-ell-two-norm</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-lattice-join-irreducible-decomposition</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-lch-partition-of-unity-near-a-compact-set</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-length-duality-over-a-regular-local-base</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-length-objects-decompose-into-indecomposables</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-lie-engel-trace-criterion-and-killing-nondegeneracy</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-lie-triangularization-and-rank-one-complete-reducibility</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-linear-group-invariant-polynomials-separate-orbits</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-local-modules-admit-minimal-free-resolutions</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-loopless-quiver-nilpotent-category-is-hereditary-finitary</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-lower-central-coordinate-systems-exist</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-matrix-semilinear-variation-of-constants</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-measure-bounded-l-p-functionals-are-integration-against-rn-densities</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-measure-sets-admit-compact-open-sandwiches-with-small-excess</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-measure-sets-are-approximable-by-a-countable-generating-algebra</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-measure-sets-are-approximable-by-a-generating-algebra</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-measure-sets-are-approximable-by-finite-unions-of-boxes</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-measure-uniqueness-on-a-pi-system</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-message-fano-for-density-observation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-miller-terminal-error-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-minima-of-continuous-unit-interval-maps</loc>
<lastmod>2026-08-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-mode-car-canonical-inclusions-are-isometric</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-mode-car-occupation-matrix-units</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-modified-hamiltonian-close-to-original</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-modified-hamiltonian-exists</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-module-duality-is-exact-with-commuting-bimodule-actions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-modules-over-noetherian-rings-are-noetherian</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-modules-with-connection-over-a-polynomial-open-are-locally-free</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-moment-moving-window-increments</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-morphism-affine</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-multiset-randomized-rank-is-uniform</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-nilpotence-via-normal-sylow-subgroups</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-node-equation-reconstruction-equivalence</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-normal-push-off-count-for-an-even-dimensional-euclidean-immersion</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-normal-surface-cover-completed-local-degree-bound</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-normalization-compatible-with-principal-opens</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-or-euclidean-likelihood-ratio-network-coding</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-order-statistic-and-rank-maps-are-measurable</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-over-projective-noetherian-affine-base-is-projective</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-partial-prime-ideal-extension</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-planar-graph-disk-cuts-and-euler-count</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-plane-graph-ear-and-face-facts</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-polygonal-disk-and-collar-surgery</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-polyhedral-covering-dimension-bounds-all-sheaf-cohomology</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-population-design-law-is-a-probability-measure</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-population-permutation-clt</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-poset-diagrams-have-bounded-finite-bar-models</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-positive-circle-measures-have-lebesgue-decomposition-under-countable-choice</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-potent-trace-existence-and-uniqueness</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-potent-trace-linearity-and-conjugation</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-powers-of-countable-sets-are-countable</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-predecessor-closure-is-a-set</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-presentation-image-constructible</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-prime-avoidance</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-prior-lan-bayes-envelope-convergence</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-priors-approximate-gaussian-shift-bayes-risk</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-probability-basic-laws</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-probability-maximal-ergodic-inequality</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-product-measure-with-density</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-product-norms-are-equivalent</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-product-of-nonzero-reals-is-nonzero</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-product-of-quotients</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-products-and-comparison-cones-have-finite-type</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-products-of-dominated-kernels-have-product-density</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-products-of-probability-kernels</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-products-of-standard-borel-spaces-are-standard-borel</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-projective-dual-basis-gives-tensor-hom-isomorphism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-projector-domain-compact</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-purely-inseparable-rational-extension-envelope</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-quiver-hall-extension-orbit-count</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-rademacher-blocks-are-equidistributed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finite-random-variables-are-measurable</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-range-sequences-are-uniformly-dense-in-ell-infinity</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-rank-compressions-converge-in-trace-norm</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-rank-operators-are-compact</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-rank-spectral-pieces-of-compact-convolution</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-real-coefficient-lists-have-at-most-degree-many-roots</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-real-gaussian-increment-comparison</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-rectangle-unions-form-a-generating-algebra</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-refining-small-diameter-covers-of-compact-metric-spaces</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-reflection-along-constructible-levels</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-reflection-invariant-generators-are-algebraically-independent</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-regular-base-algebra-dualizing-biduality</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-relative-homotopy-lifting-across-a-weak-equivalence</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-relative-mixed-handle-movies-give-marked-kirby-moves</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-renyi-generators-are-convex</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-residue-field-projective-dimension-forces-depth-equals-dimension</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-right-n-module-frame-from-projection-model</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-roof-squares-and-composable-pairs-can-be-cleared</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-saddle-omega-graph-is-strongly-connected</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-scan-range-basis-is-borel</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-second-moment-covariance-matrix-is-well-defined</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-sectional-vector-field-locally-lipschitz</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-semisimple-cartan-root-and-string-structure</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-semisimple-pbw-and-highest-weight-construction</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-separable-normal-surface-extension-preserves-bounded-h1</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-serre-word-form-and-classical-rank-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-set-has-max</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-signed-measure-sets-have-only-finite-subset-values</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-simple-random-sampling-identities</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-simplex-entropy-continuity-and-concavity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-simplicial-approximation-for-homology-comparison</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-simplicial-constructible-sheaves-have-a-derived-incidence-model</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-simplicial-maps-have-explicit-compatible-triangulated-mapping-cylinders</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-simplicial-open-stars-have-explicit-conical-product-charts</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-simplicial-weak-topology-agrees-with-euclidean-topology</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-sine-harmonic-sums</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-sine-transform-orthogonality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-stable-base-change-composition</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-stage-l-history-and-limit-level-absoluteness</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-star-refinement-for-compact-hausdorff-spaces</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-straight-line-program-defines-c1-map</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-straight-line-program-defines-c2-map</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-strong-interference-block-lift</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-subcoalgebras-in-multiplicative-coordinate-algebras</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-subsets-listable</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-sum-gradient-is-average</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-sum-laws</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-sum-permutation-invariance</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-sum-reindexing-and-fubini</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-sums-of-product-tests-are-dense-on-product-open-sets</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-support-constructibility-absoluteness</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-support-families-of-finite-dimensional-vector-spaces-are-locally-finite</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-support-iteration-size-bound</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-support-of-ideal-valuations</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-support-projection-selection-is-borel</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-support-regularization-of-quantum-label-weight-modules</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-support-risk-set-proportion-limits</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-tangent-zero-count-and-inward-boundary-sum-without-general-thom-existence</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-temperature-density-domain-compact</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-temperature-entropy-continuous-at-endpoints</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-temperature-minimizer-is-interior</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-tensor-products-of-smooth-vector-bundles</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-thom-classifying-detector-map-exists-and-is-continuous</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-tori-are-compact-hausdorff-character-spaces</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-torsionfree-modules-over-dedekind-domains-are-projective</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-torus-fourier-orthogonality-and-affine-change</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-transient-block-geometric-escape</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-trellis-prefix-score-recurrence</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-triangulated-surface-reduces-to-a-one-polygon-schema</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-truncations-are-dense-in-c0-and-ell-one</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-tuple-satisfaction-is-absolute</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-tuples-admit-effective-prefix-free-encodings</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-type-a-full-tensor-source-upper-charts-and-string-leading-terms</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-type-a-tensor-hecke-bars-and-complementary-coefficient-charts</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-type-and-odd-primary-acyclicity-of-k-f2-q</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-type-field-zero-differentials-finite-separable</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-type-jacobson-residue-extension</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-type-kac-moody-roots-descend-to-simple-roots</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-type-local-on-source-and-target</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-valued-convex-hamiltonian-equals-its-biconjugate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-variable-polynomial-algebras-over-fields-are-noetherian-direct</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-variable-polynomial-rings-over-fields-are-ufds</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-variation-integration-by-parts-for-counting-process-martingales</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-vector-space-copowers-in-a-linear-abelian-category</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-volume-discrete-summation-by-parts</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-volume-hilbert-schmidt-rescaling</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-weighted-upper-tail-pvalues-and-randomized-ties</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-weyl-closed-chambers-and-stabilizers</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-weyl-positive-roots-and-simple-reflections</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-weyl-strong-exchange-and-deletion</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-window-gibbs-density-ratio-is-papangelou</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finite-window-pair-count-is-measurable</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finitely-additive-integral-is-well-defined-and-isometric</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-finitely-cornered-regular-plane-curve-separates-without-choice</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finitely-generated-euclidean-cones-are-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finitely-many-critical-values-can-be-separated-locally</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finitely-many-number-field-ideals-of-bounded-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-finiteness-support-residue-sum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fip-generates-filter</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-firmly-nonexpansive-picard-iteration-converges</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-and-second-moments-of-the-heat-kernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-chern-form-agrees-with-the-topological-line-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-companion-pencil-residual-transfer</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-connective-complex-k-theory-postnikov-invariant-is-integral-sq-three</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-essential-loop-of-a-transverse-family-is-a-vanishing-cycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-false-claim-survives-with-root-bound-probability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-false-round-is-caught-by-root-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-hitting-time-of-an-adapted-process-is-a-stopping-time</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-homotopy-group-of-a-wedge-of-higher-spheres-has-its-cell-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-jantzen-filtration-term-is-the-verma-maximal-submodule</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-main-theorem-injectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-main-theorem-local-block-existence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-main-theorem-surjectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-moment-of-the-unit-sphere-vanishes</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-first-order-asymptotically-hyperbolic-operator-is-fredholm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-order-hadamard-factorization-near-a-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-plus-construction-is-separated</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-first-return-decomposition-of-a-nonempty-dyck-path</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-first-row-insertion-basic-subsequences</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-first-saddle-lobe-admits-a-collar-fixed-center-saddle-cancellation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-first-variation-hinge-derivative-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fisher-scoring-irls-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fista-energy-estimate-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fitting-ideals-presentation-independent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-five-term-homology-sequence-for-a-free-presentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-base-simplicial-cotangent-represents-derived-derivations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-cap-transverse-product-glues-by-unique-transverse-flow-roots</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-coding-primitive-recursive-arithmetic-and-sequences</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-colourings-factor-by-cycle-type</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fixed-component-core-multipartitions-are-cyclotomic-jantzen-connected</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-design-gaussian-regression-controls-local-likelihood-distances</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-design-gaussian-regression-exponential-tests</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-design-subgaussian-score-concentration</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-field-of-the-relative-frobenius</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-grid-sampling-spectral-alias-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-leafwise-cap-gives-a-joint-transverse-product-with-exact-collar</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-loci-and-centralizers-of-torus-actions-are-connected</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-locus-and-normal-orbit-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-machine-history-predicate-is-primitive-recursive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-pivot-barycentric-identities</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fixed-pivot-coagulation-fragmentation-quadrature-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fixed-point-free-disk-map-produces-a-retraction</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fixed-point-sum-of-the-two-lifts-of-a-self-map</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-points-are-graph-diagonal-intersections</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fixed-residue-node-cubes-realize-fock-i-strings-and-crystal-lattices</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fixed-scale-truncated-covariance-deviation</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fixed-support-test-function-spaces-are-complete</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fixed-transverse-fences-have-a-finite-crossing-word</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fixed-vertical-height-relative-morse-handle-normalization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flag-line-bundle-degree-on-minimal-parabolic-fibre</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flag-variety-canonical-bundle-weight-minus-two-rho</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flag-variety-of-a-vector-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flasque-kernel-lifts-quotient-sections</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-deformations-form-a-zariski-sheaf-of-groupoids</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-drift-realizes-a-period-annulus-frontier-as-an-omega-limit</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-fp-fibre-dimension-lower-semicont</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-fp-relative-dimension-strata</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-local-ascent-of-regularity</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-local-depth-formula-regular-sequence-split</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-local-map-faithfully-flat</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-locus-open-finitely-presented-algebra</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-morphisms-stable-base-change</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-morphisms-stable-composition</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-pullback-chow-groups</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flat-sheaf-sections-flat-over-base</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flatness-affine-local-source-target</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flatness-by-fibres-for-polynomial-chart</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-flatness-criteria-and-flat-covers-for-abelian-sheaves</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-floater-hormann-denominator-lower-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-floater-hormann-gap-partial-sums-positive</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-floater-hormann-local-mesh-ratio-bounded-by-global</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-floater-hormann-weight-and-blend-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-floater-hormann-window-newton-remainder</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-floater-hormann-window-polynomial-interpolates</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-flow-cut-identity-and-weak-duality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-flow-reparametrization-realizes-a-level-isotopy</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-flux-of-a-single-component-field-through-an-oriented-graph-face</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-foata-transformation-is-bijective</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fock-creation-annihilation-satisfy-car</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-folner-nets-give-reiter-nets</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-forbidden-induced-subgraph-classes-are-hereditary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-forced-heat-energy-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-forcing-monotonicity-density-and-decision</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-forcing-names-and-name-ranks-are-absolute</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-forcing-transfer-for-finite-zfc-fragments</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-forcing-truth-lemma</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-forgetful-sheaf-compatibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-forgetting-configuration-points-is-locally-trivial</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fork-detection-transports-to-arbitrary-boundary-crosscuts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-form-to-bounded-operator-by-hilbert-riesz</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-adjoints-of-differential-operators-exist-and-are-unique</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-cohen-forcing-verification-compiler</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-full-faithfulness-on-regular-punctured-spectrum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-immersion-gives-the-tangent-normal-bundle-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-immersion-homotopies-extend-over-a-collar</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-immersion-homotopies-extend-over-a-subcritical-handle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-immersions-of-the-circle-in-the-plane-are-classified-by-the-winding-number</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-letters-act-by-permutations-on-reduced-words</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-ma-iteration-verification-compiler</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-matrix-geometric-series</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-order-laws</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-pfa-iteration-verification-compiler</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-power-series-evaluation-converges</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-power-series-evaluation-unique-continuous-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-residue-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-tangent-and-artanh-series-are-compositional-inverses</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formal-triviality-of-one-parameter-semisimple-algebras</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-forms-annihilated-by-a-nowhere-vanishing-one-form-are-divisible-by-it</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-formula-arithmetization-degree-and-evaluation-cost</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-formula-substitution-satisfaction</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-forward-difference-jacobian-error-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-forward-euler-reaction-step-preserves-invariant-rectangle-and-mass</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-four-dividing-a-sum-of-three-squares-forces-even-coordinates</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-four-lemma-for-modules</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-four-spaces-for-a-fixed-linear-recurrence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-four-square-congruence-for-primes</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-four-square-descent</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-analysis-of-margulis-adjacency</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-coefficients-of-a-periodic-weak-derivative</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-coefficients-of-lattice-periodisation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-maximal-weak-bound-closes-almost-everywhere-convergence</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-pairing-for-a-finite-measure-and-schwartz-data</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-partial-sum-operator-norm-equals-the-lebesgue-constant</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-partial-sums-are-dirichlet-convolutions</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-partial-sums-are-uniformly-bounded-on-periodic-lp</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-stieltjes-transform-of-a-positive-measure-is-positive-definite</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-stieltjes-transforms-determine-finite-radon-measures</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-transform-of-a-gaussian</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fourier-transform-on-tempered-distributions-is-well-defined-and-continuous</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fppf-quotient-representability-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fppf-sheafification-exists</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fpqc-cover-submersive</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fpqc-descent-properness-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fr-descent-and-direction-growth-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fraction-field-coefficients-of-an-integral-lkb-class-are-laurent-polynomials</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fractional-boundary-norm-is-independent-of-atlas</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fractional-ideal-operations-well-defined</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fractional-integral-kernel-power-integral</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fractional-integral-semigroup</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fractional-level-set-kernel-measure-estimate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-framed-circles-in-four-dimensional-two-handle-traces-move-to-the-base</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-framed-cobordant-submanifolds-have-homotopic-collapse-maps</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-framed-cobordism-is-an-equivalence-relation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-framed-kauffman-link-evaluation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-framed-oriented-tangles-have-the-ribbon-generator-and-relation-presentation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-framed-points-in-one-component-of-the-frame-bundle-are-framed-cobordant</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-framing-obstruction-lives-in-the-normal-bundle-of-the-surgery-sphere</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-francis-compact-bulge-support-propagation</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-francis-double-shift-bulge-chase-matches-explicit-qr</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-frattini-subgroup-is-characteristic</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-frattini-subgroup-nongenerator-characterization</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fredholm-determinant-logarithmic-derivative</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fredholm-determinant-spectral-product-from-power-traces</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fredholm-determinant-trace-norm-continuity-and-growth</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fredholm-determinant-zeros-and-algebraic-multiplicities</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fredholm-maps-have-countable-proper-local-restrictions</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fredholm-splitting-and-parametrix</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-complex-unit-entry-splits-contractible-pair</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-cyclic-resolution-and-transfer-for-power-operations</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-differentials-imply-regular-in-characteristic-zero</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-fi-modules-have-explicit-weight-and-stability-bounds</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-fibre-flat-module-free-noetherian-target</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-group-augmentation-ideal-has-the-generator-difference-basis</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-free-homotopy-classes-of-loops-are-conjugacy-classes</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-lie-construction-for-finite-kac-moody-generators</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-presentation-bicomplex-collapses-in-positive-middle-group-degree</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-free-presentation-construction-is-a-central-extension</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-free-word-rings-are-unital-rings</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-freezing-coefficients-and-schauder-error-estimate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fresh-bound-variable-renaming</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fresh-henkin-axiom-preserves-consistency</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fresnel-series-geometric-tail</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-freudenthal-identifies-the-eventual-suspension-system-for-spheres</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-frobenius-character-extension-construction</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-frobenius-character-extension-is-irreducible</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-frobenius-characteristic-is-an-isometry</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-frobenius-characteristic-preserves-outer-products</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-frobenius-divisibility-gives-d-omega-equals-eta-wedge-omega</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-frobenius-kernel-cardinality</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-frobenius-kernel-is-an-intersection-of-character-kernels</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-frobenius-sewing-derived-moves</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-frontdoor-interventional-identities</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-frozen-slow-euler-local-defect-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-frozen-slow-euler-one-step-stability</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-frozen-slow-euler-variation-bounds</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-full-column-rank-matrix-has-economy-qr</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-full-column-rank-matrix-least-squares-solution</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-full-lattice-fundamental-domain-and-bounded-points</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-full-memory-bfgs-dennis-more-condition</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-function-limit-preserves-order</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-function-limit-unique</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-function-with-poles-defines-map-p1</loc>
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<priority>0.5</priority>
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<loc>https://alphabetamath.cc/item/lem-functional-induced-measures-are-absolutely-continuous-with-respect-to-mu</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-functionals-vanishing-on-the-common-kernel-of-an-independent-family</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-class-of-a-boundary-pushes-forward-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-class-of-a-product-of-closed-manifolds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-cut-of-a-spanning-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-cycle-of-a-spanning-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-group-label-is-the-obstruction-to-contracting-the-whitney-circle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-lemma-of-the-calculus-of-variations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-path-fibration-class-has-the-normalized-relative-lift</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-theorem-and-integration-by-parts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-theorem-of-calculus-for-banach-valued-continuous-curves</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fundamental-weights-of-split-semisimple-groups-have-primitive-multiples</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fusion-category-global-dimension-is-nonzero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-fusion-control-and-centralizer-transitivity</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fusion-control-gives-a-nontrivial-p-quotient-of-the-p-residual</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-fusion-ring-character-orthogonality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-fv-conforming-companion-and-test-recovery</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-g-equivariant-maps-are-the-fixed-points-of-the-dual-tensor-representation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ga-torsors-over-affine-schemes-are-trivial</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-galerkin-orthogonality-for-conforming-galerkin-approximations</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-galois-action-on-the-quadratic-gauss-sum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-galois-conjugates-have-equal-scalar-extension-multiplicity</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-galois-fixed-points-recover-a-finite-dimensional-scalar-extension</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-galois-orbit-sums-of-split-central-idempotents-descend</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-game-covering-composition-and-continuity</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-game-covering-transfers-winning-strategies</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gamma-2-is-torsion-free-and-has-no-elliptic-points</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gamma-density-normalization</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gamma-functional-equation-meromorphic-extension</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gamma-integral-converges-locally-uniformly</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gan-ginzburg-skryabin-inputs-hold-for-the-type-a-pyramid-good-grading</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gap-three-sat-reduces-to-gap-independent-set</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gapped-projector-map-well-defined</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-garnir-straightening-of-polytabloids</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-bonnet-expression-is-independent-of-the-metric</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-collocation-weighted-defect-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-content-lemma</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-half-system-permutation</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-hypergeometric-series-geometric-tail</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-jacobi-rule-data-well-defined</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-jacobi-weight-finite-moment-measure</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-lemma-over-a-ufd</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-lower-half-lattice-count</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-monic-three-term-recurrence</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-quadrature-rule-data-well-defined</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-reduction-step-improves-a-positive-definite-form</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gauss-weight-residual-gap-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-anchored-conditional-quantile-coupling</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-anchored-sum-density-moderate-deviation-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-anchored-sums-have-cumulant-and-fourier-bounds</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-centering-for-bounded-symmetric-quasiconvex-loss</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-convolution-kl-and-log-square-second-order-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-decay-gives-an-entire-fourier-laplace-transform</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-density-integrals-for-supplied-length-measures</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-elimination-produces-a-pivot-permutation</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-error-contrast-is-multivariate-normal</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-even-moment-bound-for-brownian-increments</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-exponential-mixture-integral</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-fourier-summability-kernel-is-an-approximate-identity</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-integral-is-finite-and-positive</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-kernels-form-an-approximate-identity</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-kullback-leibler-covariance-formula</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-linear-and-quadratic-statistic-tail</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-location-kl-formula</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-matrix-law-normalization-and-second-moments</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-matrix-orthogonal-unitary-invariance-and-block-independence</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-maximum-differential-entropy-under-variance</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-mixture-boundary-crossing-equivalence</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-noise-orthogonalization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-quadratic-form-centered-even-moment-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-sequence-empirical-bayes-posterior-formula</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-smoothing-of-finite-complex-measures</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-sparse-covariance-mixture-lower-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-square-is-the-plane-gaussian-integral</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-squared-norm-tail</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gaussian-superposition-nonunique-han-kobayashi-region</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-gcd-basic-values</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gcd-euclidean-step</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gcd-scaling</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gcr-kernel-and-mackey-borel-characterizations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-hecke-cellular-simple-labels-match-the-basic-crystal</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-general-hecke-residue-branching-endpoints-from-normalized-schur-cells</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-ito-integral-is-independent-of-the-approximating-sequence-and-ae-representative</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-linear-group-scheme-and-its-coordinate-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-linear-quotient-stacks-are-algebraic</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-linear-stiefel-frame-spaces-have-the-cohomology-gap</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-linear-stiefel-perverse-normalization-is-exact-and-conservative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-measurable-finite-group-randomization-validity</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-position-makes-a-whitney-disk-embedded-and-interior-disjoint-in-the-stable-range</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-solution-of-the-one-dimensional-wave-equation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-thom-isomorphism-from-the-relative-serre-spectral-sequence</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-general-variety-function-field-charts</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-generalized-bayes-loss-update-normalizes-to-a-probability-measure</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-generalized-central-character-submodules-are-direct-summands</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-generalized-delta-system-for-small-supports</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-generalized-eigenspace-trace-decomposition</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-generalized-inverse-sublevel-identity</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-generalized-niceness-yields-four-reduction-outcomes</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-generalized-ritz-values-monotone-under-nested-subspaces</loc>
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<priority>0.5</priority>
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<loc>https://alphabetamath.cc/item/lem-generalized-weight-space-decomposition-for-a-nilpotent-subalgebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generated-boolean-filter-and-ultrafilter-tests</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generated-in-degree-d-is-a-quotient-of-free-fi-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generated-lambda-system-closed-under-intersections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generated-lambda-system-exists-and-is-minimal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generated-monotone-class-closed-under-complements</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generated-monotone-class-closed-under-intersections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generated-monotone-class-exists-and-is-minimal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generated-submodule-as-finite-linear-combinations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generation-degree-bounds-surjectivity-degree-and-weight</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generator-hom-functor-is-exact-coproduct-preserving-and-faithful</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generator-of-a-unitary-group-is-skew-adjoint</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generator-of-the-contour-semigroup-is-the-sectorial-operator</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-complex-algebraic-whitney-regularity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-cyclotomic-local-dictionaries-glue-to-a-tower</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-cyclotomic-type-a-support-is-bounded-by-rank</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-freeness-finite-type-algebra-module</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-klr-induction-and-restriction-mixed-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-linear-coordinate-makes-a-holomorphic-germ-regular</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-nondegenerate-local-inverse-tables</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-pfaffian-ring-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-pfaffian-straightening</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-shapovalov-radical-on-a-casimir-hyperplane</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-symmetric-determinantal-ring-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-generic-symmetric-minor-straightening</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-geodesic-scaling-identity</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-geodesic-segments-have-isometric-ultralimits</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geodesic-triangles-in-trees-are-tripods</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geodesics-can-be-continued-while-their-velocity-lifts-remain-in-a-compact-subset</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-geometric-braids-admit-generic-polygonal-representatives</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-geometric-cancellation-is-a-unit-entry-in-the-handle-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-geometric-dirac-operator-is-well-defined</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-geometric-drift-minorization-reduces-to-bounded-small-set</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-geometric-far-commutativity</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-fibre-choice-independent</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-intersection-descends-through-oriented-cobordism-of-cycles</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-geometric-intersection-numbers-are-isotopy-invariants</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-geometric-markov-chain-has-adjacent-iid-split-tours</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-median-majority-radius-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-oscillation-decay-implies-a-holder-modulus</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-reversible-chain-rho-mixing</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-sequence-null</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-series-invertibility-in-the-completed-character-ring</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-simplices-intersect-in-the-realization-of-their-common-face</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-geometric-split-renewal-gives-integrable-hitting-time</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-strong-mixing-gives-lp-poisson-solution</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-three-strand-braid-relation</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometric-total-variation-rate-controls-strong-mixing</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometrically-ergodic-chain-has-standard-borel-observation-factor</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-geometry-tensor-gap-bounds-cellwise-form-defect</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-germ-equivalence-relation</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-germ-neighborhoods-form-a-riemann-surface-basis</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-germs-of-local-diffeomorphisms-form-a-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-germs-of-orientation-preserving-diffeomorphisms-of-the-line-at-zero-are-torsion-free</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-getzler-radial-gauge-oscillator-leading-term</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gibbs-block-refresh-is-conditionally-independent</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gibbs-block-update-is-a-probability-kernel</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gibbs-block-update-is-reversible-and-invariant</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gibbs-scan-schemes-are-probability-kernels</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-giraud-tangent-directions-and-controlled-transforms</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gitik-restriction-amalgamation-and-prikry-property</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gitik-strong-compact-support-homogenization</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gitik-support-approximation-and-bounded-stage</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-glm-mean-and-variance-identities</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-glm-product-density</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-global-cubic-model-minimizer-decrease</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-global-dimension-is-detected-on-cyclic-modules</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-global-fiber-basis-trivializes-serre-monodromy</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-global-intersection-length-sum-local-lengths</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-global-residue-pairing-dimension-balance</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-global-residue-pairing-injective-left</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-global-section-effective-divisor</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-global-sections-left-exact</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-global-sheaf-ext-long-exact-in-first-variable</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-global-smooth-strictly-psh-defining-function</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-global-square-class-approximation</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gls-information-matrix-is-positive-definite</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-glueing-homogenized-ideals</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-gluing-broken-index-two-trajectories-gives-collar-ends</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gluing-continuation-solutions-gives-collar-ends</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-gluing-handle-morse-models-along-collars</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gluing-lemma-for-plane-subharmonic-functions</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gluing-manifolds-with-boundary-along-a-boundary-diffeomorphism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-gnf-left-recursion-elimination-preserves-language</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gnf-substitution-step-preserves-language</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-godbillon-vey-form-is-independent-of-the-choice-of-eta-up-to-an-exact-form</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-godbillon-vey-form-is-invariant-under-rescaling-the-defining-form</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-godel-beta-coding-and-q-remainder</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-godunov-flux-for-burgers-is-continuous-and-consistent</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-good-clopen-family-for-summable-slaloms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-good-copy-extension-count</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-good-cover-nerve-computes-singular-cohomology</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-good-polynomial-reduction-kills-inertia</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-good-quotient-local-on-target</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-good-reduction-stable-under-base-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-good-tree-watson-omega-sequence-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-good-tree-watson-selector-obstruction</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-goursat-four-triangle-boundary-cancellation</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-goursat-nested-triangle-selection</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-graded-additive-functor-preserves-colimits-iff-right-exact-and-coproduct-preserving</loc>
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<loc>https://alphabetamath.cc/item/lem-graded-algebra-isomorphism-transports-the-graded-module-category</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-balanced-tensor-and-shift-isomorphisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-c-n-modules-equivalent-to-ungraded-c-n-1-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-chern-character-respects-relative-maps-and-skeletal-filtrations</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-degreewise-direct-sums-and-homogeneous-free-covers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-fitting-decomposition-preserves-homogeneous-summands</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-grothendieck-group-of-a-m-is-free-on-the-shifted-vertex-projectives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-hard-lefschetz-has-a-canonical-primitive-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-invariants-of-localization-at-an-invariant-element</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-module-kernels-cokernels-and-biproducts-are-degreewise</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-nakayama</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-section-module-finite-projective</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-graded-tensor-functor-is-k-linear-right-exact-coproduct-preserving-and-shift-coherent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-gradient-flow-identifies-the-local-and-global-attaching-regions</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gradient-like-perturbation-separates-adjacent-critical-levels</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-gram-map-fibers-and-rank-strata</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-gram-map-torsor-descent-and-codimension-extension</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-grand-maximal-function-controls-admissible-radial-and-nontangential-maximal-functions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-grand-maximal-function-is-dominated-by-the-tangential-maximal-function</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-graph-as-pullback-diagonal</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-graph-closed-separated-target</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-graph-distance-is-a-metric-on-each-component</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-graph-patch-extension-family-has-dispersive-and-ltwo-slice-bounds</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-graph-reachability-is-an-equivalence-relation</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-graph-transversality-is-fixed-point-nondegeneracy</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-graphs-on-three-vertices-are-not-prime</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-grassmannian-standard-affine-charts</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-greedy-colouring-bound</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-greedy-set-cover-charging-bound</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-green-boundary-cancellation-under-finite-gluing</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-coproduct-products-converge</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-green-cross-square-counting-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-green-distinguished-summands-are-mutually-inverse</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-envelope-dichotomy-and-logarithmic-pole</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-exceptional-family-containment-and-fusion</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-green-function-uniformizes-simply-connected-surface</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-hall-coproduct-coefficients-are-finite</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-green-hall-coproduct-is-coassociative</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-induction-has-one-distinguished-summand</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-kernel-exists-after-removing-a-chart-disc</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-kernel-resolvent-identity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-green-kernel-symmetry-on-riemann-surfaces</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-green-mackey-intersections-force-proper-vertices</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-restriction-has-one-distinguished-summand</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-type-i-boundary-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-green-type-ii-boundary-identity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-green-vertex-retention-and-inducing-lift</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-grid-cycle-for-runge-approximation</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-grid-reduction-of-a-multivariate-polynomial</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-grid-stability-transfers-under-uniform-norm-comparison</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ground-aleph-n-is-countable-in-the-feferman-levy-model</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-group-algebra-bimodule-is-induced-from-the-diagonal</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-group-cancellation</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-group-homomorphism-basic-properties</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-group-inverse-laws</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-group-labelled-homology-lemma-realizes-group-ring-handle-bases-by-isotopy</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-group-labelled-whitney-tricks-realize-the-diagonalized-handle-complex</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-group-power-laws</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-group-ring-modification-lemma-for-embedded-spheres</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-group-rings-have-invariant-basis-number-via-augmentation</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-groups-of-order-pq-have-a-normal-q-subgroup</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-growth-comparison-is-a-preorder</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-growth-is-unchanged-by-quotienting-a-finite-normal-subgroup</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-gysin-specialization-bivariant-and-base-change</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-h-cobordism-handle-complex-is-contractible-over-the-group-ring</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-h-cobordisms-admit-two-index-normal-form-presentations</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-h-five-and-co-e-free-family-has-the-erdos-hajnal-property</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-h-five-overlap-classes-are-connected</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-h-five-overlap-quotient-iteration-terminates-at-a-pure-blockade</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-h-one-local-length-comparison-for-a-conjugate-free-geodesic</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-h-one-regular-local-implies-koszul-regular</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-h1-stabilizes-downward-point-removal</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-h2-zero-boundary-p1-interpolant-conforming</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-haar-averaging-projects-onto-the-intertwiner-space</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-haar-candidate-sets-have-the-finite-intersection-property</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-haar-change-of-variables-under-inversion</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-haar-covering-functionals-are-asymptotically-additive</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-haar-covering-ratios-are-finite-and-positive</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-haar-integral-comparison-inequality</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-haar-lifts-and-borel-descent-on-a-homogeneous-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-haar-measure-is-positive-on-nonempty-open-sets-and-finite-on-compact-sets</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-haar-regularization-of-transitive-unitary-cocycles</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-haar-translations-are-strongly-continuous-on-lp-one-and-two</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-hadamard-gaps-bound-additive-representations</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-haefliger-nulltransversal-disk-has-a-minimal-one-sided-cycle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-hahn-banach-one-step-extension</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-half-nine-lemma</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-half-open-boxes-form-an-elementary-family</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-half-open-boxes-generate-the-borel-sigma-algebra-on-rn</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-half-order-kernel-translation-modulus-in-l1</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-half-order-product-integration-stability-and-consistency</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-half-order-product-weights-closed-form</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-half-order-singular-integral-exists</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-half-space-chart-transitions-extend-locally-to-side-preserving-diffeomorphisms</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-half-space-stokes-for-a-compactly-supported-form</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-half-space-trace-has-the-fractional-slobodeckij-bound</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-hall-and-dj-borel-conventions-are-isomorphic</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-hall-composition-full-exactly-finite-dynkin</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hall-euler-form-is-additive</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<loc>https://alphabetamath.cc/item/lem-halting-oracle-is-not-computably-dominated</loc>
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<loc>https://alphabetamath.cc/item/lem-hh-classical-tensor-centralizer-by-polarization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-coefficient-extension-and-finite-tensor-separation</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-coinvariants-form-a-subspace</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-coinvariants-of-free-hopf-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-colored-permutation-rsk-and-tableau-square-count</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-commutative-or-cocommutative-antipode-is-involutive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-commuting-left-right-hecke-length-operators</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-comodule-kernels-quotients-and-coefficient-identities</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-componentwise-initial-row-straightening</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-convolution-algebra-associativity-and-unit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-counit-uniqueness-and-finite-sweedler-calculus</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-cyclotomic-anti-involution-fixes-generators</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-cyclotomic-commuting-jucys-murphy-generators</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-cyclotomic-component-shift-and-dominance-ideals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-cyclotomic-straightening-spanning</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-demazure-lusztig-operators-satisfy-affine-relations</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-dihedral-root-recurrence-and-root-sign</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-double-coalgebra-and-antipode-descent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-double-crossing-map-and-associativity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-every-comodule-element-lies-in-a-finite-subcomodule</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-comatrix-coalgebra-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-direct-summands-over-khh-are-free</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-dual-regular-hopf-module-construction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-matrix-and-module-preliminaries</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-matrix-rank-under-specialization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-polynomial-and-localization-constructions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-semisimple-matrix-double-commutant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-spanning-list-contains-a-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-finite-tensor-duality-and-canonical-coevaluation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-formal-deformation-matrix-unit-lifting</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-free-associative-ring-and-relations-descent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-free-right-right-hopf-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-group-and-polynomial-hopf-algebras-exist</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-hecke-anti-involution-bar-and-normalization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-hopf-module-coinvariant-projection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-idempotents-lift-over-formal-power-series-rings</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-langlands-dominant-projection</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hh-local-braiding-operators-obey-braid-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-one-parameter-formal-series-local-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-positive-affine-parameter-has-infinite-quantum-characteristic</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-quantum-and-hecke-tensor-actions-commute</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-quantum-presentation-and-tensor-action-descent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-quasitriangular-counit-and-yang-baxter-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-rank-one-cyclotomic-quotient-monic-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-rational-spectral-r-matrix-satisfies-yang-baxter</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-reduced-word-independence-and-length-multiplication</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-regular-module-detects-linear-and-tensor-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-regular-trace-criterion-in-characteristic-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-right-dual-and-bidual-conditions</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-root-datum-affine-geometry-and-wall-parameters</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-signed-alcove-products-and-oriented-basis</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hh-sl2-q3-lattice-tree-and-iwahori-orbits</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-taft-algebra-pbw-and-hopf-structure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-tensor-algebra-regular-detection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-tensor-coherence-on-elementary-tensors</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-tensor-injections-quotients-and-kernels-over-a-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-tensor-product-coalgebra</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hh-type-a-finite-hecke-basis-in-multiplicative-normalization</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-type-a-garnir-straightening-and-murphy-cell-law</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-type-a-murphy-strong-tableau-straightening</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-type-a-quantum-antipode-descends</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-type-a-tensor-operator-is-a-hecke-symmetry</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hh-universal-presentations-and-base-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hierholzer-maximal-unused-edge-trail-closes</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-high-relative-cells-do-not-change-lower-homotopy</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-higher-direct-image-affine-localization</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-higher-direct-image-local-section-formula</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-higher-divided-quantum-serre-relations-by-skew-derivation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-higher-index-handle-attachments-do-not-change-lower-homology</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-higher-order-analytic-normal-form-reduces-to-a-first-order-system</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-higher-order-rolle</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-highest-and-lowest-weight-submodules-at-principal-series-reducibility-points</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-highest-weight-characters-are-unitriangular-in-weyl-orbit-sums</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-highest-weight-modules-have-weights-below-the-top-weight</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-highest-weight-of-a-finite-dimensional-module-is-dominant-integral</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-highest-weight-tensor-maps-and-their-adjunction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-highest-weight-vectors-in-a-schur-tensor-product-are-lr-tableaux</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-and-riesz-transforms-are-calderon-zygmund-operators</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-basis-degree-cancellation</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-cesaro-averages-converge-to-the-fixed-subspace</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-coherent-projective-bundle-construction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-complex-solver-from-coercive-estimate</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-cube-has-a-bimeasurable-real-coding</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-euler-polynomial-for-ample-polarization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-families-fpqc-descent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-family-vanishing-locus</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-noetherian-base-fixed-polarization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-polynomial-finite-scheme-length</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-projection-characterisation-by-a-variational-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-projective-space-construction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-proper-relative-ample-projectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-propositional-and-equality-rules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-rank-flattening-finite-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-regularity-independent-of-ambient-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-regularity-propagation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-relative-grassmannian-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-relative-regularity-and-base-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-symbol-depends-only-on-square-classes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-tikhonov-noise-amplification-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-tikhonov-normal-operator-invertible</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-transform-has-signum-fourier-multiplier</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-transform-is-skew-adjoint-on-ltwo</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-uniform-regularity-fixed-polynomial</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-uniform-sections-after-flat-pullback</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-universal-scheme-theoretic-flattening</loc>
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<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hilbert-valuative-flat-closure</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hk-smooth-mixed-derivative-formula</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hlr-balanced-cluster-tree-size-and-depth</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hlr-block-cluster-leaves-partition-index-pairs</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hlr-bottom-up-recompression-error-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hochschild-chains-are-bar-tensor-chains</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hodge-riemann-for-large-positive-deformation</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holder-cz-kernels-satisfy-hormander-cancellation</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holder-fourier-coefficients-have-weighted-ltwo-decay</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holder-interpolation-with-an-epsilon-loss</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holm-rejection-events-are-measurable</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-dependence-of-slice-laurent-coefficients</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-difference-quotient-is-holomorphic-in-each-variable</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-difference-quotient-is-jointly-continuous</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-difference-quotient-segment-formula</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-differentials-form-a-g-dimensional-space</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-differentials-separate-generic-points</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-functional-calculus-is-contour-independent</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-line-bundle-has-a-nonzero-meromorphic-section-on-a-compact-riemann-surface</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-logarithms-for-two-omitted-values</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-power-sums-of-slice-zeros</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holomorphic-structure-lifts-to-covering-surface</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holonomy-classes-form-a-groupoid-congruence</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holonomy-germ-is-independent-of-the-foliation-chart-chain</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-holonomy-respects-path-concatenation-and-reversal</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hom-from-a-finite-free-module</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hom-from-a-projective-object-makes-the-injective-resolution-columns-exact</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hom-from-projectives-counts-simple-composition-factors</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hom-into-an-injective-object-makes-the-projective-resolution-rows-exact</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hom-module-over-a-commutative-ring</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hom-to-costandards-counts-verma-flag-factors</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homeomorphism-criteria</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogeneous-curves-and-automorphisms-of-p1</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogeneous-dual-basis-sums-are-basis-independent-and-weightwise-finite</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogeneous-free-presentations-prove-the-graded-comparison</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogeneous-number-is-monotone-under-induced-subgraphs</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogeneous-poisson-ordered-event-time-density</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogeneous-polynomial-zero-locus-well-defined</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogeneous-right-multiplication-reconstructs-the-graded-kernel-action</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogeneous-sets-in-pure-blockade-patterns-lift-to-homogeneous-blockades</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogenization-dehomogenization-correspondence</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogenized-ideal-is-equivalent</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogenized-ideal-properties</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homogenized-ideal-under-smooth-morphisms</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homological-ahss-exact-couple-from-the-skeletal-filtration</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homological-and-internal-shifts-on-khovanov-seidel-k-zero</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homology-lemma-realizes-handle-bases-by-isotopy</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homology-of-an-infinite-cw-complex-is-the-colimit-of-skeletal-homology</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homomorphisms-from-a-simple-verma-module-have-dimension-at-most-one</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homomorphisms-respect-commutators-and-derived-series</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopic-grassmannian-maps-classify-isomorphic-bundles-and-conversely</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopic-maps-have-chain-isomorphic-mapping-cones</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopic-maps-with-a-common-regular-value-have-framed-cobordant-preimages</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopic-simple-proper-arcs-in-the-punctured-disk-are-isotopic-relative-to-their-endpoints</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopy-cardinality-base-change</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopy-cardinality-pushforward-is-functorial</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopy-excision-for-a-single-relative-cell-layer</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopy-fiber-component-weight-ratio</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopy-reflexive-and-symmetric</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-homotopy-transitivity-by-reparametrisation</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hone-functional-has-compatible-local-ltwo-representatives</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-honest-prover-maintains-the-claim-invariant</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hook-product-branching-identity</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hook-product-change-under-corner-removal</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hooks-are-bead-gap-pairs-on-an-abacus</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hooks-correspond-to-removable-border-strips</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hopf-first-lyapunov-coefficient-from-multilinear-data</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hopf-formula-subgroups-are-normal-and-the-quotient-exists</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hopf-ideal-kernels-and-quotients</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hopf-lax-infima-localise</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hopf-lax-minimiser-satisfies-the-characteristic-euler-relation-at-differentiability-points</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hopf-smooth-eigenpair-branch</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hopf-trace-formula</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hopf-weighted-trajectory-space-is-banach</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-horizontal-composition-of-natural-transformations-is-natural</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hormander-solver-on-smooth-pseudoconvex-domain</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-horn-replacement-block-has-injective-commutator-meridian</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-horseshoe-gives-a-short-exact-sequence-after-applying-a-right-exact-functor</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hp-analytic-polynomial-approximation-on-a-triangle</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hp-corner-uniform-degree-dof-count</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hp-simplex-p-explicit-conforming-interpolant</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hp-triangle-degree-uniform-strong-edge-lift</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hp-unweighted-legendre-derivative-tail</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hp-weighted-analytic-corner-pointwise-control</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-huber-contamination-mixtures-can-be-equalized-under-tv-threshold</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-huber-covariance-ambient-action-tail-lower-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-huber-covariance-contamination-modulus-lower-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-huber-covariance-mixture-is-a-probability-measure</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-huber-matrix-depth-estimator-operator-error</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hunt-exceptional-set-and-distribution-estimates</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hurwitz-matrix-exponential-decay-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hurwitz-negative-shift-matrix-invertible</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hybrid-guard-derivative-along-mode</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hybrid-mimetic-backward-euler-energy-and-compactness</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hyperbolicity-is-transported-by-a-quasi-isometry</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hyperderived-functors-are-independent-of-the-supplied-cartan-eilenberg-resolution-up-to-natural-isomorphism</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hyperelementary-permutation-subring-reduction</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-hypergeometric-binomial-contiguity-for-permutation-samples</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<loc>https://alphabetamath.cc/item/lem-hypersurface-deformations-classified-by-equation-deformations</loc>
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<loc>https://alphabetamath.cc/item/lem-hypersurface-smooth-iff-multiplicity-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-i-string-components-of-a-crystal-lattice</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ideal-class-group-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ideal-criterion-and-intersections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ideal-gas-entropy-conservative-flux-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ideal-generated-by-homogeneous-elements-is-graded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ideal-tukey-morphism-controls-add-and-cof</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-idempotent-gives-clopen-spectrum-partition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-idempotents-lift-through-finite-commutative-algebra-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-identity-diagram-large-limit-and-initial-objects</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-identity-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-bounded-variance-bernstein-tail</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-finite-moment-vector-strong-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-linear-truncation-occurs-only-finitely-often</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-normal-sample-mean-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-posterior-contraction-under-countable-sieves</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-posterior-denominator-lower-bound-from-kl-mass</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-sample-covariance-converges</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-sequential-likelihood-ratio-factorization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-iid-sieve-entropy-produces-exponential-tests</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-image-sheaf-is-sheafification-presheaf-image</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-images-of-finitely-generated-and-finite-groups-are-finitely-generated-and-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-imex-euler-local-branch</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-immersion-with-closed-image</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-immersions-and-localizations-monomorphisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-implicit-bidiagonal-qr-bulge-chase-unitary-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-implicit-q-uniqueness-for-unreduced-hessenberg</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-implicit-rk-stage-jacobian-nonsingular-on-branch</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-implicit-sensitivity-error-controlled-by-residual</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-improper-integral-splitting-and-tail-invariance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-incidence-convolution-associative-and-distributive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-incidence-convolution-inverses-by-recursion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-incidence-locus-is-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-incoherence-implies-restricted-eigenvalue</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-increasing-cech-complex-extends-to-alternating-tuples</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-increasing-reparametrization-of-finitely-many-critical-levels</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-increasing-sequence-of-coherent-subsheaves-stabilizes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-indecomposable-type-a-soergel-bimodules-are-classified-by-top-support</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-indented-arc-residue-limit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independence-has-finite-character</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-centered-hilbert-elements-have-zero-expected-inner-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-copy-symmetrization-tail-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-events-remain-independent-under-complements</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-families-pass-to-subfamilies</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-initial-vectors-give-independent-jordan-strings</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-list-is-injective</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-loxodromics-have-disjoint-pole-neighbourhoods</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-noise-extends-a-conditional-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-observation-posterior-denominator-lower-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-posterior-splitting-from-tests-and-sieve-tail</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-independent-tail-replacement-errors-are-monotone</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-index-grouped-relative-descending-paths-give-based-framed-handle-movies</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-index-map-grows</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-index-of-graph-bounded-region-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-index-one-dae-algebraic-residual-to-state-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-index-one-dae-backward-euler-local-branch</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-index-one-dae-bdf2-local-branch</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-index-sum-of-an-outward-field-is-the-gauss-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-index-sum-of-an-outward-field-on-an-even-dimensional-manifold</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-indicator-basis-for-invariant-functions-on-a-finite-orbit-partition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-indicator-expectation-and-products</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-blocks-have-controlled-defect</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-induced-copies-counted-by-extending-a-deleted-vertex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-copy-number-isomorphism-and-complement</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-embeddings-compose</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-freeness-passes-to-induced-subgraphs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-modules-from-finite-dimensional-b-modules-have-type-the-weights</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-outer-measure-agrees-with-premeasure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-representations-carry-a-canonical-system-of-imprimitivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-simplicial-chain-maps-commute-with-boundaries</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-singular-chain-maps-commute-with-boundaries</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-subgraphs-of-cographs-are-cographs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induced-word-map-has-the-free-extension-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inducing-an-irreducible-inertia-module-is-irreducible</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induction-commutes-with-an-external-tensor-factor</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induction-commutes-with-inflation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induction-from-the-inertia-group-recovers-the-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-induction-ideal-of-a-subgroup-family-is-an-ideal</loc>
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<loc>https://alphabetamath.cc/item/lem-induction-image-is-an-ideal-in-the-representation-ring</loc>
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<loc>https://alphabetamath.cc/item/lem-induction-is-invariant-under-conjugation-of-subgroup-and-representation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inductive-horseshoe-step</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inertia-of-a-stack-in-setoids</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inexact-fista-energy-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inexact-newton-error-recurrence-under-lipschitz-jacobian</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inexact-newton-krylov-finite-budget-checked-return</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inexact-proximal-gradient-one-step-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inf-epsilon</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-infinite-order-elements-have-positive-stable-translation-length</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-infinite-past-conditional-block-information-rate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-infinite-pigeonhole-on-the-naturals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-infinite-real-projective-space-is-a-marked-mod-two-eilenberg-maclane-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-information-matrix-perturbation-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-injective-darboux-function-is-strictly-monotone</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-injective-modules-flasque-and-ext-of-structure-sheaf</loc>
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<loc>https://alphabetamath.cc/item/lem-injective-sheaves-flasque</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inner-product-is-jointly-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-inner-product-pairing-is-nondegenerate-and-norm-is-homogeneous</loc>
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<loc>https://alphabetamath.cc/item/lem-int-bounded-above-has-greatest</loc>
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<loc>https://alphabetamath.cc/item/lem-int-cancellation</loc>
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<loc>https://alphabetamath.cc/item/lem-int-embeds-rat</loc>
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<loc>https://alphabetamath.cc/item/lem-integer-color-degenerate-hecke-klr-local-inverse-tables</loc>
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<loc>https://alphabetamath.cc/item/lem-integer-cyclic-presentation-descends-the-simple-head-generator-line</loc>
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<loc>https://alphabetamath.cc/item/lem-integer-order-bessel-recurrences-and-ode</loc>
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<loc>https://alphabetamath.cc/item/lem-integers-lattice-is-discrete-lca-group</loc>
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<loc>https://alphabetamath.cc/item/lem-integrability-can-be-checked-on-simple-root-sl2-subalgebras</loc>
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<loc>https://alphabetamath.cc/item/lem-integrability-on-a-subinterval</loc>
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<loc>https://alphabetamath.cc/item/lem-integrability-relations-for-a-dominant-highest-weight</loc>
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<loc>https://alphabetamath.cc/item/lem-integrable-rank-one-actions-force-the-quantum-serre-relations</loc>
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<loc>https://alphabetamath.cc/item/lem-integrable-signed-function-integration-against-density</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-additivity-over-a-content-zero-almost-partition</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-alcove-facet-displacements-lie-in-closed-bottom-alcove</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-based-modules-have-saturated-weyl-filtrations</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-closure-commutes-etale-base-change</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-closure-in-a-purely-inseparable-rational-envelope-is-finite</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-closure-unchanged-across-an-integral-intermediate-domain</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-cohomology-ring-of-complex-projective-space-by-splitting</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-crystal-residues-of-the-negative-half-represent-the-crystal-basis</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-divided-power-tensor-action-surjects-onto-type-a-q-schur-algebra</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-eilenberg-maclane-offset-five-homology-vanishes</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-geometric-layers-have-rounded-cutoff-bounds</loc>
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<loc>https://alphabetamath.cc/item/lem-integral-quantum-highest-weight-modules-identify-with-normalized-q-schur-weyl-cells</loc>
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<loc>https://alphabetamath.cc/item/lem-interior-w-two-p-regularity-for-the-laplacian</loc>
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<loc>https://alphabetamath.cc/item/lem-internal-arcs-of-a-reduced-small-cancellation-diagram-are-pieces</loc>
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<loc>https://alphabetamath.cc/item/lem-internal-faces-cancel-when-elementary-solid-regions-are-glued</loc>
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<loc>https://alphabetamath.cc/item/lem-internal-shift-endofunctors-and-tensor-compatibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-interpolation-absorbs-lower-order-sobolev-terms-in-elliptic-estimates</loc>
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<loc>https://alphabetamath.cc/item/lem-interpretation-translates-finite-derivations</loc>
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<loc>https://alphabetamath.cc/item/lem-intersection-multiplicity-drop-under-point-blowup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-intersection-of-primary-submodules-with-same-radical</loc>
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<loc>https://alphabetamath.cc/item/lem-intersections-of-finite-linear-complexes-form-a-convex-cell-complex</loc>
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<loc>https://alphabetamath.cc/item/lem-invariance-passes-to-orthogonal-complements-under-the-adjoint</loc>
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<loc>https://alphabetamath.cc/item/lem-invariant-forms-on-soergel-bimodules-are-unique-up-to-scalar-and-nondegenerate</loc>
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<loc>https://alphabetamath.cc/item/lem-invariant-irrep-produces-a-projective-inertia-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-irrational-circle-orbits-are-dense</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irrational-torus-flow-is-free-with-dense-orbits</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducibility-criteria-and-open-subspaces</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-affine-module-has-irreducible-ground-space</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-c-star-representations-separate-arbitrary-c-star-algebras</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-complex-varieties-are-analytically-connected</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-components-of-a-topological-space</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-group-vector-functionals-are-extreme-in-the-positive-dual-ball</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-holomorphic-germ-is-prime</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-polynomial-coefficients-in-a-complete-valuation-ring</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-row-substochastic-matrix-has-strict-weighted-contraction</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-space-open-intersections</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-submodule-is-primary-noetherian</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducible-weak-containment-in-a-family-selects-one-coefficient</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-irreducibles-are-prime-in-a-principal-ideal-domain</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isaacs-linear-character-step</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ising-unitary-normal-data-and-ribbon-coherence</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isogeometric-pullback-energy-norm-equivalence</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isolated-point-kelley-repair</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isolated-same-index-trajectory-passage-is-a-framed-handle-slide</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isometry-is-an-embedding</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isomorphism-characterised-by-composition-bijections</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isoparametric-cofactor-normal-perturbation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isoparametric-laplace-tensor-defect</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isoparametric-pullback-and-surface-metric</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isotopy-extension-for-a-compact-source-with-boundary</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isotropic-gaussian-noise-is-subgaussian</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-isotypical-evaluation-and-subspaces-of-multiplicity-spaces</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-awgn-feedback-estimation-covariance-update</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-awgn-feedback-rate-splitting-achievable</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-channel-resolvability-soft-covering</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-classical-wiretap-auxiliary-cardinality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-compact-compander-quantizer-is-borel-and-finite-distortion</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-conditional-type-class-cardinality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-conditional-typical-fan-cardinality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-cover-elgamal-salehi-conditional-packing</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-cq-typical-projector-dimension</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-degradable-channel-coherent-information-concavity-and-subadditivity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-dimension-dependent-quantum-entropy-continuity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-dmc-caid-conditional-variance-identity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-dmc-capacity-output-law-is-unique</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-dmc-dispersion-attains-minimum</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-dmc-mutual-information-concave-in-input</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-entanglement-assisted-information-is-additive</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-exponential-cq-spectral-projectors</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-fano-for-finite-message-density-observations</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-affine-slice-error-bound</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-classical-kl-nonnegative-equality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-codebook-covering-selection-law</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-conditional-entropy-continuity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-cq-block-sum-is-a-state</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-cq-wiretap-strong-secrecy-achievability</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-dmc-information-density-concentration</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-extension-from-purification-channel</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-gaussian-mixture-entropy-bounds</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-gentle-measurement</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-iid-rate-distortion-mutual-information-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-iid-source-lossless-code-achievability</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-kl-agrees-with-measurable-kl</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-log-sum-inequality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-marginals-and-conditionals-are-pmfs</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-mixture-entropy-bounds</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-pinsker-euclidean-bound</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-positive-square-root-is-order-preserving</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-povm-measurement-channel</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-product-law-is-iid</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-quantum-entropy-continuity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-random-bin-packing-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-rate-distortion-minimum-attained</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-relative-entropy-continuity-on-simplex</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-selected-codeword-markov-typicality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-superadditive-sequence-limit</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-type-class-cardinality-bounds</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-unitary-averaging-decoupling-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-vector-gaussian-water-level-allocation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-weyl-twirl-partial-trace</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-wiretap-product-kernel-is-stochastic</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-finite-wyner-ziv-function-convexity-continuity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-flagged-state-entropy-formula</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-flat-input-coherent-information-achievability</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-flat-input-entanglement-assisted-achievability</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-flat-spectral-type-information-approximation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-gallager-input-maxima-attained</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-gaussian-reference-kernel-information-lower-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-hayashi-nagaoka-finite-operator-inequality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-inverse-compression-resolvent</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-maximum-coherent-information-attained</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-multisource-block-conditional-law-factorization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-multisource-typicality-probability</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-n-type-approximation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-nearest-center-quantizer-is-borel-and-finite-distortion</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-number-of-n-types-polynomial-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-operator-jensen-negative-log</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-optimized-constant-composition-gallager-identity</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-ozarow-feedback-sum-corner-achievable</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-partial-traces-of-a-state-are-states</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-point-density-cumulative-map-is-c2-diffeomorphism</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-private-information-is-coherent-information-difference</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-quantum-and-private-information-product-additivity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-quantum-coherent-information-complement-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-quantum-entropy-maximized-at-maximally-mixed-state</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-quantum-entropy-support-and-finiteness</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-quantum-relative-entropy-isometric-invariance</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-quantum-relative-entropy-support-regularization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-qudit-erasure-channel-coherent-information</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-qudit-erasure-channel-complement-and-degradability</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-it-random-cut-ergodic-block-channel-approximation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-rate-distortion-convexity-and-monotonicity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-relative-modular-representation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-schmidt-rank-compression-fidelity-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-square-root-cq-packing-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-stationary-block-rdf-limit-and-endpoint-continuity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-type-class-cardinality-bounds</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-type-class-probability-bounds</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-type-probability-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-weighted-centroid-squared-error-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-it-wyner-ziv-auxiliary-cardinality-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iterated-brownian-integral-identities</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iterated-cofibers-rotate-with-suspension-reflection</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iterated-down-shifting-terminates-in-a-downward-closed-family</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iterated-kernel-density-convolution-bounds</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iterated-radial-derivative-identity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iterated-restricted-sparsification-reaches-the-target-scale</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iterated-sparse-restriction-reaches-the-target-sparsity-threshold</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iterated-suspension-and-winding-control-for-clifford-families</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iteration-restrictions-and-complete-embeddings</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iv-first-stage-is-complier-proportion</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iv-observed-contrasts-equal-potential-outcome-contrasts</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-iv-reduced-form-is-complier-effect</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jacobi-product-formula-for-the-discriminant</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jacobi-theta-transformation-laws</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jacobson-ring-prime-as-intersection-of-maximals</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-james-formula-defines-a-norm</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-james-noncompactness-sequence</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-james-norm-attainment-compactness-criterion</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-james-space-dual-and-bidual-identification</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jantzen-layer-dimensions-equal-the-gram-determinant-valuation</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-japanese-bracket-powers-preserve-schwartz-space</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jech-sochor-socks-transfer-is-uniformly-formalizable</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jensen-for-integrable-cost-random-variable</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-john-domain-admits-bounded-overlap-ball-chains</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-john-nirenberg-stopping-cubes-have-geometric-decay</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-join-irreducible-is-join-prime</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-joint-gaussian-blocks-with-zero-cross-covariance-are-independent</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-joint-jet-continuity-and-the-weak-smooth-topology</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-joint-measurability-of-spatial-recentering</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jointly-measurable-radon-nikodym-derivatives-for-probability-kernels</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jones-normal-density-discrete-bound</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jordan-block-automorphism-count</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jordan-chevalley-parts-agree-under-adjoint-representation</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jordan-holder-factors-of-verma-modules-lie-above-the-head</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jordan-quiver-category-is-finitary</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jordan-quiver-isoclasses-are-partition-indexed</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jordan-schoenflies-extension-for-plane-curves</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jordan-set-integral-well-defined</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jordans-lemma-rational-functions</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jucys-murphy-local-relations</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jump-is-well-defined-on-degrees</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-jumps-of-the-variation-function</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-finite-vectors-are-dense-and-stable-under-the-derived-action</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-finite-vectors-detect-nonzero-closed-invariant-subspaces</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-flat-abelian-sheaf-complexes-preserve-quasi-isomorphisms</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-sample-null-centering</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-theory-of-projective-space-and-projections</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-transitive-actions-are-k-homogeneous-and-lower-transitive</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-type-coefficient-formulas-for-the-sl2-discrete-and-principal-series</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-type-decomposition-of-the-sl2-principal-series</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-type-eigenvalue-recurrence-for-the-sl2-intertwiner</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-k-zero-vector-bundles-versus-coherent-sheaves</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kac-moody-chamber-boundary-stabilizers</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kac-moody-opposite-simple-centralizer-vanishes</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kac-moody-reduced-words-and-coroot-signs</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kac-moody-relation-module-embeds-in-verma-modules-and-obeys-the-casimir-constraint</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kahler-commutators-and-laplacian-type-preservation</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kak-integration-formula-for-k-bi-invariant-functions-on-sl2-r</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kalman-filter-is-exact-conditional-on-nonlinear-path</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kato-inequality-for-two-entropy-solutions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-katona-cyclic-interval-bound</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kazhdan-lusztig-mu-edges-and-left-cells-are-transported-by-star-operations</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kde-evaluation-is-a-measurable-statistic</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kde-jointly-measurable-in-sample-and-evaluation-point</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kelvin-inversion-and-the-laplace-operator</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kempe-component-colour-swap</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-and-rank-sequences-of-powers</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-basis-extension-gives-image-basis</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-composition-is-well-defined-and-associative</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-conjugation-by-an-element-of-the-coefficient-group-corresponds-to-a-principal-crossed-homomorphism</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-generators-for-the-weak-bgg-complex</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-inclusion-implies-the-norm-inequality</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-inclusion-implies-weak-containment</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-of-a-direct-sum-of-representations-is-the-intersection</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-of-an-induced-character-lies-in-the-inducing-subgroup</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-of-degree-two-inflation-is-the-transgression-image</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-of-identity-minus-compact-is-finite-dimensional</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-of-the-unit-logarithm-is-the-roots-of-unity</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-range-orthogonality-for-hilbert-adjoints</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-subgroup-in-a-group-extension-is-normal-and-the-quotient-is-the-base</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernel-tail-integrals-of-weighted-l-p-functions-are-finite</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kernels-of-finite-projections-form-an-open-normal-neighbourhood-basis</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-keyhole-branch-boundary-values</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kfold-cv-variance-covariance-decomposition</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-khovanov-rozansky-braid-oriented-kink-shifts</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-khovanov-rozansky-complex-is-invariant-under-braid-conjugation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-khovanov-seidel-basic-arcs-detect-the-identity-braid</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-khovanov-seidel-complexes-satisfy-far-commutativity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-khovanov-seidel-complexes-satisfy-the-three-term-braid-relation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-khovanov-seidel-curve-complexes-intertwine-the-braid-generators</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-khovanov-seidel-generator-complexes-are-mutually-inverse</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kification-compact-tests-and-finite-constructions</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-killed-and-absorbed-kernels-are-probability-kernels</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-killing-length-of-a-root-is-nonzero</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kirby-color-full-band-slide-and-coupon-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kks-form-is-independent-of-lie-algebra-representatives</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kl-invariant-under-measurable-bijections</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kl-neighborhood-prior-mass-likelihood-denominator-lower-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kleene-star-has-the-expected-least-closure-property</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-klr-maximal-tail-restriction-and-induction-have-a-unique-simple-head</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-klr-module-categories-are-krull-schmidt-with-shift-orbit-bases</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-klr-one-step-simple-restriction-induction-and-first-dot-index</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-klr-projective-duality-and-positive-divided-string-leading-terms</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-klr-two-color-jump-formula-and-strict-elementary-embeddings</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kneser-glaeser-rough-composition-on-flat-sets</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kojman-shelah-subspace-is-closed</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kojman-shelah-subspace-is-cofinal-and-has-successor-size</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kojman-shelah-tail-supremum-closure</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kolmogorov-atomic-kernel-maxima</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kolmogorov-block-maxima-diverge-off-a-null-limsup-set</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kolmogorov-block-polynomial-with-large-partial-sums</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kolmogorov-gliding-hump-series-converges-in-lone</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kolmogorov-simultaneous-phase-approximation</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-konig-alternating-reachability-cover</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kostant-adjoint-isotypic-multiplicities-have-zero-weight-rank</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kostant-harmonics-give-an-invariant-polynomial-complement</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kostant-laplacian-is-scalar-on-weight-components</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kostka-change-of-basis-is-dominance-unitriangular</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-append-one-element-mapping-cone-identification</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-coherence-for-derived-sheaf-tensor</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-complex-concatenation-tensor-isomorphism</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-complex-flat-base-change</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-complex-localises-termwise</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-depth-first-nonzero-cohomology</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-differential-coordinate-formula</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-differential-is-well-defined-and-squares-to-zero</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-differential-square-pairwise-cancellation</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-euler-characteristic-first-element-reduction</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-formula-is-necessary-for-a-levi-civita-connection</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-generator-contraction-homotopy</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-generator-matrix-chain-map</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-generators-act-null-homotopically</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-homology-finite-length-for-an-ideal-of-definition</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-mapping-cone-homology-exact-sequence</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-regular-implies-h-one-regular</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-resolution-and-flat-fibre-restriction</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-resolution-minimality-maximal-ideal-sequence</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-row-operations-and-variable-exclusion-preserve-factorization-homotopy-type</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-koszul-structure-of-the-abelian-sheaf-tensor-product</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kronecker-pairing-is-multiplicative-under-cross-products</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kronecker-reduction-lemma</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kronecker-summation-lemma</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kst-common-neighbour-double-count</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ku-representability-and-skeletal-postnikov-d-three-comparison</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-kuratowski-minors-are-topological-minors</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-class-of-complex-projective-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-genus-is-an-oriented-rational-bordism-ring-homomorphism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-genus-of-complex-projective-space-is-one</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-one-fourier-transform-is-well-defined</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-one-of-a-second-countable-group-is-separable</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-p-functions-have-sigma-finite-essential-support-for-finite-p</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-polynomials-form-a-well-defined-multiplicative-sequence</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-reductions-transfer-apx-hardness</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-series-coefficient-identity-for-projective-spaces</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-smoothness-descent-inequality</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l-two-with-the-integral-pairing-is-a-hilbert-space</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l1-action-of-a-unitary-representation</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l1-convolution-norm-inequality</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l1-convolution-with-an-l-infinity-function-is-left-uniformly-continuous</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l1-positive-weights-and-discrete-comparison</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l1-probability-densities-are-weak-star-dense-in-the-mean-set</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-l2-basis-projections-converge-and-satisfy-parseval</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ladder-separation-from-hyp</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lagrange-multiplier-is-unique-when-constraint-gradients-are-independent</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lagrangian-relation-sends-lagrangian-to-lagrangian</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lambda-fibres-are-gamma-2-orbits</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lambda-good-sets</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lambda-system-with-finite-intersections-is-sigma</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lambda-transformation-laws</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-landweber-filter-and-residual-identities</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-langevin-diffusion-density-reversibility-and-compact-minorization</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-langevin-gaussian-proposal-kernel</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-langevin-potential-exponential-generator-drift</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-language-concatenation-is-associative</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-laplace-fundamental-kernel-is-locally-integrable</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-laplace-fundamental-solution-is-harmonic-off-its-pole</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-laplace-resolvents-of-a-unitary-group</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-laplace-transform-uniqueness-identifies-two-exponentially-bounded-semigroups</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-large-cantor-cubes-are-not-separable</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-large-delaunay-supertriangle-exists</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-large-induced-subgraphs-in-the-property-star-four-outcome-theorem-contain-a-pure-or-x-sparse-polynomial-blockade</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-large-induced-subgraphs-without-a-polynomial-clique-or-stable-set-force-complete-or-anticomplete-blockades</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-large-positive-divisors-nonspecial</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-large-radius-polynomial-circle-loop-has-degree</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-large-semicircle-vanishing</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-large-y-part-in-a-structural-comb-partition-yields-a-homogeneous-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-largest-entry-of-a-standard-tableau-is-removable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-largest-summand-bound-for-symmetric-independent-variables</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lasso-objective-has-minimizer</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-last-vertex-map-is-carried-by-original-simplices</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lattice-eisenstein-sums-converge</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lattice-fundamental-parallelotope-partitions-euclidean-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lattice-paths-are-determined-by-their-step-words</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lattice-periodic-continuous-functions-are-determined-by-their-lattice-fourier-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-laurent-binomial-valuation-at-one-over-any-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-laurent-non-archimedean</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-laurent-series-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-laurent-valuation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-laver-guided-iteration-size-collapse-and-factorization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-law-of-a-random-element-is-a-probability-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-laws-commute-with-measurable-maps</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-layer-cake-identity-for-nonnegative-integrable-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lazy-walk-lengths-within-root-t-have-close-endpoint-laws</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lbfgs-curvature-bounds-imply-uniform-spectrum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lbfgs-two-loop-equals-stored-updates-and-cost</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-boolean-generic-truth</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-boolean-generic-zfc-and-ordinals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-complete-measures-small-fibres-and-inaccessibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-fine-measure-coordinate-family</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-fine-ultrapower-seed-and-normality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-generic-boolean-ground-joins</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-generic-evaluation-of-measurable-densities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-henkin-truth-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-inaccessible-size-and-rank-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-nonreflection-regressive-injection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-probability-algebra-completeness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-random-algebra-preserves-cardinals-and-sets-continuum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-random-coordinate-product-measure-pullback</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-scott-quotients-are-sets-and-membership-is-setlike</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-solovay-density-locality-and-null-joins</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-solovay-measure-on-generic-subsets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-tree-partition-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-ultrapower-critical-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lc-ultraproduct-quotient-well-defined</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-fourier-transform-intertwines-translation-modulation-and-convolution</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-fourier-transforms-form-a-dense-czero-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-group-has-an-open-compactly-generated-subgroup-with-no-open-subgroup-of-infinite-index</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-haar-measure-is-inversion-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-lone-character-topology-is-the-compact-open-topology</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-lone-convolution-is-a-commutative-banach-star-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-parseval-pairing-on-the-integrable-core</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-positive-convolution-squares-form-an-inversion-core</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-scalar-unitization-character-space-and-spectrum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-transform-range-is-dense-in-ltwo-of-the-dual</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lca-translations-and-normalised-local-approximate-identities</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lch-urysohn-cutoff-for-a-compact-set-inside-an-open-set</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-leading-coefficient-bound-for-a-reduced-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-leading-coefficient-ideals</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-leading-coefficient-is-minimal-in-a-reduced-class</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-leading-multidegree-of-a-symmetric-polynomial-is-a-partition</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-leading-multidegrees-of-elementary-symmetric-monomials</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-leading-tabloid-coefficient-of-a-standard-polytabloid</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-leaf-extension-copy-or-blockade</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-leaf-extension-copy-or-sparse-pair</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-leaf-reducible-families-yield-a-large-anticomplete-pair-or-a-more-restricted-induced-subgraph</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-least-absolute-remainder</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-least-absolute-residue-quadruple-of-a-multiple</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-least-feasible-sample-size-exists</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lebesgue-measurable-sets-have-small-open-excess</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lefschetz-hopf-index-formula-for-nondegenerate-fixed-points</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-lefschetz-numbers-of-the-two-lifts-sum-to-twice-the-base-lefschetz-number</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-left-and-right-amenability-agree-by-inversion</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-left-and-right-cosets-equinumerous</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-left-cell-equivalence-forces-equality-of-recording-tableaux-in-type-a</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-left-total-derived-functor-is-independent-of-the-supplied-projective-replacement-up-to-unique-natural-isomorphism</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-legal-tableaux-iff-all-local-windows-and-boundaries-are-legal</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-legendre-gauss-lobatto-nodes-are-distinct</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-legendre-weighted-derivative-orthogonality-and-norm</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-leibniz-determinant-forward-error-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-length-additive-products-of-standard-intertwiners</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-length-increasing-hecke-products</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-leray-hirsch-isomorphism-on-associated-graded-modules-lifts-without-extension-ambiguity</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-level-one-cusp-chart-and-compactness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-level-one-node-order-and-conjugation-dictionary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-levenberg-marquardt-large-damping-forces-sufficient-decrease</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-levenberg-marquardt-step-is-scaled-trust-region-minimizer</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-levi-pseudoconvexity-is-independent-of-defining-function</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-levy-maximal-inequality-for-independent-tail-sums</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-levy-prokhorov-distance-is-a-metric</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-levy-sigma-one-existential-normal-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lichnerowicz-formula-for-geometric-dirac-operators</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lichtenbaum-schlessinger-complex-and-cotangent-ext</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lie-algebra-of-a-semisimple-group-in-characteristic-zero-is-semisimple</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lie-algebra-of-the-general-linear-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lie-algebra-of-the-stabilizer-of-a-subspace-and-lie-stable-subspaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lie-algebra-quotient-bracket-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lie-algebra-tangent-space-and-functoriality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lie-ideals-and-normal-connected-subgroups-in-characteristic-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lie-strang-local-error-expansions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lift-a-map-through-degree-zero-of-a-projective-resolution</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lifted-determinant-sign-matches-sphere-side</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lifted-flip-potential-decreases</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lifted-power-sphere-determinant-identity</loc>
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<loc>https://alphabetamath.cc/item/lem-lifting-idempotents-in-complete-deformation-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lifting-residue-frobenius-by-galois-conjugates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lifts-of-circle-loop-concatenation-and-reversal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-likelihood-ratio-test-is-measurable-and-exact-size</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-likelihood-ratio-threshold-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-likelihood-tilted-measure-is-sigma-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-liminf-le-limsup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-liminf-passage-makes-the-weak-limit-a-minimiser</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limit-abs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limit-implies-local-boundedness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limit-is-local</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limit-legs-are-jointly-monic-and-colimit-legs-jointly-epic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limit-of-tail</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limit-points-of-unbounded-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limit-preserves-order</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limit-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limitwise-nullhomotopy-predicate-descends-to-a-normal-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limsup-epsilon-characterisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limsup-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limsup-monotone-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-limsup-reflection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lindeberg-condition-implies-feller-negligibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lindelof-degree-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-line-bundles-on-projective-three-space-restrict-by-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-line-integrals-are-independent-of-the-piecewise-c1-partition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-cardinal-interpolant-on-an-edge</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-clutching-splits-into-eigenbundles</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-combinations-of-compact-operators-are-compact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-congruence-reduction-by-the-gcd</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-contrast-statistics-are-borel-measurable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-elasticity-mixed-pressure-gauge-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-elasticity-rigid-body-gauge-system-is-nonsingular</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-functional-annihilating-kernel-of-a-surjection-is-a-transpose-multiple</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-functionals-separate-points-from-subspaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-gaussian-reference-ensemble-reproduces-kalman-filter</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-interpolation-error-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-isoperimetry-implies-uniformly-thin-geodesic-bigons</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-map-elementary-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-matrix-odes-have-unique-global-solutions-on-a-given-interval</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-multistep-order-conditions-from-taylor</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-order-completion-existence-uniqueness-and-density</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-primary-companion-block-is-similar-to-a-jordan-block</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-smoother-gcv-expression</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-subspace-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-subspace-is-a-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linear-system-incidence-is-smooth</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-linearity-of-the-bochner-integral</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linearizations-powers-and-equivariant-section-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-linearly-degenerate-characteristic-contact</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-linfinity-bmo-functions-dualise-hone-boundedly</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lipschitz-curves-and-dominated-interval-vector-measures</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lipschitz-formula-for-the-lattice-sum</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lipschitz-images-of-lebesgue-null-sets-are-lebesgue-null</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lipschitz-sde-local-solution-has-finite-path-moment</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lipschitz-sde-map-is-well-defined</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-listed-infinite-sigma-algebra-has-a-disjoint-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-littlewood-internal-product-outer-compatibility</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-littlewood-paley-reproducing-formula-in-tempered-distributions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lkb-deleting-the-last-puncture-gives-a-saturated-absolute-homology-inclusion</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lkb-lifted-absolute-cellular-boundary-and-fraction-field-rank</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lkb-small-end-neighbourhoods-stabilize-equivariantly</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-analytic-separation-and-saturated-borel-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-block-projection-controls-generalized-decomposition-support</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-local-boundary-separator-for-strongly-pseudoconvex-domain</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-boundedness-of-separately-holomorphic-functions</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-local-c-one-volume-distortion</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-local-c1-step-consistency-implies-tangent-adjoint-gradient-order</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-center-manifold-for-a-simple-hopf-point</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-characteristic-shock-curve</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-local-chevalley-restriction-for-kostant-freeness</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-compact-subgroups-of-hausdorff-groups-are-closed</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-comparison-of-a-riemannian-metric-with-the-euclidean-metric</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-composition-of-complex-power-series</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-composition-of-real-power-series</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-local-convergence-of-the-baker-campbell-hausdorff-series</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-coordinate-cup-products-generate-top-relative-cohomology</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-critical-value-lowering-preserves-the-upper-sublevel</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-dimension-reduced-variety-components</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-domain-dominated-by-valuation-overring</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-dvr-condition-implies-dimension-one</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-fibre-dimension-bound-via-polynomial-quasifiniteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-finite-dimensional-reduction-for-a-fredholm-map</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-fixed-point-index-is-coordinate-and-neighbourhood-independent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-fixed-point-index-is-invariant-under-diffeomorphism-conjugation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-fixed-point-index-splits-under-perturbation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-gauss-bonnet-sums-over-a-supplied-finite-geodesic-triangulation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-gch-absorbs-sums-and-squares</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-gch-hartogs-dichotomy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-generalized-poincare-bendixson-for-a-precompact-planar-orbit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-geodesics-in-a-hyperbolic-space-are-uniform-quasi-geodesics</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-global-dimension-equals-residue-field-projective-dimension</loc>
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<loc>https://alphabetamath.cc/item/lem-local-graph-flux-from-fubini-and-the-fundamental-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-hamiltonian-flow-preserves-symplectic-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-hartogs-extension-across-polydisc-shells</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-holder-cauchy-transform-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-holomorphic-logarithm-nonvanishing-function-on-disc</loc>
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<loc>https://alphabetamath.cc/item/lem-local-homomorphism-residue-field-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-index-is-additive-under-a-transverse-perturbation</loc>
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<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-intersection-as-vanishing-order-on-smooth-curve</loc>
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<loc>https://alphabetamath.cc/item/lem-local-intersection-forms-embed-in-primitive-lefschetz-forms</loc>
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<loc>https://alphabetamath.cc/item/lem-local-intersection-length-finite</loc>
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<loc>https://alphabetamath.cc/item/lem-local-isometries-send-geodesics-to-geodesics</loc>
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<loc>https://alphabetamath.cc/item/lem-local-koszul-acyclicity-inductive-converse</loc>
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<loc>https://alphabetamath.cc/item/lem-local-koszul-h-one-detects-first-regularity-failure</loc>
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<loc>https://alphabetamath.cc/item/lem-local-lemma-conditional-probability-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-local-length-comparison-for-a-conjugate-free-geodesic</loc>
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<loc>https://alphabetamath.cc/item/lem-local-linear-normalized-moment-matrix-converges-in-probability</loc>
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<loc>https://alphabetamath.cc/item/lem-local-lipschitz-class-empirical-process-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-local-lipschitz-derivative-quadratic-remainder</loc>
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<loc>https://alphabetamath.cc/item/lem-local-logarithmic-derivative-zeta</loc>
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<loc>https://alphabetamath.cc/item/lem-local-morse-sublevel-pair-is-a-handle-pair</loc>
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<loc>https://alphabetamath.cc/item/lem-local-normal-p-complements-force-control-of-fusion</loc>
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<loc>https://alphabetamath.cc/item/lem-local-normal-surface-modification-dimension-and-projective-cohomology</loc>
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<loc>https://alphabetamath.cc/item/lem-local-normalized-point-blowup-sequences-spread-at-closed-points</loc>
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<loc>https://alphabetamath.cc/item/lem-local-polynomial-projections-match-moments-through-order-s</loc>
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<loc>https://alphabetamath.cc/item/lem-local-postcomposition-chain-rule-for-w-one-two</loc>
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<loc>https://alphabetamath.cc/item/lem-local-q-one-deformation-proves-integrable-highest-weight-universality</loc>
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<loc>https://alphabetamath.cc/item/lem-local-rarefaction-fan</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-reciprocal-of-a-real-power-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-reciprocal-of-complex-power-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-residue-annihilator-regular-sections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-root-from-uniformly-small-residual</loc>
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<loc>https://alphabetamath.cc/item/lem-local-root-in-max-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-slice-for-a-free-proper-action</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-solvability-of-the-augmented-characteristic-ode</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-special-copy-trichotomy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-sphere-orientations-and-finite-puncture-excision</loc>
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<loc>https://alphabetamath.cc/item/lem-local-subharmonic-peak-function-globalizes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-sylow-conjugacy-ascent-for-fusion</loc>
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<loc>https://alphabetamath.cc/item/lem-local-wave-energy-conservation-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-local-yang-baxter-operators-satisfy-the-artin-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localisation-identity-for-a-divergence-form-weak-solution</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localisation-of-a-graded-ring-at-a-homogeneous-element</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localisation-of-a-primary-submodule</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localisation-of-cohen-macaulay-module-depth-dimension-equality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localisation-of-hom-natural-map</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-localisation-preserves-surjectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localisation-spectrum-map-homeomorphism-onto-image</loc>
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<url>
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<loc>https://alphabetamath.cc/item/lem-localised-hom-finite-presentation-kernel-step</loc>
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<loc>https://alphabetamath.cc/item/lem-localised-module-fraction-equivalence-is-an-equivalence-relation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locality-determines-formal-ope-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locality-of-subharmonicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localized-cone-triangles-satisfy-the-octahedral-axiom</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localized-cone-triangles-satisfy-tr-one-through-tr-three</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-localized-curved-patch-measure-transform-decay</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-bounded-holomorphic-families-are-locally-equicontinuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-bounded-separately-holomorphic-functions-are-locally-lipschitz</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-compact-second-countable-spaces-have-compact-exhaustions</loc>
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<loc>https://alphabetamath.cc/item/lem-locally-constant-functions-form-a-sheaf</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-contractible-metric-spaces-have-singular-constant-sheaf-cohomology</loc>
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<loc>https://alphabetamath.cc/item/lem-locally-finite-families-of-supports-have-locally-finite-cozero-families</loc>
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<loc>https://alphabetamath.cc/item/lem-locally-finite-linear-combinations-of-sections-are-smooth</loc>
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<loc>https://alphabetamath.cc/item/lem-locally-finite-smooth-partition-of-unity-on-domain</loc>
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<loc>https://alphabetamath.cc/item/lem-locally-finite-sums-are-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-finite-union-of-sigma-locally-finite-bases</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-split-cech-nerves-give-derived-cartesian-sheaf-descent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-trivial-acyclic-fibers-give-bounded-derived-pullback-equivalences</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-unique-ode-solutions-agree-and-glue-on-overlaps</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-locally-zero-locus-clopen-holomorphic-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-log-determinant-concavity-on-positive-definite-matrices</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-log-gaussian-density-supnorm-controls-local-likelihood-distances</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-log-power-regularity-after-endpoint-substitution</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-log-series-extends-by-the-product-law</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithm-branch-for-a-linear-factor-on-a-disc</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmic-caccioppoli-estimate-for-positive-supersolutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmic-derivative-of-the-radial-volume-jacobian-is-the-distance-laplacian</loc>
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<loc>https://alphabetamath.cc/item/lem-logarithmic-derivative-order-residue</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmic-derivative-zeta-left-half-plane</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmic-energy-strict-positivity-for-zero-mass-charges</loc>
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<loc>https://alphabetamath.cc/item/lem-logarithmic-integral-asymptotic-expansion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmic-norm-bounds-the-matrix-exponential</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmic-norm-is-real-and-variational</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmic-potential-distributional-laplacian</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmic-unit-image-is-discrete</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logarithmically-many-iterations-reach-constant-gap</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logdet-information-perturbation-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-loggamma-product-tail-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-loggamma-series-convergence-and-gamma-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-loggamma-shift-independent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-loghom-barrier-gradient-is-dual</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logrank-risk-fraction-converges</loc>
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<loc>https://alphabetamath.cc/item/lem-logrank-risk-set-empirical-fractions-converge</loc>
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<loc>https://alphabetamath.cc/item/lem-logrank-score-martingale-expansion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-logspace-machines-have-polynomially-many-configurations</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-long-exact-sequence-of-a-triple-in-singular-homology</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-long-run-covariance-is-trace-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-loop-products-in-a-topological-group-agree-up-to-homotopy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lorentz-cone-log-barrier</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lorentz-stabilizers-and-connected-cover-preimages</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-low-arity-stasheff-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-low-degree-filtration-sequence-for-a-first-quadrant-bicomplex</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-lower-central-quotients-of-finitely-generated-nilpotent-groups-are-finitely-generated-abelian</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lower-central-series-terms-are-characteristic-ideals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lower-lifted-facets-cover-the-convex-hull</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lower-limit-line-is-regular-and-lindelof</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lower-limit-plane-antidiagonal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lower-median-of-odd-empirical-sample-is-middle-order-statistic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lower-posterior-median-is-measurable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lower-rank-artin-letters-conjugate-x-letters-within-the-free-kernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lowest-weight-space-is-the-nilradical-invariant-line</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-loxodromic-elements-have-north-south-boundary-dynamics</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lp-interpolation-absorbs-lower-order-derivatives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ltwo-almost-orthogonality-of-dyadic-pieces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ltwo-and-divergence-data-embed-in-h-minus-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ltwo-atoms-have-uniform-hone-quasinorm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ltwo-fourier-decay-implies-absolute-convergence-by-cauchy-schwarz</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ltwo-fourier-multiplier-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ltwo-normalisation-of-sine-modes-on-the-interval</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lub-implies-nested-intervals</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-lusztig-and-kashiwara-normalizations-match-by-root-color</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lusztig-asymptotic-algebra-and-specialization-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lusztig-divided-power-form-is-a-hopf-integral-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-luzin-property-n-gives-an-integral-growth-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-lz78-distinct-parse-ziv-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-m0w-finite-projection-and-tail-bvm-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-m0w-separable-and-projection-tails</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ma-produces-an-uncountable-q-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-ma-reduction-to-small-ccc-orders</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-machine-encoding-is-injective-and-decodable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mackey-induction-classification-for-regular-euclidean-duals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mackey-support-for-homs-between-finite-principal-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-majority-error-bound-from-chebyshev</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-manifold-bump-for-a-compact-set-inside-an-open-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-manifold-exhaustion-passes-local-duality-to-the-colimit</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-many-good-two-t-vertex-sets-force-many-homogeneous-k-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-many-one-implies-turing-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-many-one-reducibility-is-a-preorder</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maps-of-compactifications-preserve-remainders</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-marcinkiewicz-interpolation-from-weak-one-one-and-strong-two-two</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-marginal-covariance-of-linear-mixed-model</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-margulis-diamond-weight-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-margulis-family-is-constant-degree-and-neighbor-computable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-markov-kakutani-fixed-point-theorem-for-abelian-affine-actions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-markov-moves-preserve-oriented-closure-isotopy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-martingale-differences-are-orthogonal-in-l2</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maslov-correction-composes-for-lagrangian-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maslov-index-four-lagrangian-cocycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-matching-nurbs-patch-traces-give-h1-conformity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-matern-native-space-fourier-identity-and-positive-definiteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-matern-spectral-integral-and-normalization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-matern-weighted-fourier-space-is-hilbert-and-injective</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-matrix-action-defect-variation-of-constants</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-matrix-algebra-is-a-c-star-algebra</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-matrix-chapman-kolmogorov-equations</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-matrix-depth-gaussian-scale-constant-exists-uniquely</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-matrix-depth-maximizer-exists-on-compact-classes</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-matrix-inversion-preserves-ck-regularity</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-matrix-rank-detected-by-nonzero-minors</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-matrix-unit-multiplication</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-matrix-variance-intrinsic-dimension-at-least-one</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-max-is-sup</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-maximal-acyclic-spanning-subgraph-is-a-spanning-tree</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-algebraically-independent-subset-is-a-transcendence-basis</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-maximal-chains-of-the-boolean-lattice</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-maximal-distributional-dbar-operator-is-closed</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-maximal-divisor-pivot-for-pid-submodules</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-maximal-dyadic-cubes-at-height-lambda</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-dyadic-cubes-covering-a-proper-open-set</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-dyadic-subcubes-of-a-cube-at-a-height</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-element-annihilator-primality-step</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-maximal-ideal-residue-field-of-an-affine-algebra-is-finite</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-ideals-are-points-over-algebraically-closed-field</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-ideals-of-c-of-x-and-zero-set-ultrafilters</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-label-vectors-in-a-finite-truncation-are-singular</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-non-finitely-generated-ideal-is-prime</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-non-finitely-generated-ideal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-ode-solution-extends-from-compact-tube</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-order-preserved-by-controlled-transform</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-orthogonal-family-of-cyclic-reducing-subspaces</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-pattern-pure-blockades-force-many-blocks</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-proper-closed-subgroups-of-a-profinite-group-are-open</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-regular-sequence-stops-at-associated-prime</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-regular-sequences-have-common-length-ext</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-residue-injective-subfield</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-tori-extension-conjugacy-and-derived-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-verma-is-projective-in-a-finite-truncation</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maximal-weight-verma-peels-off-a-standard-filtration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maxwell-discrete-incidence-identities</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-maxwell-edge-ritz-projection-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maxwell-finite-dimensional-ode-existence-uniqueness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maxwell-magnetic-compatible-initial-projection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maxwell-nedelec-smooth-interpolation-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maxwell-periodic-yee-consistency</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maxwell-rectangular-stokes-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-maxwell-yee-step-matrix-is-positive-definite</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-mccormick-envelope-equals-graph-convex-hull</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-mct-implies-archimedean</loc>
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<loc>https://alphabetamath.cc/item/lem-mct-implies-lub</loc>
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<loc>https://alphabetamath.cc/item/lem-meagre-master-codes-below-summable-slaloms</loc>
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<loc>https://alphabetamath.cc/item/lem-mean-and-covariance-determine-gaussian-finite-dimensional-laws</loc>
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<loc>https://alphabetamath.cc/item/lem-mean-measure-and-integrals-of-a-random-point-process</loc>
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<loc>https://alphabetamath.cc/item/lem-mean-value-inequality-for-a-differentiable-banach-valued-curve</loc>
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<loc>https://alphabetamath.cc/item/lem-mean-value-theorem-on-closed-interval</loc>
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<loc>https://alphabetamath.cc/item/lem-mean-zero-kernel-scale-estimate</loc>
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<loc>https://alphabetamath.cc/item/lem-mean-zero-ltwo-functions-on-a-cube-embed-continuously-in-hone</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mean-zero-poincare-estimate-on-bounded-connected-extension-domains-for-p-less-than-n</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-density-chart-integrals-agree-on-overlaps</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-fields-of-nonempty-compact-sets-have-measurable-dense-selections</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-functions-preserve-independence</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-gram-schmidt-and-constant-field-trivializations</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-matrix-depth-maximizer-selection</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-minimum-norm-geometric-median-selection</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-null-code-orders-bound-constructible-null-unions</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-observation-does-not-increase-mixing-coefficients</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-posterior-quantile-and-cdf-bracketing</loc>
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<loc>https://alphabetamath.cc/item/lem-measurable-rejection-function-defines-randomized-test</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-measurable-sections-have-measurable-pointwise-inner-products</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-measurable-von-neumann-algebra-fields-have-measurable-commutants-and-centers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mehler-supertrace-normalization-is-ahat-times-relative-chern-character</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-meromorphic-jensen-formula-with-centre-divisor</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mesh-of-iterated-barycentric-subdivision-tends-to-zero</loc>
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<loc>https://alphabetamath.cc/item/lem-mesh-of-iterated-simplicial-barycentric-subdivision-tends-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metastable-cohomology-of-eilenberg-maclane-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metastable-embedding-for-maps-from-a-compact-manifold</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-ball-neighbourhood-base</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-borel-hierarchy-monotonicity-and-operations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-cauchy-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-cauchy-with-convergent-subsequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-convergent-implies-cauchy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-critical-crossing-preserves-pointed-disk-pairs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-end-flow-matching-gives-local-broken-charts</loc>
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<loc>https://alphabetamath.cc/item/lem-metric-graph-kirchhoff-green-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-graph-p1-interpolation-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-limits-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-morse-smale-end-counts-form-chain-complexes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-nonnegativity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-open-covers-have-point-finite-refinements</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-outer-measure-boundary-layer-continuity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-point-finite-refinements-can-be-made-locally-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-projection-onto-a-nonempty-closed-convex-set-is-nonexpansive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-properness-agrees-with-proper-discontinuity-on-proper-discrete-metric-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-reverse-triangle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-spaces-have-sigma-discrete-open-bases</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-spaces-have-sigma-locally-finite-bases</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metric-uniformity-dictionary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metrics-on-rn</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metrizable-spaces-are-collectionwise-normal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-metropolis-hastings-density-ratio</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mgf-of-independent-finite-sum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mgrit-exact-coarse-elimination</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mgrit-recursive-work-and-visits</loc>
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<loc>https://alphabetamath.cc/item/lem-mgrit-two-level-call-counts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-middle-dimensional-intersection-form-is-symmetric-and-nondegenerate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-middle-handle-pairs-with-one-geometric-intersection-cancel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-middle-lefschetz-primitive-polarization-follows-from-nonmiddle-polarizations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-midpoint-bvp-discrete-linearized-inverse</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-midpoint-convexity-extends-to-dyadic-weights</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-midpoint-nystrom-collective-compactness-and-consistency</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-midpoint-quadrature-defect-for-p1-stiffness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mihlin-dyadic-pieces-sum-to-an-off-support-kernel-representation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-milnor-sphere-bundles-with-euler-number-plus-or-minus-one-are-simply-connected</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-milstein-local-defect-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mimetic-fv-parabolic-limit-identification</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-minimal-algebraic-relator-area-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-minimal-area-diagrams-are-reduced</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-minimal-cauchy-filter-associated-to-a-cauchy-filter</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-minimal-cauchy-filter-space-is-complete</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-minimal-free-matrix-induces-zero-on-residue-ext</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-free-resolution-differentials-land-in-maximal-ideal</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-free-resolution-reduces-to-zero-differential</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-free-resolutions-unique-up-to-chain-isomorphism</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-normal-subgroups-of-finite-groups-are-characteristically-simple</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-minimal-parabolic-diagrams-have-pbw-bubble-normal-form</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-parabolic-polynomial-flag-model-realizes-the-graded-diagram-relations</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-parabolic-relative-canonical-line-bundle-root-weight</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-polynomial-is-invariant-under-field-extension</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-power-diagram-has-a-periodic-boundary-shell</loc>
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<loc>https://alphabetamath.cc/item/lem-minimal-walk-functions-are-coherent-and-finite-to-one</loc>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/lem-mixed-hodge-complexes-give-functorial-cohomology-and-simplicial-weights</loc>
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<loc>https://alphabetamath.cc/item/lem-mod-null-invariant-sets-have-strictly-invariant-representatives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mod-two-cohomology-ring-of-infinite-real-projective-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mod-two-cohomology-rings-of-complex-projective-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mod-two-degree-is-well-defined-and-homotopy-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mod-two-eilenberg-maclane-base-and-path-loop-inputs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modc-bounded-rank-structure-varieties-have-finitely-many-orbits</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modc-internal-end-reconstruction-and-eilenberg-watts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modc-module-category-rank-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modc-module-deformation-complex-contracts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modc-module-functor-categories-are-finite-semisimple</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modc-module-functors-have-adjoints-and-separable-monads-split</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modc-separable-algebra-object-duals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modc-surjective-orbit-tangents-give-finite-orbits</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-models-of-coded-zf-are-infinite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modification-lemma-for-embedded-spheres-in-a-handle-presentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modified-patankar-euler-positive-tube-local-error-and-stability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modified-pcp-reduces-to-pcp</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modular-gauss-sums-and-kirby-color</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modular-group-reduction-to-the-standard-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modular-hom-state-spaces-have-exact-sewing-inverses</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modular-hopf-matrix-squared</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modular-quotient-local-charts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modular-trace-depends-only-on-the-p-regular-part</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modular-trace-functions-of-simple-modules-are-linearly-independent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-module-criteria</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-module-elementary-consequences</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-module-finite-domain-extension-lifts-finite-prime-chains</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-module-jacobi-formal-delta-substitution-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-module-relative-hilbert-samuel-polynomial-for-koszul-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-modules-are-complement-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mollification-commutes-with-weak-derivatives-in-the-interior</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mollified-biot-savart-kernel-is-smooth-globally-lipschitz</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-moment-bound-for-a-random-sign</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-moments-give-derivatives-of-the-characteristic-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monic-polynomial-capacity-lower-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monogenic-prime-factorisation-by-polynomial-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monoid-units-form-a-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monomial-bases-of-bergman-spaces-of-disc-ball-and-polydisc</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monomial-induced-representations-transversal-model-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monomial-inequivalence-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monomial-integrals-over-disc-ball-and-polydisc</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monomial-irreducibility-criterion</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-monomial-representation-has-a-monomial-matrix-model</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monomiality-lifts-along-a-quotient</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monomorphism-diagonal-isomorphism</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotone-and-diagonal-lattice-paths-correspond</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotone-chebyshev-tauberian-desmoothing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotone-fv-discrete-kruzhkov-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotone-fv-local-compactness-and-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotone-fv-update-preserves-range-and-tvd</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotone-good-sets-for-algebra-elements</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotone-unbounded-diverges</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotone-with-interval-image-is-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-monotonicity-of-union-and-intersection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-moore-club-extension-for-minimal-walks</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-moore-no-cross-injection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-moore-penrose-products-are-orthogonal-projectors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-moore-topology-is-hereditarily-lindelof</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-moore-topology-is-nonseparable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-morphism-equality-on-dense-open</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-morphism-schemes-local-on-source-target</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-morphisms-from-the-constant-sheaf-are-global-sections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-morphisms-of-mixed-hodge-structures-are-strict</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-morphisms-of-sheaves-determined-by-stalks</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-morse-functions-are-transverse-differentials</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-morse-smale-transversality-is-equivalent-to-surjectivity-of-the-linearized-flow-operator</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-morse-splitting-induction-preserves-the-residual-hessian</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-morse-trajectories-have-positive-energy-drop</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-moser-iteration-for-positive-supersolutions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-moser-pullback-differentiation-equation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-most-strings-are-incompressible</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-moving-block-bootstrap-conditional-covariance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-mprk22-1-positive-tube-local-error-and-stability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multicolored-ribbon-coupon-evaluation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multidimensional-refinement-inequalities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multilinear-extension-streaming-evaluation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multilinear-extension-table-evaluation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multilinear-minor-pfaffian-ideal-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multilinearization-preserves-boolean-values</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multinomial-law-normalization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multiple-choice-produces-maximal-antichains</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multiples-below-a-prime-power</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multiplication-by-n-on-abelian-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multiplicative-filtered-cochains-induce-products-on-all-spectral-sequence-pages</loc>
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<loc>https://alphabetamath.cc/item/lem-multiplicative-type-affineness-by-field-descent</loc>
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<loc>https://alphabetamath.cc/item/lem-multiplicative-type-groups-are-linearly-reductive</loc>
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<loc>https://alphabetamath.cc/item/lem-multiplicative-type-groups-split-separably</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multiplicative-type-local-hopf-dictionary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multiplicity-of-a-type-i-factor-representation-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multiscale-primitive-map-to-continuous-cdfs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multistep-martingale-characterization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multitape-simulation-has-quadratic-time-overhead</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multivariable-geometric-series-on-a-distinguished-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-multivariate-mean-rate-given-correct-scale-event</loc>
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<loc>https://alphabetamath.cc/item/lem-multivariate-trimmed-mean-selector-total-and-measurable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-murnaghan-littlewood-top-degree-reduced-coefficients-are-lr-coefficients</loc>
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<loc>https://alphabetamath.cc/item/lem-mutual-independence-under-subfamilies-and-complements</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-n-minus-coinvariants-map-injectively-into-the-kernel-of-the-differential</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-n-plus-invariants-exist-in-every-nonzero-o-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-na-bernoulli-polynomial-identities</loc>
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<loc>https://alphabetamath.cc/item/lem-na-cell-average-l2-projection</loc>
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<loc>https://alphabetamath.cc/item/lem-na-chebyshev-degree-bound-from-recurrence</loc>
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<loc>https://alphabetamath.cc/item/lem-na-chebyshev-recurrence-angle-identity</loc>
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<loc>https://alphabetamath.cc/item/lem-na-clenshaw-curtis-dct-i-orthogonality</loc>
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<loc>https://alphabetamath.cc/item/lem-na-closed-newton-cotes-eight-panel-weights-and-exactness</loc>
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<loc>https://alphabetamath.cc/item/lem-na-compact-support-hcurl-fourier-splitting</loc>
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<loc>https://alphabetamath.cc/item/lem-na-complex-product-six-operation-roundoff-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-na-computed-unitary-butterfly-error-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-na-continuous-pressure-recovery-from-solenoidal-residual</loc>
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<loc>https://alphabetamath.cc/item/lem-na-contractible-lipschitz-polyhedron-boundary-connected</loc>
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<loc>https://alphabetamath.cc/item/lem-na-convex-support-localization-and-lipschitz-dual-gradient</loc>
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<loc>https://alphabetamath.cc/item/lem-na-coordinate-soft-threshold-minimizer</loc>
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<loc>https://alphabetamath.cc/item/lem-na-d4-multilevel-detail-support-and-moments</loc>
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<loc>https://alphabetamath.cc/item/lem-na-diagonal-diffusion-discrete-initial-trace</loc>
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<loc>https://alphabetamath.cc/item/lem-na-diagonal-diffusion-stencil-is-monotone</loc>
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<loc>https://alphabetamath.cc/item/lem-na-discounted-bellman-policy-matrix-inverse-positive</loc>
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<loc>https://alphabetamath.cc/item/lem-na-discrete-gradient-lift-gap-estimate</loc>
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<loc>https://alphabetamath.cc/item/lem-na-elliptic-spacetime-jets-imply-parabolic-hjb-inequalities</loc>
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<loc>https://alphabetamath.cc/item/lem-na-eno2-reconstruction-third-order</loc>
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<loc>https://alphabetamath.cc/item/lem-na-full-dirichlet-hcurl-regular-decomposition</loc>
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<loc>https://alphabetamath.cc/item/lem-na-graded-whitney-mesh-size-and-boundary-shifts</loc>
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<loc>https://alphabetamath.cc/item/lem-na-weak-hcurl-tangential-trace</loc>
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<loc>https://alphabetamath.cc/item/lem-na-weak-local-potentials-and-continuation</loc>
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<loc>https://alphabetamath.cc/item/lem-na-weno5-optimal-linear-reconstruction</loc>
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<loc>https://alphabetamath.cc/item/lem-na-whitney-averaged-pullback-moment-bounds</loc>
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<loc>https://alphabetamath.cc/item/lem-na-whitney-cochain-correction-and-strong-convergence</loc>
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<loc>https://alphabetamath.cc/item/lem-na-whitney-moments-commute-with-grad-curl-div</loc>
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<loc>https://alphabetamath.cc/item/lem-nagao-error-terms-have-zero-trace-on-the-relevant-p-section</loc>
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<loc>https://alphabetamath.cc/item/lem-naive-all-pairs-collision-search-has-quadratic-work</loc>
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<loc>https://alphabetamath.cc/item/lem-nakayama-kernels-give-well-defined-adjoint-functors</loc>
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<loc>https://alphabetamath.cc/item/lem-names-for-pairs-functions-and-ordinals</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-add-associative</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-add-cancellative</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-add-commutative</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-add-identity</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-add-successor-left</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-discrete</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-embeds-int</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-finite-sum-laws-and-the-canonical-embedding</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-mult-cancellative</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-mult-commutative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-mult-distributive</loc>
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<loc>https://alphabetamath.cc/item/lem-nat-mult-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-no-zero-divisors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-nonzero-is-successor</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-order-add-compatible</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-order-is-membership</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-successor-neq-self</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-transitive-irreflexive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nat-trichotomy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-natural-cubic-spline-second-derivative-perturbation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-natural-higher-diagonal-approximations-on-singular-chains</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-natural-logarithm-bounded-by-argument</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-natural-number-game-strategies-have-continuum-many-plays</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-natural-singular-cohomology-identities-are-detected-on-finite-regular-complexes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-near-identity-c-one-maps-sandwich-cubes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-near-iid-exchangeable-arrays-have-convergent-means</loc>
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<loc>https://alphabetamath.cc/item/lem-near-iid-exchangeable-arrays-have-convergent-sample-covariances</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-negation-scales-the-local-index-by-minus-one-to-the-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-negative-half-reversal-preserves-integral-and-crystal-lattices</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-negative-laurent-powers-are-cleared-by-hopf-line-stabilization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-negligible-morphisms-form-a-tensor-ideal-by-partial-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nelder-mead-finite-budget-returns-status</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nerode-equivalence-is-a-right-congruence</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-nested-domain-induction-for-interior-elliptic-derivatives</loc>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-nested-model-deviance-nonnegative</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-nested-pinched-center-frontier-has-a-strict-inner-disk-search</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-neumann-compatibility-from-the-divergence-theorem</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-neumann-invertibility-for-finite-matrices</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-neumann-series-and-small-perturbations-of-bounded-inverses</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-nevanlinna-growth-dominates-logarithm</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-nevanlinna-poisson-jensen-derivative-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nevanlinna-ramification-counting-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nevanlinna-sup-mean-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-newman-damped-contour-estimates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-newton-contraction-near-an-invertible-derivative</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-newtonian-potential-is-well-defined-for-compactly-supported-bounded-data</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nice-refinement-exists-and-is-not-lindelof</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nilpotent-group-structure-and-maximal-torus-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nilpotent-lefschetz-filtration-is-canonical-and-self-dual</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nilpotent-orbit-equivariant-tensor-covariants-extend-and-polarize</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-nitsche-fractional-weak-green-and-flux-cancellation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nitsche-h-one-zero-functions-have-zero-facet-traces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nitsche-local-polynomial-flux-inverse-trace</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-nitsche-scaled-fractional-simplex-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-augmenting-path-gives-tight-cut</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-large-epsilon-sparse-subgraph-bounds-k-stable-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-new-critical-points-under-a-compact-c1-small-perturbation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-nowhere-zero-tangent-field-on-a-positive-even-sphere</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-property-star-outcome-forces-a-small-structural-block-partition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-recursive-bound-covers-all-recursive-unary-languages</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-return-sets-have-null-preimage-towers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-small-subgroups-in-a-lie-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-transversal-leaf-bounds-a-positive-accessibility-region-with-finite-inward-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-no-vertex-is-mixed-on-many-blocks-of-a-semisparse-blockade</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-noether-normalisation-finite-field-exponent-substitution</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-noether-normalisation-inductive-integrality</loc>
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<loc>https://alphabetamath.cc/item/lem-noether-normalisation-nonzero-polynomial-made-monic</loc>
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<loc>https://alphabetamath.cc/item/lem-noether-normalisation-one-relation-reduction</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-approximation-fp-algebra-module-system</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-approximation-proper-fp-flat-sheaf</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-domains-are-atomic</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-flatness-by-fibres-finite-target-module</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-local-flatness-criterion-finite-over-target</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-local-flatness-tor-killing-base-change</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-minimal-primes-induction-split</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-open-subsets-are-quasi-compact</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-ring-maximal-element-annihilator-exists</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-space-has-finitely-many-irreducible-components</loc>
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<loc>https://alphabetamath.cc/item/lem-noetherian-subspaces-and-compact-opens</loc>
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<loc>https://alphabetamath.cc/item/lem-non-braid-like-reidemeister-moves-are-generated-by-braid-like-moves-and-reductions</loc>
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<loc>https://alphabetamath.cc/item/lem-nonabelian-supersolvable-group-has-a-noncentral-normal-abelian-subgroup</loc>
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<loc>https://alphabetamath.cc/item/lem-nonabelian-supersolvable-group-has-the-required-abelian-normal-subgroup</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-affine-and-finite-morphism-fppf-descent</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-affine-group-faithful-representation</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-affine-nilpotent-thickening</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-affine-normal-subgroup-products</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-ample-finite-type-projective-immersion</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-ample-line-bundle-field-descent</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-antiaffine-factor-rigidity</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-centre-is-stable-jet-kernel</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-characteristic-zero-group-smooth</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-commutative-torsor-norm-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-connected-group-geometrically-connected</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-divisorial-valuation-restriction-model</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-effective-affine-algebra-descent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-exact-group-sequence-affine-smooth-connected-properties</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-finite-field-descent-of-morphisms</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-finite-field-descent-scheme-with-affine-orbits</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-finite-relation-saturated-affine-neighbourhood</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-flat-hypersurface-slice</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-generic-quasisection-flat-groupoid</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-group-target-rational-indeterminacy-divisors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-holomorphic-rational-map-product-curves-algebraic</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-line-bundle-affine-space-parameter-constancy</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-multiplication-pullback-symmetric-line-bundle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-normal-completion-smooth-locus-antiaffine</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-normal-subgroup-inverse-multiple-character</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-pseudo-abelian-separable-field-extension</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-rational-action-composition-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-rational-map-normal-to-proper-codimension-two</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-reduced-neutral-subgroup-over-perfect-field</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-regular-local-picard-principal-localization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-rigidity-proper-geometrically-integral-factor</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-smooth-affine-open-cartier-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-smooth-connected-group-has-ample-line-bundle</loc>
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<loc>https://alphabetamath.cc/item/lem-nonaffine-subgroup-scheme-stabilizer-of-line</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonaffine-theorem-of-the-cube-for-abelian-variety</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonarchimedean-absolute-value-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-noncharacteristic-complex-stratified-pullback-is-perverse-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-noncommutative-filtered-exponential-and-logarithm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonconstant-local-uniform-limits-of-univalent-functions-are-univalent</loc>
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<loc>https://alphabetamath.cc/item/lem-nondegenerate-critical-points-are-isolated</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nondegenerate-czero-representations-have-regular-pvms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nondegenerate-dyadic-simplex-determines-unique-sphere</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nondegenerate-gaussian-small-ball-controls-log-radius</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nondegenerate-interval-is-not-null</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nondegenerate-local-holder-beltrami-coordinates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nondentability-produces-a-vector-measure-without-density</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nondeterministic-two-tape-simulation-with-linear-acceptance-time</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonempty-countable-set-has-a-padded-enumeration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonempty-fixed-vertex-set-of-a-tree-automorphism-is-a-subtree</loc>
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<loc>https://alphabetamath.cc/item/lem-nonempty-forest-has-low-degree-vertex</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonequivariance-defect-of-an-infinitesimal-moment-map-is-a-constant-lie-algebra-two-cocycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nongreen-simply-connected-surface-is-plane-or-sphere</loc>
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<loc>https://alphabetamath.cc/item/lem-noninaccessibility-in-l-produces-a-real-with-correct-omega-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonnegative-kde-integrates-to-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonnegative-square-root-exists-and-unique</loc>
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<loc>https://alphabetamath.cc/item/lem-nonnegative-test-pairings-imply-a-e-nonnegativity-for-ltwo-functions</loc>
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<loc>https://alphabetamath.cc/item/lem-nonreachability-has-an-inductive-counting-certificate</loc>
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<loc>https://alphabetamath.cc/item/lem-nonsingular-complex-algebraic-curve-holomorphic-charts</loc>
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<loc>https://alphabetamath.cc/item/lem-nonsingular-principal-minor-of-the-symmetrized-cartan-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonsingular-square-root-lift-modulo-odd-prime-powers</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonsquare-tangent-conic-rational-surface-blowups-terminate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nontrivial-limitwise-nullhomotopy-class-forces-compact-boundary-leaf</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nontrivial-normal-subgroup-of-a-n-contains-a-three-cycle</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nontrivial-normal-subgroup-of-a-solvable-group-has-an-abelian-normal-subgroup</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-compact-kernel-operators-yield-nonzero-positive-compact-k-star-k</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-derivative-gives-local-biholomorphism</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-echelon-rows-form-a-basis-of-the-row-space</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-finite-dimensional-complex-invariant-subspaces-have-unitary-eigenvectors</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-highest-weight-images-survive-modulo-n-minus</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-map-invertible-to-locally-free-injective</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-maps-between-specht-quotients-force-dominance</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-multiplicative-functionals-on-lca-lone-are-fourier-evaluations</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-number-field-ideal-has-finite-quotient</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-positive-compact-self-adjoint-operators-have-positive-finite-dimensional-eigenspaces</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nonzero-section-vanishing-at-a-point-has-positive-degree</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-norm-closed-convex-sets-are-weakly-closed</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-norm-implies-strong-implies-weak-operator-convergence</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-norm-of-a-self-adjoint-operator-from-its-quadratic-form</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-norm-point-of-a-compact-self-adjoint-operator-is-an-eigenvalue-up-to-sign</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-addition-is-a-local-diffeomorphism-along-the-zero-section</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-bundle-of-the-diagonal-is-canonically-tm</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-bundle-of-the-zero-locus-of-a-transverse-section</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-closure-of-a-radical-extension-is-radical</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-complete-surface-nonsingular-formal-arc-blowups-terminate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-cone-maximal-monotone-and-projection-resolvent</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-density-has-total-mass-one</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-domain-implies-r-one</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-domain-implies-s-two</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-extension-separable-over-maximal-purely-inseparable-subextension</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-finite-type-surface-resolution-globalizes-from-complete-local-points</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-form-pde-determines-a-unique-formal-taylor-series</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-form-string-types-and-their-geometric-intersection-contributions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-hall-subgroup-gives-a-coprime-extension</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-isotypical-component-is-inertia-stable</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-isotypical-components-are-permuted-by-translation</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-local-surface-radical-multiple-of-a-principal-divisor</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-location-scale-density</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-location-scale-mean-and-variance</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-measure-rowbottom-homogeneity</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-noetherian-domain-intersection-of-height-one-localizations</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-p-complements-pass-to-subgroups-and-p-local-normalizers</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-p-subgroup-has-proper-commutator-in-a-p-group</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-pontryagin-class-is-the-rational-inverse-of-the-tangent-pontryagin-class</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-projective-surface-dualizing-module-over-regular-local-base</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normal-push-off-zeros-are-self-intersection-points</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-quasisimple-subnormal-dichotomy</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-relative-property-t-controls-distance-to-invariant-vectors</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-restriction-constituents-form-one-conjugacy-orbit</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-second-derivative-recovered-from-the-elliptic-equation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-sequences-of-entourages</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-set-theoretic-tree-sequence-representation</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-stiefel-whitney-class-is-the-multiplicative-inverse-of-the-tangent-class</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-subgroup-containing-a-three-cycle-is-a-n</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-surface-fibre-divisor-conormal-degree-positive</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-surface-modification-leray-short-exact-sequence</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-surface-modification-no-derived-residue-map</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-surface-modification-uniform-principal-torsion-bound</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-surface-normalization-commutes-with-base-completion</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-surface-trace-cokernel-dualizes-h1-and-bounds-it</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-thom-class-realizes-the-poincare-dual-of-a-submanifold</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normal-upper-triangular-matrix-is-diagonal</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normality-is-closed-hereditary</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normality-local-on-affine-opens</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normality-via-shrinking</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normalization-commutes-with-restriction-open</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normalization-defect-euler-and-lengths</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normalization-factors-through-blowup-of-curve-point</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normalization-isomorphism-over-normal-locus</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normalization-lowers-arithmetic-genus-delta</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalization-unchanged-under-finite-birational-curve-map</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-approximate-haar-functionals-are-positive-and-invariant-in-the-limit</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-normalized-clutching-data-for-bundles-over-x-times-s-two</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-coefficient-approximation-for-irreducible-weak-containment</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-complex-gaussian-block-affine-spectral-second-moments</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-complex-rangefinder-direct-spectral-expectation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-fixed-halting-machine-for-boone-simulation</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-gradient-crosses-a-compact-regular-band-in-controlled-time</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-pin-spin-product-and-norm-laws</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-point-blowups-dominate-local-normal-surface-modifications</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-surface-point-blowup-resolution-descends-from-completion</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-two-cocycles-and-coboundaries-form-groups</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-two-square-count-is-multiplicative</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalized-type-a-soergel-bimodules-are-self-dual-and-have-length-degree-bounds</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalizer-action-permutes-weight-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalizing-a-locally-finite-positive-family</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalizing-a-locally-finite-positive-smooth-family</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-normalizing-a-scale-at-existing-least-upper-bounds</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nowhere-separable-suslin-line-nested-interval-tree</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nowhere-vanishing-algebras-approximate-the-constant-one</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-npsem-ie-implies-cross-world-independence-for-mediation</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nth-root-of-constant-tends-to-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nth-root-of-n-tends-to-one</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nth-term-test</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-nuclear-series-characterizes-trace-norm</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-nufft-certified-gaussian-gridding-returns-a-status</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<loc>https://alphabetamath.cc/item/lem-nufft-finite-euclidean-norm-triangle</loc>
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<loc>https://alphabetamath.cc/item/lem-nufft-gaussian-grid-alias-identity-and-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-nufft-gaussian-image-tail-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-nufft-gaussian-periodization-converges</loc>
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<loc>https://alphabetamath.cc/item/lem-nufft-gaussian-periodization-fourier-series</loc>
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<loc>https://alphabetamath.cc/item/lem-nufft-gaussian-spread-truncation-tail</loc>
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<loc>https://alphabetamath.cc/item/lem-null-characteristic-frontier-cap-transports-nullity-to-adjacent-annulus</loc>
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<loc>https://alphabetamath.cc/item/lem-null-homology-gives-the-plane-or-disc-alternative</loc>
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<loc>https://alphabetamath.cc/item/lem-null-homology-implies-connected-spherical-complement</loc>
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<loc>https://alphabetamath.cc/item/lem-null-is-cauchy</loc>
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<loc>https://alphabetamath.cc/item/lem-null-master-codes-and-summable-slaloms-are-tukey-equivalent</loc>
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<loc>https://alphabetamath.cc/item/lem-null-maximal</loc>
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<loc>https://alphabetamath.cc/item/lem-null-meagre-ideal-transfer-cantor-real</loc>
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<loc>https://alphabetamath.cc/item/lem-null-meagre-master-codes-are-cofinal</loc>
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<loc>https://alphabetamath.cc/item/lem-null-meagre-tukey-inequalities</loc>
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<loc>https://alphabetamath.cc/item/lem-null-sets-in-rn-closed-under-subsets-and-countable-unions</loc>
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<loc>https://alphabetamath.cc/item/lem-null-simple-center-frontier-supplies-the-exact-cancellation-scalar</loc>
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<loc>https://alphabetamath.cc/item/lem-null-times-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-nullhomotopy-persists-under-a-compact-transverse-deformation</loc>
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<loc>https://alphabetamath.cc/item/lem-number-field-completions-as-local-polynomial-factors</loc>
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<loc>https://alphabetamath.cc/item/lem-numerated-real-vector-bundle-embeds-in-finite-trivial-bundle</loc>
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<loc>https://alphabetamath.cc/item/lem-numerical-serre-rank-one-skew-kernel-is-integrable</loc>
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<loc>https://alphabetamath.cc/item/lem-nurbs-homogeneous-data-perturbation-geometry-bounds</loc>
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<loc>https://alphabetamath.cc/item/lem-nurbs-knot-cell-simplicial-geometry-adapter</loc>
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<loc>https://alphabetamath.cc/item/lem-nurbs-laplace-tensor-gap-under-map-error</loc>
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<loc>https://alphabetamath.cc/item/lem-nystrom-square-root-projector-identity</loc>
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<loc>https://alphabetamath.cc/item/lem-o-modules-admit-finite-highest-weight-filtrations-after-truncation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-objectwise-comparison-of-two-projective-resolution-data-induces-an-isomorphism-on-derived-objects</loc>
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<loc>https://alphabetamath.cc/item/lem-obm-consistency-from-strong-brownian-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-observed-data-likelihood-under-response-model</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-octonion-conjugation-is-an-anti-involution</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-odd-dimensional-wave-kernels-obey-the-radial-recursion</loc>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/lem-one-dimensional-p1-interpolation-error</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-one-dimensional-trace-truncation-compatibility</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-one-handle-slides-become-relative-kirby-slides-after-trading</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-one-point-extension-for-finite-dimensional-nonexpansive-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-one-quadrant-homoclinic-disk-has-one-more-interior-center-than-saddle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-one-relative-map-cell-kills-its-class-with-the-correct-fundamental-group-action</loc>
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<url>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/lem-open-restriction-of-desingularization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-open-subsets-of-r-are-countable-unions-of-rational-intervals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-open-subspace-complete-remetrisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-operational-chern-classes-and-whitney-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-operator-norm-is-a-norm</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-operators-commuting-with-a-point-separating-family-of-multiplications-are-multiplications</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-opposite-deligne-product-identifies-with-finite-bimodules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-opposite-index-nondegenerate-zeros-cancel-in-a-ball</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-opposite-local-signs-give-the-compatible-whitney-circle-framing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-opposite-rouquier-generator-complexes-are-homotopy-inverse</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-opposite-symmetrizable-kac-moody-borels-are-root-degreewise-dual-lie-bialgebras</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-oppositely-framed-points-are-framed-null-cobordant-in-pairs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-oppositely-monotone-functions-of-independent-coordinates-have-nonpositive-covariance</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-optimal-prover-may-be-deterministic</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-oracle-computation-has-a-finite-query-witness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-oracle-diagonalization-finite-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-oracle-truncated-covariance-and-vector-concentration</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-orbit-dimension-and-closed-orbits-for-complex-group-actions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-orbit-map-faithfully-flat-and-orbit-locally-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-orbit-map-fibres-and-stabilizer-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-orbit-maps-of-isometric-actions-are-coarse-lipschitz</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-orbit-polynomial-has-invariant-coefficients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-and-snc-under-smooth-morphisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-characterisation</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-function-one-dimensional-local-domain</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-order-ideals-form-a-distributive-lattice</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-order-of-a-power-in-a-finite-cyclic-group</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-of-element-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-of-five-modulo-two-powers</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-of-one-plus-pu-modulo-prime-powers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-of-the-relative-frobenius</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-p-actions-on-a-cyclic-q-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-order-semicontinuity-and-snc-strata</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ordered-arithmetization-evaluates-to-the-truth-value</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ordered-field-is-an-ordered-ring</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ordered-pairs-lie-in-the-double-power-set</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ordered-rational-automorphism-stabilizers-are-extremely-amenable</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ordered-ring-cone-and-order-agree</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ordinal-basics</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ordinal-definable-maximal-proper-ideal-in-the-basic-cohen-model</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ordinal-order-topology-is-t3</loc>
<lastmod>2026-08-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ordinal-product-as-an-order-type</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ordinal-sum-as-an-order-type</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ordinal-trichotomy</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ordinary-exchange-moves-are-markov-sequences</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orientation-coefficients-as-deck-eigenspaces-and-product-pairings</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-orientation-lines-orient-continuation-moduli-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-orientation-reversal-is-inverse-in-theta-n</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-orientation-twisted-diagonal-realizes-the-lefschetz-trace</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-area-vector-under-surface-reparametrization</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-boundary-of-a-compact-oriented-one-manifold-has-zero-signed-count</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-boundary-of-an-intersection-trace-has-opposite-end-signs</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-oriented-facet-cancellation-on-matching-meshes</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-grassmannian-has-two-lifted-schubert-cells</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-intersection-detects-nonvanishing-rational-homology</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-minimal-parabolic-klr-normal-forms-and-cyclotomic-cap-ideal-intersection</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-real-two-plane-splitting-with-injective-real-pullback</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-similarities-are-nonzero-complex-multiplications</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-simplex-comparison-for-an-ordinary-homology-theory</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oriented-simplicial-subdivision-commutes-with-boundary</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthogonal-complement-counting-for-the-commutator-pairing</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthogonal-complement-is-closed</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthogonal-complement-of-an-eigenspace-is-invariant</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthogonal-complements-under-invariant-forms-are-ideals</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthogonal-fv-compressible-viscous-flux-consistency</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthogonal-projection-is-linear-self-adjoint-contractive</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthogonal-projector-power-error-inequality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthogonality-of-characters-on-a-finite-cyclic-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-orthonormal-frame-fields-along-a-clean-whitney-disk-in-the-stable-range</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oscillation-characterisation-in-rn</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-oscillation-superlevel-sets-are-closed</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-outer-function-properties</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-outgoing-boundary-of-a-handle-attachment-trades-the-disk-factors</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-outgoing-helmholtz-kernel-is-a-fundamental-solution</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-overlap-controlled-union-lower-bound</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-overlap-of-arc-length-parametrizations-of-a-one-manifold</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-overlapping-plaques-through-a-point-have-compatible-germs</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-overlapping-proper-modules-of-a-connected-anticonnected-graph</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-adic-balls-are-clopen</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-adic-valuation-additive</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-adic-valuation-basic</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-adic-valuation-on-q</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-p-automizer-condition-implies-fusion-control</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-elementary-characters-are-induced-from-linear-characters</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-elementary-groups-are-supersolvable</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-four-free-pattern-graphs-have-square-root-homogeneous-sets</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-norms-are-norms-and-induce-the-published-metrics</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-power-polynomial-is-irreducible-when-its-constant-is-not-a-pth-power</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-power-torsion-dimensions-recover-elementary-divisors</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-primary-character-value-congruence</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-regular-elements-are-preserved-by-conjugacy-and-coprime-powers</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-residual-is-generated-by-p-prime-elements-and-idempotent</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p-surgery-kills-the-represented-pi-p-class-when-p-is-below-the-middle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-p0-box-projection-is-clipped-cell-average</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa-uniform-bounded-truth-proof-certificates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-ample-translation-splittings</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-complex-weight-central-character-separation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-flag-tdo-pbw-and-twist</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-global-section-unit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-localization-adjunction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-module-global-sections-derived-cohomology</loc>
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<loc>https://alphabetamath.cc/item/lem-pa36-nilpotent-normality-and-springer-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-p1-line-bundle-cohomology</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-partial-flag-twist-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-principal-nilpotent-borel-orbit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-qcoh-filtered-union-and-cech-colimits</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-relative-p1-singular-kernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-singular-parabolic-kernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-singular-verma-chain-and-generation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pa36-twisted-associated-bundle-and-parabolic-descent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-packing-covering-number-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-padded-irreducible-characters-have-character-polynomials</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-padding-completion-is-compatible-with-the-internal-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-padding-transfers-time-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-paired-regular-disk-sweep-is-open-across-its-base-gluing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pairing-preserves-convergence-in-probability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pairings-of-skeletal-exact-couples-induce-multiplicative-ahss</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pairwise-coprime-divisibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-bochner-l2-approximate-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-bochner-time-mollification</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-dirichlet-laplacian-is-positive-selfadjoint</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-discrete-energy-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-domain-map-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-energy-pairing-and-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-hilbert-bnb-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-mackey-biset-splitting-in-gl-n</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-measurable-form-operators-and-inverse</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-projection-time-product-rule</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-ritz-projection-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-theta-step-exists-uniquely</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-weak-compactness-separable-bochner-hilbert</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parabolic-zero-boundary-sobolev-space-is-separable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-paracompact-hausdorff-cover-shrinking</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-paracompact-hausdorff-is-regular</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-paradoxical-groups-admit-no-invariant-mean</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parallel-awgn-cost-constrained-achievability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parallel-awgn-information-density-convergence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parallel-awgn-single-use-information-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parallelizable-boundaries-form-a-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parameter-boundary-exceptions-do-not-affect-surface-integrals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parameter-dimension-drop-is-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parameter-ideal-equivalent-m-primary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parameter-ode-flow-tangent-on-common-tube</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parameter-power-series-map-injective-by-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parameter-power-series-subring-makes-ring-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parameter-selection-avoids-minimal-components</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parametric-immersion-extension-on-a-disk</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parametric-index-grouping-preserves-a-relative-descending-path</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parametric-qmd-score-has-mean-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parametrized-relative-elementary-handle-comparison</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parareal-first-k-nodes-are-fine-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parareal-sweep-work-and-span</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-parity-map-of-a-finite-contracted-complex-is-invertible</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-partial-fractions-for-a-split-recurrence-denominator</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-partition-conjugation-is-an-involution</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-partition-localization-of-stokes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pasted-squares-commute</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-path-class-projection-is-a-covering-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-path-conjugation-isomorphism-of-fundamental-groups</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-path-homotopy-traces-braid-isotopy</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-path-metric-on-a-tree-is-geodesic-and-integer-valued</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pbw-for-countably-presented-kac-moody-lie-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pbw-linear-independence-by-the-regular-representation-on-the-symmetric-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pbw-shows-the-dominant-cyclic-highest-weight-generator-survives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pbw-spanning-by-ordered-monomials</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pca-sample-covariance-is-a-measurable-estimator</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pcf-cofinality-ideals-and-cutoff-conventions</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-pchip-slope-selection-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pchip-slopes-second-order-uniform-grid</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pcp-verifier-reduces-to-gap-max-three-sat</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-pda-fragment-variables-compose</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pde-box-control-set-basic-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pde-box-control-set-weakly-sequentially-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pde-l2-control-space-separable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pdhg-one-step-gap-telescope</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe03-euler-llf-split-state-positive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe03-hll-half-cell-riemann-averages</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe04-cellwise-l2-projection-exists-best-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe05-discrete-weak-identity-with-source</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe05-hll-depth-flux-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe05-hll-dry-face-direction-and-zero-flux</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe05-strong-l1-limit-preserves-dry-admissibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe11-compact-self-adjoint-spectral-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe11-continuous-gauge-compact-embedding</loc>
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<url>
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<loc>https://alphabetamath.cc/item/lem-pe11-gauge-space-infinite-dimensional</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe11-smooth-nedelec-approximation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe11-zero-eigenvalue-is-curl-kernel</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe12-boundary-preserving-quasi-interpolation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe12-evolution-energy-chain-rule</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe12-minty-identification</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe12-outward-zero-brouwer</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe12-quasiuniform-mass-inverse-decay</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe12-space-time-gradient-weak-compactness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe12-w0p-separable-reflexive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe12-w1p-compact-l2-embedding</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe18-modal-trace-and-form-continuity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe18-outgoing-spherical-mode-expansion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe18-spherical-hankel-modulus-and-radiation-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe18-spherical-hankel-radial-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe18-spherical-harmonic-structure-and-density</loc>
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<loc>https://alphabetamath.cc/item/lem-pe26-complementary-primal-dual-spectrum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe26-discrete-trace-schur-equivalence</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe26-log-edge-cutoff-and-discrete-sobolev</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-pe26-preconditioned-operator-norm-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pe26-scaled-averaging-energy-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-peak-monotone-subsequence</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pell-norm-multiplication</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perfect-complexes-form-a-triangulated-subcategory</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perfect-dg-modules-have-finite-total-ext</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perfect-set-game-strategy-dichotomy</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perfect-subfield-of-a-one-step-root-extension-in-positive-characteristic</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perfect-vertex-deletions-imply-two-narrowness</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perfectness-is-equivalent-to-vanishing-morse-correction-polynomial</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-period-is-constant-on-a-communicating-class</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-period-pairing-is-well-defined-and-computed-by-integration</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-advection-amplification-symbols</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-averaging-on-cube</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-cell-corrector-wellposedness</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-cell-poincare</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-characteristic-map-is-orientation-preserving</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-composite-trapezoid-error</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-conjugate-square-identity</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-continued-fraction-is-quadratic</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-continuous-functions-are-determined-by-their-fourier-coefficients</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-cyclotomic-based-sl-two-tensor-corrections-escape-every-finite-cut</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-flow-departure-cells-have-positive-finite-volume</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-flux-corrector</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-fourier-mode-aliasing-under-sampling</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-fv-grid-reaction-diffusion-commutator-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-fv-grid-spatial-consistency</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-heat-difference-amplification-symbol</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-pic-shape-partition-and-quadrature-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-pic-smooth-assignment-weights</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-poincare-spectrum-matches-transverse-monodromy</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-tensor-interpolant-is-convex-and-linf-contracting</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-periodic-tensor-interpolation-hessian-error</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-permutation-consistency-from-iid-mixture</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-permutation-equivariant-score-map-preserves-exchangeability</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-permutation-mixture-coupling-for-two-sample-u-statistics</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-permutations-with-a-given-cycle-type-count</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perron-envelope-failure-of-the-supersolution-test-allows-a-local-bump</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perron-family-is-nonempty-and-bounded</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perron-kernel</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perturbed-observation-ensemble-kalman-moment-bounds</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-perverse-closed-support-splitting-is-equivalent-to-costalk-stalk-isomorphism</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pfa-raises-the-pseudointersection-number</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ph-adaptive-oracle-transcript-normal-form</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ph-circuit-matrix-final-block-encoding</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ph-quantifier-block-closure</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-phase-border-implies-periodic-bvp-linearization-bounded-inverse</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-phase-bordered-shooting-jacobian-invertibility</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-phase-field-interval-p1-projector-stability</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-phase-field-neumann-laplacian-kernel-and-gauge</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-phi-irreducible-chain-has-small-set</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-phi-series-converges-absolutely</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pi-three-so-three-generated-by-the-quaternion-double-cover</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-picard-group-and-intersection-form-of-p1-times-p1</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-picard-group-of-a-point-blowup-of-the-projective-plane</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-picard-operator-is-a-short-time-contraction</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-picard-operator-preserves-a-closed-curve-ball</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pid-complex-decomposes-into-two-term-cycle-boundary-pieces</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pid-submodules-of-free-modules-are-free-with-choice</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pid-tensor-two-term-pieces-have-the-kunneth-kernel-and-cokernel</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-piecewise-constant-control-h1-projection-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-piecewise-linear-delay-history-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-piecewise-smooth-embeddings-are-stable-under-fine-c-one-approximation</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pigeonhole</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-planar-barrier-controls-perron-solutions</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-planar-brownian-annular-exit-probability</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-planar-configuration-spaces-have-vanishing-pi-two-by-simultaneous-induction</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-planar-facial-graph-isomorphism-extension</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-planar-fmm-multipole-local-translation-identities</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-planar-fmm-pair-lists-partition-off-diagonal-pairs</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-planar-piecewise-analytic-region-triangulation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-arc-complements-and-accessible-jordan-points</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-curve-multiplicity-transform-chart</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-edge-face-incidence</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-exterior-of-a-closed-disc-is-path-connected</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-face-handshake-by-girth</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-gaussian-integral-in-polar-coordinates</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-graph-faces-are-finite-with-one-unbounded-face</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-syzygy-truncation-injectivity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plane-triangulation-is-connected</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plucker-map-well-defined-injective</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-plurality-consistency-along-middle-walk-positions</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pmea-three-quarter-separation-estimate</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poincare-dual-orbits-are-regular-homogeneous-borel-spaces</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-point-blowup-of-integral-curve-is-finite</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-point-divisor-exact-sequence-and-euler-characteristic-step</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-point-filters-are-dense-in-the-minimal-cauchy-filter-space</loc>
<lastmod>2026-08-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-point-process-law-is-determined-by-count-fidi</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-point-wedges-preserve-a-common-triangle-minsize-bound</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-points-of-fibre-primes-over-point</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-points-of-scheme-fibre-product-residue-tensors</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pointwise-cdf-convergence-to-a-continuous-law-is-uniform</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pointwise-closure-preserves-equicontinuity</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pointwise-convergent-uniformly-bounded-operators-converge-uniformly-on-compact-sets</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pointwise-limits-of-characters-are-characters</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pointwise-lipschitz-sets-in-c01-are-closed</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pointwise-potential-bound-for-compactly-supported-smooth-functions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-count-law-normalization-and-moments</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-integral-moment-identities</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-integral-of-a-singular-circle-measure-has-zero-nontangential-limit</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-integrals-are-harmonic</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-jensen-inequality-hardy-functions</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-kernel-boundary-cap-and-complement-estimate</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-kernel-is-a-boundary-approximate-identity</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-kernel-on-the-circle-is-a-positive-approximate-identity</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-kernel-properties-on-the-disc</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-tau-leap-moment-and-covariance-identities</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poisson-tau-leap-one-step-weak-defect</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polar-decomposition-and-nonzero-partial-isometries-in-factors</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polarized-hodge-structures-have-orthogonal-semisimple-substructures</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polish-closed-products-and-baire-parametrization</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polygonal-arc-does-not-separate-the-plane</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polygonal-boundary-crossing-for-affine-disk-maps</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polygonal-crossing-parity-is-locally-constant</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polygonal-length-is-monotone-under-refinement</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polygonal-ray-general-position</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polygonal-schema-reduction-moves</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polygonally-reachable-set-is-clopen</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polyhedral-event-restricts-contrast-to-interval</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-algebras-over-fields-are-integrally-closed</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-calculus-is-isometric-for-self-adjoint-operators</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-clutching-families-stabilize-to-linear-clutching</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-diagonal-differences-form-a-regular-sequence</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-extension-depth-increases-by-one</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-factorisation-into-irreducibles</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-gcd-is-stable-under-field-extension</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-highest-derivative</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-ideal-finite-generation</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-kernels-and-images-are-invariant</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-local-regularity-fibre-step</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-operations-preserve-finite-support</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-prime-contraction-height-jump-at-most-one</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-quantum-highest-vectors-satisfy-all-divided-power-relations</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-quantum-schur-first-level-weyl-filtration-and-hecke-corner</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-reductions-compose</loc>
<lastmod>2026-09-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-ring-dimension-lower-chain</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-ring-dimension-upper-bound</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-space-oracle-absorption</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-squarefree-decomposition-and-multiplicity</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomial-time-computations-have-logspace-uniform-circuits</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polynomials-and-roots-transport-along-field-isomorphisms</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-polytabloid-covariance-and-column-sign</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pontryagin-thom-converts-bordism-detection-to-a-thom-space-homotopy-problem</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pontryagin-thom-signed-preimage-count-equals-the-dg-degree</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-pooled-mixture-projection-and-variance</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-poset-mobius-recurrence</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-position-derivative-commutator-estimate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-and-negative-parts</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-area-compact-sets-are-not-conformally-removable</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-artin-relations-preserve-homogeneous-length</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-c-zero-functionals-have-finite-regular-representing-measures</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-characteristic-specht-head-and-cyclotomic-crystal-labels-agree</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-characteristic-top-differentials-map-to-blown-up-canonical-module</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-clifford-mass-difference-clutching-comparison</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-codimension-thickening-reduces-closed-sources-to-the-open-case</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-compactly-supported-transform-bump-on-the-dual</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-conormal-degree-of-a-fibre-divisor</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-convex-polygon-winding-index</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-definite-bundle-endomorphisms-have-smooth-positive-square-roots</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-definite-functions-give-positive-bounded-functionals-on-the-transform-core</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-definite-gaussian-integral</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-definite-model-has-unique-newton-step</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-degree-integral-homology-of-a-finite-group-is-order-torsion</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-depth-ring-has-regular-minimal-generator</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-df-chi-square-has-density-and-regular-cdf</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-diagonal-map-preserves-closed-convexity</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-finite-signed-measure-set-contains-a-positive-subset-of-at-least-the-same-mass</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-functionals-on-compact-metric-spaces-have-probability-representations</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-green-pairing-specializes-the-integral-half-into-the-composition-algebra</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-group-cohomology-of-the-trivial-group-vanishes</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-intermediate-cohomology-of-a-one-point-compactified-euclidean-space-vanishes</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-lebesgue-components-of-a-positive-measure</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-linear-combinations-and-finite-maxima-preserve-subharmonicity</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-linear-functionals-on-c-c-are-monotone</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-log-dirichlet-series-nonvanishing</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-measure-subsets-of-haar-measure-contain-finite-positive-measure-subsets</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-moment-gram-produces-univariate-chaos-polynomials</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-noise-regularizes-observed-covariance</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-nurbs-basis-and-quotient-derivative</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-part-is-an-admissible-weak-test-by-truncation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-part-of-a-zero-trace-function-has-zero-trace</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-powers-of-a-regular-sequence-remain-regular</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-real-has-dyadic-scale-in-factor-two</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-root-pairings-of-a-dominant-integral-weight</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-root-strings-sum-the-freudenthal-correction</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-semidefiniteness-of-the-brownian-covariance-kernel</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-smooth-collar-for-a-strictly-psh-negative-set</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-spanning-poll-set-has-uniform-angle</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-square-divisor-has-effective-multiple</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-square-root-of-a-compact-positive-operator</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-trace-class-covariance-defines-hilbert-gaussian</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-transverse-accessibility-is-a-preorder</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-triple-set-yields-uniform-overlap</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-tube-forward-euler-loop-terminates</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-type-functions-define-a-pre-hilbert-form</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-positive-type-functions-satisfy-translation-estimates</loc>
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<loc>https://alphabetamath.cc/item/lem-potts-q2-q3-q4-matrices-satisfy-temperley-lieb</loc>
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<loc>https://alphabetamath.cc/item/lem-power-decay-weights-are-doubling</loc>
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<loc>https://alphabetamath.cc/item/lem-power-rangefinder-projector-is-borel</loc>
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<loc>https://alphabetamath.cc/item/lem-power-series-coefficients-are-determined-by-real-values</loc>
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<loc>https://alphabetamath.cc/item/lem-power-series-reexpansion-double-series</loc>
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<loc>https://alphabetamath.cc/item/lem-powerset-fibres-force-well-orderability</loc>
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<loc>https://alphabetamath.cc/item/lem-precompact-trajectory-tail-limit-sets-are-nonempty-compact-connected-and-flow-invariant</loc>
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<loc>https://alphabetamath.cc/item/lem-profile-moment-generators-and-shifted-character-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-progressive-products-and-true-cofinality-transfers</loc>
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<loc>https://alphabetamath.cc/item/lem-proj-associated-sheaf-basic-sections</loc>
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<loc>https://alphabetamath.cc/item/lem-proj-irrelevant-and-nilpotent-boundaries</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proj-of-finitely-generated-graded-algebra-is-projective</loc>
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<loc>https://alphabetamath.cc/item/lem-proj-prime-localization-correspondence</loc>
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<loc>https://alphabetamath.cc/item/lem-proj-veronese-invariance</loc>
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<loc>https://alphabetamath.cc/item/lem-projected-contact-solutions-are-unique</loc>
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<loc>https://alphabetamath.cc/item/lem-projected-euler-projection-residual-certificate</loc>
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<loc>https://alphabetamath.cc/item/lem-projected-subgradient-finite-budget-returns-status</loc>
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<loc>https://alphabetamath.cc/item/lem-projected-subgradient-one-step-estimate</loc>
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<loc>https://alphabetamath.cc/item/lem-projection-formula-in-algebraic-k-theory</loc>
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<loc>https://alphabetamath.cc/item/lem-projection-formula-invertible-twist</loc>
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<loc>https://alphabetamath.cc/item/lem-projection-onto-a-closed-convex-set-has-the-variational-inequality</loc>
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<loc>https://alphabetamath.cc/item/lem-projection-onto-closed-convex-set-is-nonexpansive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projection-slab-uniform-deviation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-cech-finiteness-and-serre-vanishing-for-etale-lifting</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-closure-dense-affine-chart</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-coherent-cohomology-finite-and-vanishing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-coordinate-invariance-bezout-sum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-coordinate-morphisms-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-determinant-is-homogeneous-and-scale-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-dimension-from-last-nonzero-betti-number</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-dimension-linear-avoidance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-dualizing-complex-trace-and-embedding-independence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-embedding-dualizing-complex-existence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-hodge-perverse-package-closes-under-defect-and-image-dimension-induction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-hyperplane-sections-decrease-the-defect-of-semismallness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-hypersurface-affine-pieces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-hypersurface-cohomology-sequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-hypersurface-dimension-drop</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-irreducibility-homogeneous-prime</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-line-curve-and-divisor-basics</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-line-divisors-classified-by-degree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-line-twisting-sheaf-ample</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-modification-of-proper-integral-dvr-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-modules-are-flat-over-an-arbitrary-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-morphism-relative-proj-presentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-normal-surface-grauert-riemenschneider-vanishing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-normal-surface-modification-h1-injects-off-special-fibre</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-plane-stabilization-gives-relative-five-bordisms</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-pure-cm-dualizing-complex-concentration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-regular-function-chart-compatibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-regular-local-base-coherent-duality-by-embedding</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-representables-and-derived-colimits-of-module-diagrams</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-representations-are-twisted-group-algebra-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-simple-symmetric-block-is-a-matrix-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-action-from-linear-representation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-cech-monomial-complex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-derived-coherent-duality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-diagonal-closed</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-finite-type-over-base</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-products-are-linearly-independent-in-rational-oriented-bordism</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-products-have-triangular-characteristic-number-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-saturation-local-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-space-top-cohomology-residue-pairing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-span-homotopy-pushout-mapping-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-standard-chart-prime-and-local-ring-correspondence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projective-variety-cone-irreducible</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-projective-verma-multiplicities-equal-soergel-standard-ranks</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projectives-covering-the-simple-objects-generate-every-finite-length-object</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-projector-is-admissible-density</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-proof-fresh-constant-elimination</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-propagation-and-gluing-of-hartogs-extensions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-birational-normal-target-isomorphism-at-quasi-finite-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-closed-convex-function-affine-minorant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-cohomology-field-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-continuous-map-stability</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-fibres-proper</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-proper-flat-cohomology-perfect-complex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-flat-fp-cohomology-perfect-complex</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-geometrically-integral-affine-scheme-is-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-iteration-master-condition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-local-on-base</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-master-condition-characterizations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-normal-curve-rational-function-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-pushforward-of-cycles-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-source-to-separated-target-proper</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-stable-base-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-stable-composition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-subgroup-of-a-finite-p-group-is-properly-normalized-local</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-surface-regularity-transfers-to-and-from-completion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proper-surjective-maps-have-cohomological-descent-for-constructible-field-sheaves</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-properness-survives-a-controlled-locally-finite-perturbation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-property-star-and-leaf-reducibility-yield-a-long-x-sparse-or-complete-blockade-or-a-better-outcome</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-property-star-and-leaf-reducibility-yield-five-comb-outcomes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-protocol-value-is-computable-in-polynomial-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-prox-indicator-is-euclidean-projection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-prox-l1-is-soft-thresholding</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proximal-bundle-finite-budget-returns-status</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proximal-bundle-subproblem-has-unique-minimizer</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proximal-gradient-one-step-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proximal-objective-has-quadratic-growth-from-minimizer</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-proximal-three-point-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-prufer-decoding-produces-a-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-psd-cone-self-dual-logdet-barrier</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pseudo-arclength-border-matrix-invertibility-and-inverse-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pseudocompact-euclidean-subset-is-bounded</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-pseudocompact-euclidean-subset-is-closed</loc>
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<loc>https://alphabetamath.cc/item/lem-quasilinear-solution-lifts-to-characteristics</loc>
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<loc>https://alphabetamath.cc/item/lem-quasinilpotent-trace-class-operator-has-zero-trace</loc>
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<loc>https://alphabetamath.cc/item/lem-quasisimple-proper-normal-subgroups-are-central-and-perfect-central-actions-trivial</loc>
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<loc>https://alphabetamath.cc/item/lem-quaternion-conjugation-is-an-anti-involution</loc>
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<loc>https://alphabetamath.cc/item/lem-quaternionic-basic-clutchings-have-pontryagin-numbers-plus-and-minus-two</loc>
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<loc>https://alphabetamath.cc/item/lem-quiver-exact-sequence-correspondence-is-smooth-and-proper</loc>
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<loc>https://alphabetamath.cc/item/lem-quiver-full-flag-incidence-has-a-smooth-projective-compactification</loc>
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<loc>https://alphabetamath.cc/item/lem-quiver-hardernarasimhan-filtrations-exist-are-unique-and-descend</loc>
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<loc>https://alphabetamath.cc/item/lem-quiver-motivic-extension-stack-class</loc>
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<loc>https://alphabetamath.cc/item/lem-quiver-parabolic-levi-borel-model-comparisons</loc>
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<loc>https://alphabetamath.cc/item/lem-quiver-potential-trace-is-additive-on-extensions</loc>
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<loc>https://alphabetamath.cc/item/lem-quiver-semistable-loci-are-open</loc>
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<loc>https://alphabetamath.cc/item/lem-quotient-basis-lifts-to-an-adapted-basis</loc>
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<loc>https://alphabetamath.cc/item/lem-quotient-blocks-preserve-connectedness-and-anticonnectedness</loc>
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<loc>https://alphabetamath.cc/item/lem-quotient-by-c-zero-has-no-countable-separating-family</loc>
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<loc>https://alphabetamath.cc/item/lem-quotient-dfa-is-well-defined-and-equivalent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-quotient-map-etale-when-quotient-is-algebraic-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-quotient-of-a-c-star-algebra-by-a-closed-two-sided-ideal-is-a-c-star-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-quotient-of-an-lca-group-by-a-closed-subgroup-is-lca</loc>
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<loc>https://alphabetamath.cc/item/lem-quotient-seminorm-is-representative-independent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-quotient-seminorm-triangle-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-quotient-sheaf-base-change-along-flat-lfp-map</loc>
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<loc>https://alphabetamath.cc/item/lem-quotient-spectrum-map-is-a-closed-immersion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-qz-two-sided-local-computed-update-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-r-boundaries-embed-in-r-cycles</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-r-one-s-two-integral-element-membership</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-r-one-s-two-intersection-of-height-one-localisations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-rabinowitsch-auxiliary-ideal-has-empty-zero-locus</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-rabinowitsch-substitution-clears-denominators</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-rabinowitsch-unit-ideal-consequence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-rademacher-randomisation-converts-square-functions-to-multipliers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radial-derivative-expansion-of-the-epd-transform</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radial-derivative-of-a-spherical-average</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radial-geodesics-from-one-point-reach-every-point-under-global-exp-domain</loc>
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<loc>https://alphabetamath.cc/item/lem-radial-jacobi-tensor-is-invertible-before-the-first-conjugate-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radial-majorized-kernels-recover-lebesgue-point-values</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radial-mollification-fixes-local-mean-value-functions</loc>
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<loc>https://alphabetamath.cc/item/lem-radial-normalisation-is-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radially-decreasing-kernels-are-dominated-by-the-maximal-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radical-commutes-with-localisation</loc>
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<loc>https://alphabetamath.cc/item/lem-radical-commutes-with-quotient-correspondence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radical-intersection-proof-forward-inclusion</loc>
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<loc>https://alphabetamath.cc/item/lem-radical-intersection-proof-separating-prime</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radical-membership-by-a-power</loc>
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<loc>https://alphabetamath.cc/item/lem-radical-minimal-complexes-and-perverse-filtrations-in-the-soergel-category</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radical-of-a-finite-length-module-is-superfluous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radical-of-a-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radical-of-an-intersection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radix-two-even-odd-dft-factorisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-radon-nikodym-cocycle-of-a-homogeneous-measure</loc>
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<loc>https://alphabetamath.cc/item/lem-radon-nikodym-density-of-a-finite-positive-measure-has-a-nonnegative-representative</loc>
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<loc>https://alphabetamath.cc/item/lem-raisonnier-family-is-a-sigma-one-three-filter</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-random-field-covariance-kernel-is-positive-semidefinite</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-random-graph-short-cycle-expectation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-random-linear-inner-code-has-fewer-than-one-bad-codeword-in-expectation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-random-permutation-variance-by-transpositions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-random-posterior-quantiles-stabilize-under-bvm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-random-signed-dyadic-sums-have-uniform-mihlin-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-random-subsum-detects-a-nonzero-binary-vector</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-random-subsum-verifies-all-quadratic-equations-with-constant-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-randomized-coordinate-prox-subproblem-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-randomized-probability-integral-transform</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-randomized-rangefinder-deterministic-svd-partition-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-randomized-threshold-has-exact-level</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-randomly-selected-unit-effect-moments</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-range-of-identity-minus-compact-is-closed</loc>
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<url>
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<loc>https://alphabetamath.cc/item/lem-range-truncations-preserve-bmo-seminorm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-rank-matrices-determine-the-pivot-permutation</loc>
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<loc>https://alphabetamath.cc/item/lem-rank-one-cohomology-shifts-across-a-simple-wall</loc>
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<loc>https://alphabetamath.cc/item/lem-rank-one-hecke-parameter-for-equal-torus-characters</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-cherednik-costandard-orthogonality-and-character</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-cherednik-kz-relation-specializes-in-flat-family</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-cohomology-scalar-comparison-for-compact-smooth-manifolds</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-conditional-distribution-functions-produce-real-regular-kernels</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-differential-divisor-well-defined-class</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-expression-derivative-recursion-correct</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-first-hurewicz-after-killing-lower-torsion-homotopy</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-gorenstein-surface-tangent-conic-and-hilbert-function</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-homology-four-ball-boundary-has-square-torsion-order</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-homology-of-a-closed-smooth-manifold-is-finite-dimensional</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-homotopy-isomorphisms-and-an-endpoint-surjection-give-homology-isomorphisms</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-homotopy-of-a-sphere-below-its-first-unstable-degree</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-hurewicz-for-arbitrary-wedges-of-high-dimensional-spheres</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-k-z-n-calculation-through-weak-cw-fiber-comparison</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-local-quantum-halves-and-torus-specialize-at-q-one</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-map-equivalence-transitive</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-map-smooth-curve-to-proper-scheme-extends</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-map-to-affine-target-indeterminacy-pure-codimension-one</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-normal-surface-point-blowup-normal-and-fibre-cohomology</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-power-monotone</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-singular-point-blowup-canonical-pullback-surjective</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-surface-exceptional-ideal-powers-and-sections</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-surface-local-rings-propagate-by-point-sequence-spreading</loc>
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<loc>https://alphabetamath.cc/item/lem-rational-transfer-identifies-a-finite-regular-cover-with-deck-invariants</loc>
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<loc>https://alphabetamath.cc/item/lem-rationalization-is-exact-and-commutes-with-singular-homology</loc>
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<loc>https://alphabetamath.cc/item/lem-rattle-scaled-position-and-momentum-branches</loc>
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<loc>https://alphabetamath.cc/item/lem-rbf-augmented-system-is-invertible</loc>
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<loc>https://alphabetamath.cc/item/lem-rcbd-nested-contrast-model-and-projection</loc>
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<loc>https://alphabetamath.cc/item/lem-reachability-count-is-verifiable-in-nl</loc>
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<loc>https://alphabetamath.cc/item/lem-read-only-workspace-diagonal-machine-halts</loc>
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<loc>https://alphabetamath.cc/item/lem-reed-solomon-outer-code-has-constant-rate-and-distance</loc>
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<loc>https://alphabetamath.cc/item/lem-rees-module-finiteness-and-stable-filtrations</loc>
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<loc>https://alphabetamath.cc/item/lem-reference-jacobi-weighted-endpoint-kernel</loc>
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<loc>https://alphabetamath.cc/item/lem-reference-polynomial-norm-equivalence</loc>
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<loc>https://alphabetamath.cc/item/lem-refined-giraud-maximal-contact</loc>
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<loc>https://alphabetamath.cc/item/lem-refined-gysin-commutation-and-composition</loc>
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<loc>https://alphabetamath.cc/item/lem-refinement-inequalities</loc>
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<loc>https://alphabetamath.cc/item/lem-refinement-limit-cech-cohomology-agrees-with-sheaf-cohomology</loc>
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<loc>https://alphabetamath.cc/item/lem-refinement-of-analytic-continuation-chains</loc>
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<loc>https://alphabetamath.cc/item/lem-refining-the-largest-layout-block-forces-local-blockade-length-at-least-epsilon-inverse</loc>
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<loc>https://alphabetamath.cc/item/lem-reflection-at-the-first-visit-to-a-level-is-a-bijection</loc>
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<loc>https://alphabetamath.cc/item/lem-reflection-basic-invariants-form-a-regular-sequence</loc>
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<loc>https://alphabetamath.cc/item/lem-reflection-green-function-for-the-half-space</loc>
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<loc>https://alphabetamath.cc/item/lem-reflection-of-an-outward-field-extends-over-the-double</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-banach-constraint-directions-are-realised-by-level-set-curves</loc>
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<loc>https://alphabetamath.cc/item/lem-regular-base-dualizing-traces-compose-on-rational-modifications</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-conditional-kernels-factor-through-a-standard-borel-conditioning-variable</loc>
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<loc>https://alphabetamath.cc/item/lem-regular-conditional-kernels-push-forward-under-measurable-random-maps</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-curve-chart-and-pseudo-arclength-predictor-defect</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-element-exists-by-prime-avoidance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-elements-form-a-connected-dense-open-subset</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-exhaustion-and-dirichlet-on-riemann-surfaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-functions-form-sheaf-classical</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-holonomic-phase-residuals-control-distance-to-phase-manifold</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-holonomic-phase-space-is-symplectic-cotangent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-homotopy-preserves-the-formal-gauss-class</loc>
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<loc>https://alphabetamath.cc/item/lem-regular-immersion-koszul-ext-sheaf</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-lindelof-spaces-are-normal</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-local-graded-surjection-has-zero-kernel</loc>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-regular-trace-kernel-descends-the-complex-socle</loc>
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<loc>https://alphabetamath.cc/item/lem-regular-value-choice-does-not-change-the-framed-cobordism-class</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regularity-is-hereditary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regularity-is-monotone-in-the-parameter</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regularity-is-robust-under-small-edits</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regularity-via-closed-neighbourhoods</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regularization-of-curve-on-noetherian-ambient-by-point-blowups</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-regularized-sph-vector-field-lipschitz-on-positive-density-tube</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-reidemeister-moves-between-closed-braid-diagrams-factor-through-markov-moves</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-reidemeister-schreier-relators-are-independent-of-word-representatives</loc>
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<loc>https://alphabetamath.cc/item/lem-reiter-functions-can-be-cut-down-to-folner-sets</loc>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/lem-relative-lifts-produce-cohomological-transgressions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-middle-cup-products-are-symmetric</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-morse-bott-crossing-by-negative-normal-bundles</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-normalization-finite-stage</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-one-parameter-morse-path-with-finite-events</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-open-convex-gauge-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-path-shortening-connectivity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-poincare-primitive-near-a-submanifold</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-pontryagin-number-of-the-milnor-disk-bundle-is-controlled-by-h-minus-j</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-pontryagin-square-equals-mixed-evaluation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-pontryagin-square-glues-across-a-seven-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-proj-affine-local-gluing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projective-bundle-k-theory-generators</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projective-homogeneous-equations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projective-line-cohomology-and-apolarity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projective-line-degree-normal-form</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projective-space-derived-duality-regular-local-base</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projective-space-regular-local-base-twisted-resolution</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projective-space-universally-closed</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projectivity-forces-p-section-character-vanishing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-projectivity-mackey-intersections-for-finite-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-shape-controlled-secants-approximate-smooth-simplex-maps</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-single-cell-layer-has-compatible-homotopy-and-homology-bases</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-singular-product-chain-equivalence-for-cw-pairs</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-smooth-triangulations-can-be-fitted-while-preserving-a-bundle-projection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-smoothing-of-a-continuous-simplex-along-its-faces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-spec-glues-affine-algebras</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-subdivision-neighbourhood-adjustment</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-surface-collars-and-elementary-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-tensor-product-from-separability-idempotent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-three-bordism-surgery-presentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-three-manifolds-admit-parametrized-link-surgery-presentations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-relative-tubular-neighborhoods-preserve-a-chain-of-submersions</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-relatively-compact-boundary-coordinate-half-balls-form-a-basis</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-relator-disks-give-area-controlled-coarse-fillings</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-relator-expressions-give-controlled-singular-planar-diagrams</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-reml-error-contrast-basis-change-is-parameter-free</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-reml-error-contrast-covariance-is-positive-definite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-removing-unreachable-states-preserves-language</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-rephasing-changes-the-factor-set-by-a-coboundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-replacement-invariant-derived-enriched-mapping-spaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-replicating-a-vertex-of-a-perfect-graph-preserves-perfection</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-replication-number-is-constant-in-a-two-design</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-representations-of-affine-group-schemes-are-comodules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-representations-of-diagonalizable-groups-are-sums-of-eigenspaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-representative-functions-form-a-self-adjoint-translation-invariant-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-rescaled-ultradistance-is-a-quotient-metric</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-reset-error-after-a-mistimed-hybrid-event</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-residual-augmentation</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-residue-casimir-operators-give-local-affine-hecke-actions</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-residue-exact-differential-zero</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-residue-field-splits-off-reduced-maximal-ideal</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-residue-independent-uniformizer</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-residue-pairing-descends-cohomology</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-residue-pairing-functorial-line-bundle</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-residue-simple-pole</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-resolution-is-functorial-under-smooth-maps</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-resolvent-identity-and-holomorphy-for-closed-operators</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-resolvent-identity</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-resolvent-star-algebra-is-dense-in-c-zero</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-restricted-matern-native-space-is-sobolev</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-restricted-regular-representation-is-weakly-contained-in-subgroup-regular-representation</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-restrictedness-is-complement-invariant</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-restriction-and-extension-estimates-are-dual</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-restriction-fibres-for-embeddings-in-a-finite-tower</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-restriction-of-formal-immersion-data-has-the-parametric-lifting-property</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-restriction-of-injective-group-modules-is-injective</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-restriction-of-marked-ideal-to-a-smooth-subvariety</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-restriction-of-scalars</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-restriction-to-a-containing-p-subgroup-retains-a-vertex</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-restriction-to-two-block-subgroup-has-lr-multiplicities</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-resultant-detects-common-projective-point</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-retarded-delay-gronwall-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-retarded-euler-and-delay-midpoint-work-and-storage</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-retract-of-a-noetherian-ring-is-noetherian</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-return-cycle-occupation-measure-and-minimality</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-reversal-anti-involution-commutes-with-hecke-bar</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-reversal-is-an-involution-and-reverses-concatenation</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-reverse-holder-from-a-distribution-estimate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-reverse-triangle-inequality-in-a-normed-space</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-reversing-a-cobordism-gives-symmetry</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-revised-simplex-basic-feasible-extreme-point-equivalence</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-reynolds-operator-and-invariant-subring-properties</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rho-length-and-extremal-length-are-well-defined</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-rho-minus-w-rho-is-a-sum-of-positive-roots</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-rho-shift-intertwines-the-dot-and-ordinary-weyl-actions</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ribbon-trace-equals-the-framed-closure-evaluation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riccati-comparison-for-scalar-initial-shape</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riccati-finite-budget-wrappers-return-a-status</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ricci-curvature-is-symmetric-and-basis-independent</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-rice-witness-machine-construction</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-riemann-integrable-function-has-borel-darboux-envelopes</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-integral-linearity</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-integral-unchanged-by-content-zero-modification</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-lebesgue-comparison-for-distribution-test-integrands</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-map-extremal-derivative-is-attained</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-riemann-map-extremal-derivatives-are-positive-and-bounded</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-map-extremal-family-is-nonempty</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-riemann-map-extremizer-is-surjective</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-riemann-map-extremizer-is-univalent</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<loc>https://alphabetamath.cc/item/lem-riemann-maps-of-jordan-domains-extend-homeomorphically</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-roch-space-finite-dimensional</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-stieltjes-integral-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-stieltjes-refinement-estimate</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemann-zeta-dirichlet-series-converges-locally-uniformly</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemannian-gradient-vanishes-exactly-at-critical-points</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemannian-length-is-independent-of-piecewise-c-one-subdivision</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riemannian-trust-region-ratio-accuracy-for-small-radii</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riesz-lemma</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riesz-potential-near-far-splitting</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riesz-product-for-a-hadamard-lacunary-set</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-riesz-schauder-ascent-and-descent-stabilize</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riesz-thorin-bound-on-the-finite-simple-core</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-riesz-transform-kernels-have-explicit-size-difference-and-spherical-cancellation-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-riesz-transform-principal-value-kernel-formula</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-right-descent-soergel-bimodules-descend-to-simple-invariants-under-the-character-hypothesis</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-right-translation-scales-left-haar-measure</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-right-trivialized-differential-of-the-lie-group-exponential</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rigidity-of-alternating-multilinear-matrix-functions</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ring-detected-at-associated-prime-localizations</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ring-elementary-consequences</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-ring-homomorphism-basic-properties</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ring-homomorphism-of-fields-is-a-field-homomorphism</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-ring-units-form-a-group</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ringed-space-module-sheaves-enough-injectives</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rkc-chebyshev-stage-perturbation-amplification</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rmk-compact-set-formula-and-local-finiteness</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rmk-functional-outer-content-is-well-defined</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rn-densities-of-bounded-l-p-functionals-belong-to-l-q</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-rnp-is-invariant-under-banach-space-isomorphism</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rnp-is-separably-determined</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rnp-may-be-tested-on-the-lebesgue-interval</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-robbins-siegmund-almost-supermartingale</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-robinson-schensted-recording-tableau-is-standard</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-robust-edge-circuit-has-distance-gap</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rodl-initialization-removes-the-constant-scale-restriction-in-the-property-star-four-outcome-theorem</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rodl-initialization-upgrades-generalized-niceness-to-a-restricted-set-blockade-or-polynomial-clique-or-stable-set</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-rolle-theorem-from-extreme-values</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-roof-equivalence-is-an-equivalence-relation</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-coordinate-cells-and-generation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-datum-combinatorics</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-free-polynomial-circle-loops-are-nullhomotopic</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-group-expansion-of-a-weight-vector</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-of-unity-closed-bottom-alcove-weyl-modules-are-simple</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-of-unity-finite-highest-weight-truncations</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-of-unity-integral-weyl-specialization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-of-unity-rank-one-weight-symmetry</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-of-unity-weyl-flags-summands-and-orthogonality</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-of-unity-weyl-quantum-dimensions-and-affine-signs</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-unity-quantum-lucas-and-divided-power-generation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-root-unity-toral-quotient-by-group-like-generators</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rooted-tree-generating-function-series</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rooted-tree-parent-and-levels</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-roots-of-unity-in-a-number-field-are-finite</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-roots-of-x-q-minus-x-form-a-field</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rosenbrock-euler-jacobian-approximation-defect</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rosenbrock-euler-local-defect-and-residual-error</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rosenbrock-shifted-inverse-perturbation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rosenbrock-shifted-matrix-invertibility-bound</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rosenbrock-stage-residual-certificate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-round-circles-are-conformally-removable</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rounded-linear-and-normal-residual-certificates</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rounded-triangular-substitution-componentwise-backward-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rouquier-complexes-satisfy-far-commutativity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rouquier-complexes-satisfy-the-three-term-braid-relation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rouquier-derived-comparisons-give-unique-normalized-homotopy-maps</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rouquier-generator-complexes-have-canonical-derived-graph-models</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rouquier-normalized-comparison-isomorphisms-are-transitive</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-row-and-column-insertion-commute</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-row-bumping-route-monotonicity</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-row-insertion-and-reverse-deletion-are-inverse</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-row-operations-preserve-column-relations</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-row-operations-preserve-row-space</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rqmc-general-net-gain-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rqmc-scrambled-net-gain-formula</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rqmc-scrambled-net-variance-identity</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rqmc-smooth-anova-component-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rqmc-zero-net-sharp-gain-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rsk-union-bound-localizes-plancherel-profiles</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rt-capped-operator-normalization-and-composition</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-rt-handlebody-pairing-and-surgery-gluing</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rudin-bounded-cofinality-hull-transfer</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rudin-box-space-basic-neighborhoods-and-p-space</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-rudin-discrete-families-have-discrete-ambient-closures</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-rudin-disjoint-box-refinement</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-rudin-internal-hull-tail-domination</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-rudin-neighborhoods-of-initial-top-slices-contain-tails</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-runge-pole-pushing-lemma</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-s-rational-map-descends-along-faithfully-flat-smooth-maps</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-saddle-polycycle-rounding-preserves-the-inward-transverse-family</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-safeguarded-pr-plus-uniform-angle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-saga-estimator-and-table-recurrence</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-same-marginal-conditional-product-law-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sampling-produces-periodisation-in-frequency</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-samuel-function-pseudometrics-and-coarsening</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-samuel-uniformity-is-totally-bounded</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-samuel-uniformity-preserves-the-induced-topology-under-dependent-choice</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-sard-on-the-infinitely-flat-critical-stratum</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-sard-on-the-nonflat-critical-strata</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-sard-slicing-for-compact-null-sections</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-satisfaction-coincidence</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sc-toolkit-commuting-positive-words-have-a-common-root</loc>
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<loc>https://alphabetamath.cc/item/lem-sc-toolkit-minimal-diagrams-and-cut-vertex-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sc-toolkit-periodic-relator-overlap-is-a-piece</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sc-toolkit-periodic-word-square-alternative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scalar-and-complex-measures-from-a-pvm</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-scalar-brownian-bridge-restriction-density</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-scalar-gaussian-channel-mutual-information-power-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scalar-twist-controls-the-two-markov-stabilizations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scale-tail-suprema-have-prescribed-cofinality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-binomial-coefficients-converge</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-chebyshev-filter-bound-on-a-separated-interval</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-complex-householder-and-givens-local-backward-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-euclidean-bumps-with-compact-support-and-gradient-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-gaussian-covariance-has-depth-at-least-half</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-householder-step-meets-local-backward-error-premise</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-kernel-moments-and-derivative-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-modified-bessel-midpoint-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaled-real-householder-step-termination-and-status</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-scaling-and-squaring-error-recurrence</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schauder-coefficient-space-is-banach</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schematic-closure-and-dense-agreement</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-scheme-fibre-stalk-quotient</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-scheme-functor-is-algebraic-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-scheme-zariski-main-factorization-quasi-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schreier-coset-graph-is-connected-and-deterministic</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schreier-generators-lie-in-the-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schreier-rewriting-is-invariant-under-free-reduction</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schrodinger-weyl-system-is-regular-and-irreducible</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schur-complement-congruence-and-determinant</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schur-index-is-independent-of-the-chosen-splitting-field</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schur-leading-coefficients-and-good-asymptotic-specializations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schur-multiplier-of-a-finite-group-is-finite</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schur-reduction-for-polynomial-unit-disk-roots</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schur-specialization-coproduct-and-plethysm-identities</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schur-weyl-length-cutoff-by-column-antisymmetrization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schur-weyl-polytabloid-highest-weight</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwartz-cutoffs-from-the-standard-smooth-step</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwartz-deconvolution-along-dyadic-dilations</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwartz-dense-in-fourier-bessel-potential-space</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwartz-dilations-preserve-schwartz-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwartz-functions-and-all-derivatives-are-integrable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwartz-parameter-pairing-and-integral-interchange</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwartz-periodisation-over-a-lattice-is-smooth-and-uniformly-summable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwartz-space-is-dense-in-l-two</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwarz-additive-inverse-is-local-energy-minimum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwarz-local-corrections-are-energy-orthogonal-projections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwarz-local-matrices-are-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-schwarz-p1-product-cutoff-interpolation-energy-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sda-doubling-composition-and-psd-invariants</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sdc-fixed-point-is-collocation-stage</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sdc-scalar-linear-iteration-matrix</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sdc-sweep-work-and-storage-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-countable-group-c-star-algebra-has-a-sequential-approximate-identity</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-countable-group-c-star-algebra-is-separable-with-a-countable-dense-star-subalgebra</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-countable-lch-spaces-are-standard-borel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-countable-smooth-manifolds-have-cw-homotopy-type</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-moment-controls-tail-mass-and-number</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-order-characteristic-function-expansion</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-order-jet-on-a-regular-level-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-order-kernel-convolution-l2-bias-bound</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-second-plus-construction-is-sheaf</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-second-resolvent-identity-for-closed-operator-perturbations</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-section-nonvanishing-affine-intersection</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-section-ring-of-ample-line-bundle-finitely-generated</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-section-zero-if-all-germs-zero</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sectional-curvature-is-independent-of-the-basis-of-the-plane</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sections-near-a-compact-set-are-sections-on-that-set</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sections-of-an-associated-line-bundle-as-equivariant-functions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sections-on-compact-opens-commute-with-filtered-colimits</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sectorial-form-angle-controls-the-numerical-range-of-its-operator</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sectorial-stirling-explicit-remainder-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-segre-map-well-defined-injective</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-selected-sample-size-conditionally-superuniform-pvalue</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-self-adjoint-operator-generates-a-strongly-continuous-unitary-group</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-self-commensurating-cyclic-subgroups-and-trivial-conjugate-intersections-in-the-free-group-of-rank-two</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-self-concordant-local-newton-calculus</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-self-reference-construction-from-smn</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-selfadjoint-weight-gram-valuations-detect-jantzen-classes</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semi-infinite-wedges-are-indexed-by-partitions-and-give-node-action-formulas</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semidirect-product-bracket-satisfies-jacobi</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semifinite-measures-have-arbitrarily-large-finite-subsets</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semigroup-generator-commutes-with-orbits-on-its-domain</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semigroup-generator-resolvents-satisfy-the-resolvent-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semilagrangian-transverse-first-hit-error</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-borel-root-factorization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-bruhat-double-cosets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-flag-torsor-zariski-charts</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-groups-are-perfect-and-have-no-nontrivial-characters</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-minimal-parabolic-root-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-opposite-borel-big-cell</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-projective-orbit-flag-quotients</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-rank-one-sl2-root-homomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-rational-pluecker-highest-weight-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimple-root-exponential-algebraic-subgroups</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimplicity-and-trace-form-for-the-finite-spherical-hecke-algebra</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semisimplicity-of-rational-representations-descends-along-field-extensions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semistandard-homomorphisms-are-independent-and-dominance-triangular</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-semistandard-homomorphisms-span-in-characteristic-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semistandard-tableau-homomorphisms-to-young-permutation-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-semistandard-weight-dimensions-detect-virtual-weyl-classes</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separability-contracts-normalized-categorical-hochschild-complex</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separable-abelian-von-neumann-algebras-have-a-self-adjoint-generator</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separable-algebra-module-and-bimodule-categories-are-finite-semisimple</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separable-banach-has-countable-norming-family</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separable-group-c-star-representations-disintegrate-over-a-commuting-diagonal-algebra</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separable-group-c-star-type-i-and-smooth-dual-criteria</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separable-hilbert-bounded-sequence-weak-subsequence</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separable-trace-class-determinant-construction</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separable-type-i-factors-are-multiples-of-irreducible-representations</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separated-characteristic-disk-has-an-inclusion-minimal-nonidentity-simple-cycle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-separated-frequency-blocks-do-not-disturb-earlier-partial-sum-maxima</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separated-implies-valuative-uniqueness</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separated-integral-cosets-give-typed-parabolic-category-equivalences</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-separated-local-on-base</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separated-simple-floquet-multiplier-perturbation-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separated-sites-matern-gram-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separated-stable-under-base-change</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separated-stable-under-composition</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separatedness-of-open-and-closed-immersions</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separately-holomorphic-vanishing-on-a-real-box-is-zero</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separating-critical-values-far-from-the-boundary</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separating-hypersurface-chart-variety</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separation-augmentation-for-kuratowski-free-graphs</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separation-of-disjoint-closed-invariant-subsets-by-an-invariant</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-separative-quotient-of-a-forcing-preorder</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sequence-spaces-continuously-inject-into-the-real-line</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sequential-characterisation-of-closure-r</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sequential-closure-inside-closure</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sequential-repetition-amplifies-error</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sequentially-compact-implies-complete</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-serial-relation-successor-sets-are-open-dense</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-series-linearity</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-series-tail-invariance</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-serre-classes-are-stable-under-finite-filtrations</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-serre-elements-vanish-before-serre-generation</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-serre-fibration-replacement-preserves-fiber-homology-transport</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-serre-r-zero-s-one-characterises-reducedness</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-serre-vanishing-induction-hyperplane</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-set-partitions-of-a-finite-set-are-finite</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-set-sized-parallel-henkinization-preserves-consistency</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-setting-a-to-zero-in-a-closed-kr-factorization-gives-the-wide-edge-koszul-complex</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shamir-protocol-has-perfect-completeness</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shamir-qbf-verifier-runs-in-polynomial-time</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shape-operator-and-gauss-kronecker-curvature-of-a-graph</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shape-regular-affine-simplex-scaling</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shapiro-lemma-and-induced-modules-are-acyclic</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shapovalov-determinant-hyperplane-factorization</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shared-minimum-poisson-count-coupling</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sharp-cantor-interval-mass-bound</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sharp-dirichlet-poincare-inequality-on-an-interval</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sheaf-cohomology-classes-as-derived-morphisms</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sheaf-condition-check-on-basis</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sheaf-differentials-affine-compatibility</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sheaf-nakayama-fibre-detects-generation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sheaf-section-over-empty-set-terminal</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sheaf-supported-on-a-closed-subset-is-a-pushforward</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shear-images-of-the-unit-cube-have-lebesgue-measure-one</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shelah-continuous-unions-of-sweetness-models</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shelah-homogeneous-truth-has-baire-representatives</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shelah-inner-model-is-closed-under-ambient-omega-sequences</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shelah-real-name-capture-and-coded-meagre-unions</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shelah-sweet-density-transfer-along-complete-suborders</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shelah-sweet-forcings-are-sigma-directed-ccc</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shelah-universal-meagre-forcing-absorbs-old-nowhere-dense-sets</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shifted-adic-koszul-filtration-euler-comparison</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shifted-character-multiplication-by-p-k</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shifted-elliptic-solution-operator-is-compact-on-ltwo</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shifted-norm-of-a-weight-is-maximal-only-at-the-top-weight</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shifts-of-a-weight-one-word-realise-each-count-of-nonpositive-partial-sums-once</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-short-loop-relators-give-a-finite-dehn-presentation</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-shuffle-coproduct-coassociative-cocommutative-conilpotent</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sigma-cellular-base-yields-a-compatible-metric</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sigma-finite-caratheodory-sets-have-generated-measurable-hulls</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sigma-finite-ergodic-oscillation-sets-have-finite-measure</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sigma-series-cauchy-adjoint-and-reproducing-kernel-identities</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sign-preservation-near-a-limit</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sign-reversing-involution-on-intersecting-path-systems</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-signature-and-l-genus-agree-on-complex-projective-spaces</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-signature-and-l-genus-agree-on-products-of-complex-projective-spaces</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-signature-is-additive-under-disjoint-union-and-orientation-reversal</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-signature-is-independent-of-basis-and-field-extension-from-rationals-to-reals</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-signed-bl-norm-dominated-by-split-coupling-cost</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-signorini-contact-nodal-test-functions-surjective</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-signorini-contact-set-closed-convex-nonempty</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-signorini-dual-mortar-biorthogonality-and-infsup</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-signorini-elasticity-form-bounded</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-signorini-nodal-contact-set-conforming</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-signorini-partial-dirichlet-korn-coercivity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-signorini-partial-trace-space-bounded</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-signorini-rigid-motion-controlled-by-dirichlet-segment</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-approximants-converge-uniformly-on-a-large-closed-set</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-continued-fraction-convergents-and-cylinders</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-finite-extension-has-finitely-many-intermediate-fields</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-fold-complement-restriction-is-an-isomorphism</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-functions-satisfy-lusins-theorem-on-a-finite-measure-set</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-generator-weights-extend-to-a-weight-function</loc>
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<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-simple-highest-weight-modules-are-restricted-self-dual</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-simple-khovanov-seidel-modules-have-explicit-finite-projective-resolutions</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-simple-lifted-caps-avoid-the-original-essential-loop-and-a-fixed-intrinsic-neighborhood</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-simple-positive-braids-are-indexed-by-permutations</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-simple-pvm-integral-is-representation-independent</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-rational-representations-are-finite-dimensional</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-reflection-double-coset-rule</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-reflections-preserve-weight-multiplicities</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-ribbon-fusion-dimensions-are-nonzero</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-root-form-recovers-factor-lifting</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-root-hensel-lifts-idempotents</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-root-integrability-bounds-the-dominant-cyclic-module</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-root-power-relations-generate-the-integrable-quotient</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-root-singular-vector-in-a-verma-module</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simple-root-to-coprime-factorisation</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplex-factor-reversal-is-chain-homotopic-to-the-identity-diagonal</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplex-integrals-are-independent-of-affine-coordinate-identification</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplicial-algebra-cotangent-adjunctions-before-deriving</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplicial-boundary-is-independent-of-oriented-representative</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplicial-boundary-squared-zero</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplicial-chain-maps-carried-by-specified-cones-are-chain-homotopic</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplicial-four-polytope-facet-count</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplicial-normalization-prism-and-trivial-fibration-criterion</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simplicial-to-singular-chains-commute-with-boundaries</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simply-laced-quantum-braid-symmetries-preserve-the-integral-form</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simpson-panel-peano-kernel</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simultaneous-ae-uniqueness-of-regular-conditional-distributions</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simultaneous-rational-conditional-distribution-function-versions</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-simultaneous-smooth-approximation-in-l-one-and-l-two</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sine-and-cosine-series-converge-everywhere</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sine-chord-and-lipschitz-bounds</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sine-positive-and-cosine-decreasing-on-zero-two</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-single-wall-tensor-weight-exclusion</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-augmentation-commutes-with-boundary</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-boundary-descends-to-relative-chains</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-chain-cross-product-boundary-formula</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-dot-weights-have-zero-line-bundle-cohomology</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-kernel-sine-integral-under-countable-choice</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-planar-diagrams-have-controlled-coarse-disk-thickenings</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-product-chain-equivalence-by-simplex-models</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-uct-extension-from-cycle-projections</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-value-product-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-values-equal-approximation-numbers</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-singular-values-lipschitz-in-spectral-norm</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sipdg-adjoint-consistency-h2</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sipdg-boundedness-augmented-norm</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sipdg-discrete-flux-inverse-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sipdg-energy-seminorm-is-a-norm</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sipdg-physical-simplex-trace-green</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sir-bounded-potential-unnormalized-update-variance</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-skeletal-homology-stabilizes-away-from-the-cell-dimension</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-skew-hermitian-matrix-exponential-is-unitary</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-skolem-hull-size-and-elementarity</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-skolem-witness-closure-on-a-cardinal</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sl-n-r-is-boundedly-generated-by-elementary-root-subgroups</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sl2-r-has-no-invariant-probability-on-the-projective-line</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sl2-r-semidirect-r2-has-relative-property-t</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sl2-raising-and-lowering-formulas-in-the-compact-picture</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sl2-small-quantum-group-root-power-quotient-is-hopf</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sl2-structure-and-root-coordinates</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-slice-chart-restrictions-form-a-smooth-atlas</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-slicing-and-tracing-are-mutually-inverse-on-classes</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-slicing-lemma-for-regular-pairs</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-slim-triangles-imply-the-gromov-product-inequality</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-slobodeckij-mollification-approximation-rates</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-slobodeckij-seminorm-controls-dyadic-level-sets</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-slobodeckij-seminorm-is-well-defined</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-anticonnected-components-yield-a-complete-blockade</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-block-determinant-separation-lower-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-dowker-ch-gives-luzin-set</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-dowker-coloring-gives-ad-guessing</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-dowker-ladder-normality</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-dowker-ladder-shrinking-obstruction</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-dowker-luzin-gives-tight-coloring</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-dowker-stick-gives-ad-guessing</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-four-square-multiple-of-a-prime</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-open-excess-implies-lebesgue-measurable</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-projective-modules-are-exactly-finitely-generated-projective-modules</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-root-unity-image-has-braid-stable-pbw-decompositions</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-set-coupling-converges-from-almost-every-start</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-step-implicit-rk-branch-and-residual-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-total-copy-expectation-forces-many-homogeneous-k-sets</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-tower-exists</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-small-transitive-sets-have-small-ranks</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smc-backward-operator-oscillation-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smc-centered-filtering-feynman-kac-contraction</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smc-finite-horizon-empirical-law</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smc-multinomial-resampling-clt</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smc-multinomial-variance-unrolls</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smc-mutation-and-weighted-correction-clt</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smc-residual-resampling-clt-away-from-integer-weights</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smirnov-class-quotient-characterisation</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smolyak-adaptive-surplus-termination</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smolyak-dyadic-tensor-simpson-convergence</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smolyak-mixed-simpson-detail-decay</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smolyak-rectangular-telescope</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-arcs-and-circles-are-removable-for-quasiconformal-maps</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-beltrami-coefficients-admit-quasiconformal-solutions</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-bump-between-concentric-euclidean-balls</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-smooth-chart-compatibility-is-symmetric-and-reflexive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-smooth-closed-immersion-regular-conormal-sequence</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-smooth-closed-subvariety-dualizing-line-bundle-adjunction</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-smooth-compactly-supported-functions-are-dense-in-ltwo-of-an-open-set</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-smooth-compactly-supported-functions-are-dense-in-schwartz-space</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-compactly-supported-functions-are-dense-in-slobodeckij-spaces</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-complex-pullback-is-exact-for-the-middle-perverse-t-structure</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-composite-sum-preserves-proper-closed-convexity</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-curve-coherent-torsion-free-locally-free</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-curve-realizing-a-tangent-direction</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-density-on-reference-simplex</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-euclidean-hypersurface-graph-and-localization</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-extension-from-a-closed-neighbourhood</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-families-and-path-components-in-the-weak-topology</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-fibres-smooth</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-finite-point-motions-extend-to-boundary-fixed-disk-isotopies</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-finite-type-schemes-have-schematically-dense-rational-points</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-flag-incidence-correspondences-have-the-required-oriented-push-pull-calculus</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-functional-extends-to-negative-sobolev-space</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-half-space-extensions-have-the-same-derivatives-on-the-half-space</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-handle-attachment-is-independent-of-corner-rounding-up-to-diffeomorphism</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-hyperplane-slice-at-transverse-point</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-immersion-normal-sequence-and-deformation-charts</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-map-tangent-surjectivity-criterion</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-maps-paste-over-an-open-cover</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-maximal-functions-of-tempered-distributions-are-borel-measurable</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-multiplicative-type-groups-are-generated-by-their-finite-subgroups</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-orientation-sign-is-the-local-integral-homology-multiplier</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-parametric-primitives-for-a-smooth-exact-family-on-a-compact-manifold</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-plane-curve-unique-tangent</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-polynomially-bounded-multipliers-on-schwartz-space</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-projective-analytification-has-rational-kahler-polarization</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-projective-embedding-gysin-trace-compatibility</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-projective-modification-preserves-open-cohomology-images</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-projective-morphisms-give-polarizable-rational-gauss-manin-variations</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-projective-rational-point-koszul-residue-normalization</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-proper-complete-dvr-geometric-generic-connectedness</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-psh-exhaustion-implies-hartogs-pseudoconvexity</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-pullback-of-multiple-test-blowups</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-quasiprojective-varieties-admit-snc-projective-compactifications</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-regularization-of-psh-exhaustion</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-relative-isotopy-extension-for-disk-arcs-with-puncture-endpoints</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-residual-quotient-extension</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-simple-characteristic-eigenpairs</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-sphere-data-have-a-harmonic-replacement</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smooth-trigonalizable-group-normal-series-refinement</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smoothing-backward-kernel-bayes-factorization</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smoothing-formal-immersion-families</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smoothing-genuine-immersion-families</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smoothness-at-the-boundary-is-independent-of-charts-and-extensions</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-smoothness-stable-under-product-classical</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sobolev-integration-by-parts-for-dual-exponents</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sobolev-level-set-iteration-step</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sobolev-norm-is-well-defined-and-definite</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sobolev-pasting-across-an-overlap</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sobolev-trace-agrees-with-continuous-boundary-values</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sobolev-zeros-bound-on-a-cone-domain</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sokal-local-operator-norm-lower-bound</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-absorption-factorization-and-homogeneity</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-almost-disjoint-extension-under-ma</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-borel-code-and-regularity-absoluteness</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-collapse-localizes-countable-ordinal-data</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-construction-is-uniformly-formalizable</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-homogeneous-truth-has-borel-representatives</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-inner-model-is-closed-under-ambient-omega-sequences</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-perfect-tree-of-mutually-generic-name-interpretations</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-random-and-cohen-generics-are-large</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-solovay-universal-measurability-transfers-to-euclidean-spaces</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-source-algebra-is-caratheodory-measurable</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-space-bounded-machine-configuration-count</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-space-bounded-machines-have-exponentially-many-configurations</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-space-bounded-universal-simulation</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-space-diagonal-machine-halts</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-span-is-the-set-of-linear-combinations</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-span-monotone-and-idempotent</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-span-of-a-single-vector</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spanning-tree-exchange</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spanning-tree-set-is-finite</loc>
<lastmod>2026-08-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spanning-trees-and-schreier-systems-correspond</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sparse-hamming-packing</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sparsity-depends-only-on-the-induced-subgraph</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sparsity-is-monotone-in-the-parameter</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sparsity-transfers-to-a-large-subset</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spatial-and-time-derivatives-pass-through-heat-convolution-for-positive-time</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-specht-branching-subspaces-are-invariant</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-specht-branching-successive-quotients</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-specht-gram-gcd-detects-p-regularity</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-specht-module-has-nondegenerate-self-pairing-in-characteristic-zero</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-specht-modules-classify-irreducibles-over-characteristic-zero-fields</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-special-copy-trichotomy-produces-a-restricted-blockade</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-specialization-dense-domains-and-union</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectral-flattening-preserves-gap-and-symmetries</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectral-form-domain-and-core-of-a-semibounded-operator</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectral-gap-persistence-and-uniform-resolvent-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectral-measure-multiplicity-model-for-a-transitive-system</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectral-measure-of-a-representation-of-an-abelian-lch-group</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectral-permanence-for-unital-c-star-subalgebras</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectral-sequence-subquotient-and-local-lifting-calculus</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-compactness-open-cover-to-unit-ideal</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-compactness-unit-expression-finite-subcover</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-localization-open-immersion</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-map-preimage-of-vanishing-set</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-map-respects-composition-and-identities</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-map-stalk-homomorphisms-local</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-of-a-finite-product-ring-is-a-disjoint-union</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-of-a-positive-operator-is-nonnegative</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spectrum-of-a-self-adjoint-operator-is-real</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sph-pair-forces-antisymmetric-and-central</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sphere-and-ball-measures-scale</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sphere-and-torus-monomial-integrals</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sphere-contact-guard-normal-and-reset-lipschitz-bounds</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sphere-endomorphisms-act-by-the-same-integer-in-every-ordinary-theory</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sphere-finite-graph-charts-and-surface-density</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spheres-of-adjacent-critical-levels-have-product-neighbourhoods</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spherical-bessel-and-hankel-radial-solutions</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spherical-cap-and-dual-slab-scales</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spherical-harmonics-form-complete-basis-and-addition-formula</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spherical-means-of-smooth-data-are-smooth</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spherical-principal-series-is-the-flag-permutation-module</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spherical-surface-integrals-project-onto-weighted-ball-integrals</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spin-structures-exist-iff-w2-vanishes-and-form-h1-torsor</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-spinor-and-clifford-associated-bundles-are-well-defined</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-splicing-edge-disjoint-closed-trails</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-splitting-cofinal-branch-gives-antichain</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-splitting-reaping-comparison-with-b-and-d</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-splitting-stationary-regular-cardinals</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-splitting-stationary-sets-of-fixed-cofinality</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sqp-convex-quadratic-subproblem-has-unique-kkt-certificate</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sqp-kkt-matrix-nonsingularity-under-reduced-curvature</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-free-reduction-of-holomorphic-germ</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-integrable-kernels-define-bounded-compact-integral-operators</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-integrable-markov-transition-conditional-expectation</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-integrable-predictable-step-ito-integral-is-finite-sum</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-continued-fraction-state-recurrence</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-convergent-norm-identity</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-kalman-gram-perturbation-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-kalman-householder-error-rational-envelope</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-kalman-measurement-block-factor-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-kalman-prearray-qr-error-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-kalman-prediction-factor-identity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-kalman-schur-perturbation-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-root-kalman-triangular-solve-forward-bound</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-summable-orthogonal-families-have-norm-convergent-finite-sums</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-summable-sequences-form-a-hilbert-space</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-tangent-conic-blowup-singularities-controlled-by-a-cubic</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-square-zero-coderivation-is-higher-jacobi-identities</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-squarefree-integer-polynomial-root-separation-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-squares-modulo-eight</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stability-of-slice-zero-count-under-holomorphic-parameters</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilizability-and-detectability-pbh-necessary-conditions</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilization-of-a-framed-submanifold-suspends-the-pontryagin-thom-map</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilized-upper-gauge-cancellation-by-block-rotation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilizer-dimension-semicontinuity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilizer-is-a-subgroup</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilizer-of-the-r-n-action-on-a-compact-connected-regular-fibre-is-a-full-lattice</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilizers-in-one-orbit-are-conjugate</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilizing-a-normal-bundle-suspends-its-thom-space</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stabilizing-game-coverings-have-inverse-limits</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stable-and-unstable-manifolds-are-flow-invariant</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stable-gaussian-autoregression-invariant-law</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stable-normal-data-supplies-framings-below-the-middle-dimension</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stable-squares-on-universal-thom-classes</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stable-thom-cohomology-is-a-square-module-coalgebra</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stable-thom-cohomology-is-degreewise-eventually-constant</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stable-thom-detector-coordinates-commute-with-suspension</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stably-trivial-bundles-over-spheres-below-the-rank-are-trivial</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stacking-corresponds-to-loop-concatenation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stalk-inverse-image-sheaf</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stalk-tensor-product</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-stalks-and-colimits-of-the-abelian-sheaf-tensor-product</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-and-reflected-two-sphere-immersions-have-homotopic-formal-data-in-r-three</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-basis-of-f-n</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-borel-conditional-mutual-information-chain-rule-and-data-processing</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-borel-memoryless-channel-mutual-information-tensorization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-complementary-pair-fills-an-n-ball</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-complete-metric-on-a-countable-product</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-containments-relativize</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-costandard-hom-and-ext-vanishing</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-disk-twists-generate-a-free-abelian-subgroup</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-fock-vectors-expand-in-the-upper-global-basis</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-gaussian-is-determined-by-its-moments</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-handle-admits-an-adapted-morse-function</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-hermitian-form-on-functions-on-a-nonempty-finite-set-is-an-inner-product</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-intertwiners-form-a-basis-of-the-principal-series-endomorphism-algebra</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-levi-subgroup</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-normal-cdf-is-continuous-and-strictly-increasing</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-normal-cdf-quantiles-and-symmetry</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-normal-cdf-quantiles-and-tail-symmetry-for-power</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-normal-fourth-moment</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-normal-matrix-has-full-row-rank-almost-surely</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-normal-mills-ratio</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-open-affine-chart-of-a-projective-quotient</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-opens-proj-affine</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-parabolic-double-cosets-are-young-double-cosets</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-polynomial-resolution-admissibility</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-projective-opens-are-affine-spaces</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-pure-braids-generate-each-free-kernel</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-standard-rational-quiver-vanishing-cycles-realize-critical-correspondences</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-standard-tableau-removal-recursion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-standard-twists-fix-the-complementary-basic-arcs-and-commute</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-standard-wishart-independent-normal-quadratic-form-is-f</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-star-or-special-vertex-obstructions-force-wonderfulness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-start-accept-and-transition-constraints-have-polynomial-size</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-starting-point-free-dependent-choice</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-state-elimination-preserves-path-language</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-state-equivalence-is-a-right-congruence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-state-field-reconstruction-from-local-generators</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-states-of-a-concretely-represented-c-star-algebra-are-weak-star-limits-of-vector-states</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stationary-chain-tv-convergence-implies-strong-mixing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stationary-phase-decay-for-spherical-surface-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stationary-phase-for-a-nondegenerate-compactly-supported-phase</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stationary-set-minus-its-trace</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-statistic-induces-deterministic-procedure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stay-put-right-left-macro-simulation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-steenrod-squares-commute-with-relative-cohomology-connectors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-steep-polygonal-functions-are-dense-in-c01</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stein-tomas-tt-star-bound-from-fractional-integration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-steinhaus-and-pettis-for-second-countable-locally-compact-groups</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-step-by-step-interpreter-for-machine-codes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-step-functions-have-vanishing-torus-fourier-coefficients</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-step-functions-on-one-period-are-dense-in-l-one-on-the-torus</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-step-up-leave-one-out-rejection-partition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stiefel-manifolds-are-connected-and-simply-connected-in-positive-codimension</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-stiefel-whitney-classes-of-the-tangent-bundle-of-real-projective-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stirling-constant-from-wallis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stirling-formula-up-to-a-positive-constant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stochastic-local-to-global-rms-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-stokes-for-piecewise-smooth-surface-regions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stokes-theorem-for-the-standard-simplex</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-stopped-kernel-discretization-bias</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-stopped-random-variable-is-measurable-at-the-stopping-time</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-stopping-time-ito-step-interval-sum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-stopping-time-sigma-algebra-is-a-sigma-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-straight-line-homotopies-are-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-strict-blowup-increases-finite-normalization-subalgebra-at-singular-center</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-strict-column-dominance-implies-nonnegative-inverse</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-strict-linear-alternative-for-gcm-trichotomy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-strict-right-minima-of-a-quasiperiodic-partial-sum-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-strict-subharmonic-perturbation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-strict-subsolution-perturbation-for-the-heat-operator</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-strictification-of-a-viscosity-test-function-by-a-quartic-perturbation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-string-ideal-decomposition-of-the-integral-lattices</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-string-ideal-triples-are-balanced</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-strong-continuity-at-zero-implies-orbit-continuity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-strong-convexity-implies-strong-monotonicity-of-gradient</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-strong-distribution-convergence-implies-weak-convergence</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-strong-increase-gives-bounding-projections</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-strong-lp-closed-constraints-pass-through-rellich-limits</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-strong-ltwo-compactness-preserves-unit-normalisation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-strong-mixing-quantile-covariance-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-strong-rrqr-column-swap-volume-ratio</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-strong-rrqr-interpolative-decomposition-returns-a-status</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-strong-transcendence-descends-to-minimal-prime-quotients</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-strong-wolfe-step-exists-on-a-bounded-below-ray</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-strongly-monotone-continuous-map-is-bijective</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-strongly-transcendental-finite-one-variable-algebra-is-nowhere-quasi-finite</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-structure-presheaf-basic-open-well-defined</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-structure-sheaf-euler-characteristic-is-one-minus-genus</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-student-t-and-f-cdfs-are-continuous-and-strictly-increasing</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-su2-hopf-link-sine-data-from-truncated-fusion</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-subdivision-compatible-continuous-polyhedral-homology-comparison</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-subgroup-criterion</loc>
<lastmod>2026-07-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-subgroup-lattice-of-a-finite-cyclic-group</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-subgroup-quotient-of-universal-cover</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-subgroups-of-finite-p-groups-are-p-groups</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subgroups-of-free-abelian-groups-are-free</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subgroups-of-z-are-cyclic</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sublinear-minsize-makes-every-cone-geodesic-a-limit-geodesic</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-submean-inequality-for-heat-subsolutions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-submodule-criterion-sums-and-intersections</loc>
<lastmod>2026-08-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-submodules-of-finite-modules-over-noetherian-rings-are-finite-direct</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-submultiplicative-root-limit</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-subnets-preserve-eventual-properties-and-limits</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subreciprocal-functions-close-under-the-density-recursion</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subring-criterion</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subring-plus-ideal-and-intersection</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subscheme-intersection-fibre-product</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subsequence-inherits-limit</loc>
<lastmod>2026-08-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subset-construction-state-invariant</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subset-of-countable</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subsheaf-generated-by-sections</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-subspace-leverage-score-identities</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-substitution-commutes-with-complementation</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-successive-minima-attainment-and-adapted-flag</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-successive-p-multiple-quotients-recover-elementary-divisors</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-successive-small-integral-geometric-layers-contradict-a-large-x-part</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-successor-cardinal-exists</loc>
<lastmod>2026-08-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-successor-of-extremal</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sugawara-commutator-on-all-restricted-modules</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sugawara-mode-one-commutator</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sugawara-modes-act-on-currents</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-sugawara-quadratic-modes-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sum-check-perfect-completeness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sum-check-verifier-is-polynomial-time-given-point-evaluation</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-sum-is-span-of-union</loc>
<lastmod>2026-07-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-sum-of-all-proper-submodules-of-a-verma-module-is-proper</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-sum-of-three-squares-is-never-seven-modulo-eight</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-summability-of-truncated-normalized-variances</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-summatory-logarithm-asymptotic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sunflower-maximal-disjoint-subfamily</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sup-epsilon</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sup-metric-is-a-metric</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sup-monotone</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sup-of-extremals</loc>
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<loc>https://alphabetamath.cc/item/lem-sup-scale</loc>
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<loc>https://alphabetamath.cc/item/lem-sup-sum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sup-translate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sup-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-supersaturation-for-induced-copies</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-supg-general-p1-interpolation-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-supg-one-dimensional-l2-interpolation-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-supg-one-dimensional-optimal-parameter</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-support-dimension-preserved-field-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-support-is-specialisation-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-support-membership-by-annihilator</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-support-of-a-cyclic-module-is-its-vanishing-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-support-of-a-finite-module-is-union-of-generator-cyclic-supports</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-complete-equicharacteristic-finite-integral-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-complete-equicharacteristic-formal-fibres</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-completed-polynomial-generic-fibre</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-completion-base-change-preserves-closed-fibre-local-completions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-derivations-and-regular-hypersurfaces</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-finite-completion-factors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-finite-type-formal-fibres</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-finite-type-normalization-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-flat-base-change-coherent-cohomology-by-cech</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-generic-power-series-formal-fibres</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-geometric-regularity-field-test-and-generic-spread</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-green-identity-on-smooth-bordered-domain</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-integral-is-independent-of-c-one-boundary-charts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-modification-isomorphism-in-codimension-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-non-pth-power-detected-by-derivation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-null-edges-admit-small-gradient-cutoffs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-open-regular-locus</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-p-basis-subfield-separation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surface-regular-fibres-preserve-normality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surgery-gluing-has-a-canonical-smooth-structure-up-to-diffeomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-surjectivity-modulo-n-minus-for-free-weight-generated-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-suslin-algebra-refining-antichain-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-suslin-line-nowhere-separable-quotient</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-suslin-tree-branch-first-difference-order</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-suslin-tree-forcing-is-countably-distributive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-suslin-tree-normal-splitting-refinement</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-suspension-homotopy-classes-have-natural-group-structures</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-svrg-unbiasedness-and-variance-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sylow-subgroups-of-a-normal-subgroup-are-intersections</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sylow-times-normal-subgroup-covers-when-index-is-a-p-power</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sylvester-inertia-makes-morse-index-intrinsic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sylvester-separation-controls-the-frobenius-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-sylvester-vectorization-isometry-and-kronecker-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-algebra-has-an-ordered-commutative-monomial-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-algebra-qc-and-base-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-and-alternating-rank-coordinate-rings</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-chain-decomposition-induction-step</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-difference-formula-for-fourier-partial-sums</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-difference-of-two-matchings</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-entourages-form-a-base</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-gaussian-alternating-sum-vanishes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-group-conjugation-to-inverse-within-the-preceding-group</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-group-is-a-group</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-groups-up-to-four-are-solvable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-kernel-moment-cancellation</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-matrix-operator-norm-rayleigh</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-pole-polygons-have-clean-energy-critical-manifolds</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-polynomial-centers-have-primitive-split-content-idempotents</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetric-shifted-solution-operator-is-positive-and-self-adjoint</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetrisation-has-the-same-normal-closure</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetrization-for-independent-random-series</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-symmetry-lemma-for-forcing-automorphisms</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-t-cohomology-is-additive-shift-compatible-and-detects-amplitude</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-t0-t1-and-hausdorff-are-hereditary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tableau-cell-alphabet-is-constant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tableau-formula-is-satisfiable-exactly-for-accepting-computations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tableau-stabilizers-transform-by-conjugation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tableau-to-cnf-map-has-polynomial-size-and-time</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-taboo-games-reduce-to-pruned-residual-games</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tagged-sums-approximate-a-contour-integral</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tail-events-are-independent-of-every-finite-initial-sigma-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tail-filter-preserves-net-convergence-and-cluster-points</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tail-sum-integrability-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tame-dvr-inertia-and-abhyankar-ramification-killing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tamed-euler-uniform-moment-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-and-obstruction-spaces-for-hypersurface-deformations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-bundle-chart-transitions-are-smooth-with-smooth-inverses</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-bundle-of-complex-projective-space-and-its-pontryagin-classes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-cone-ideal-containment</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-cone-initial-ideal-presentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-cone-linear-span-tangent-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-curve-reachability-is-an-equivalence-relation</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-direction-contains-the-support</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-of-the-milnor-disk-bundle-has-the-required-stable-splitting</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-points-over-square-zero-vector-extensions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-principal-branch-is-bijective</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-space-functoriality-classical</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-space-product</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-space-to-a-regular-level-set-is-the-kernel-of-the-constraint-derivative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangent-vectors-as-dual-number-points</loc>
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<loc>https://alphabetamath.cc/item/lem-tangential-difference-quotient-test-function</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangential-h-two-estimate-near-a-flat-dirichlet-boundary</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tangential-maximal-function-norm-bound</loc>
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<loc>https://alphabetamath.cc/item/lem-taper-window-l2-normalization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tapered-block-bootstrap-conditional-covariance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tauber-block-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tautological-cotangent-moment-map-is-equivariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tautological-degree-one-class-is-well-defined-and-fiber-generating</loc>
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<loc>https://alphabetamath.cc/item/lem-taylor-expansion-with-integral-remainder-for-banach-valued-curves</loc>
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<loc>https://alphabetamath.cc/item/lem-taylor-integral-remainder</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-taylor-lagrange-remainder-from-mean-value</loc>
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<loc>https://alphabetamath.cc/item/lem-taylor-polynomial-derivatives</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-teichmuller-lift-is-multiplicative-and-unique</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-telescoping-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-annular-central-element-and-reflection-maps</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-boundary-tensor-ideal-has-the-embedded-components</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-cell-forms-detect-semisimplicity-over-c</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-closure-trace-component-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-closure-trace-is-cyclic-and-markov</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-critical-gram-unit-interval</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-critical-standard-modules-are-simple</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-diagram-tower-conditional-expectation-identities</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-exact-truncation-reduces-decomposition-to-trivial-factors</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-general-theta-net-evaluation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-generators-satisfy-local-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-integral-spin-representation-is-split-injective</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-jones-wenzl-partial-trace-and-uniqueness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-jones-wenzl-projector-exists-iff-trivial-projective</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-jones-wenzl-quantum-binomial-criterion-over-fields</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-jones-wenzl-recursion-properties</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-jones-wenzl-ring-descent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-link-state-gram-determinant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-link-state-gram-form-is-invariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-link-state-module-action-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-link-state-restriction-filtration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-negligible-morphisms-form-tensor-ideal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-quantum-binomial-digit-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-rank-one-ribbon-structure-from-the-finite-r-series</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-rank-one-tilting-character-and-dimension</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-rank-one-weyl-and-dual-weyl-filtrations</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-right-closure-preserves-trace-radical</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-root-fusion-paths-have-nonzero-pairings</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-root-gram-rank-and-reflection-dimensions</loc>
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<loc>https://alphabetamath.cc/item/lem-temperley-lieb-root-noncritical-radicals-and-simple-heads</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-signed-forest-candidates-and-their-composition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-spencer-support-binomial-and-reflection-calculus</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-support-character-carry-and-simple-extras</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-temperley-lieb-zero-loop-perfect-matching-standard-module-is-simple</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-and-hom-representations-are-rational</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-consistency-test-soundness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-hom-adjunction-for-bimodules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-place-operators-span-the-symmetric-centralizer</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-product-moment-functional-equals-product-measure-integral</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-product-of-real-symmetric-forms-has-multiplicative-inertia</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-products-of-integrable-weight-modules-are-integrable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-products-of-primitive-vectors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-q1-interpolation-h1-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-qc-modules-quasi-coherent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-ring-presentations-for-base-change</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensor-unfoldings-are-frobenius-isometries</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensoring-a-projective-with-a-finite-dimensional-module-is-projective</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensoring-a-verma-module-by-a-finite-dimensional-module-shifts-types</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensoring-defines-a-pseudofunctor-with-interchange</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensoring-preserves-relative-projectivity-for-finite-group-modules</loc>
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<loc>https://alphabetamath.cc/item/lem-tensoring-with-a-finite-dimensional-module-preserves-verma-flags</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tensoring-with-a-right-module-is-additive-right-exact-and-preserves-direct-sums</loc>
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<loc>https://alphabetamath.cc/item/lem-tensoring-with-b-s-preserves-hodge-riemann-signs</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-term-substitution-denotation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-terminal-e-overlap-quotient-pattern-is-e-free</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-terminal-h-five-overlap-quotient-pattern-is-h-five-and-co-e-free</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-terminal-reachability-and-residual-game-positions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-test-function-cutoffs-and-euclidean-localization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-test-function-inclusion-in-schwartz-space-is-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-test-function-lf-topology-universal-property</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-test-zero-one-loss-risk-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-testing-a-coercive-weak-solution-with-itself-gives-the-energy-bound</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-affine-simple-root-alpha-zero-is-delta-minus-the-highest-root</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-ahss-first-differential-is-the-cellular-coboundary</loc>
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<loc>https://alphabetamath.cc/item/lem-the-alexander-module-of-a-link-complement-is-finitely-presented</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-antidiagonal-subgroup-of-a-central-product-is-a-central-normal-subgroup</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-associated-graded-of-filtered-homology-is-a-subquotient-of-chain-level-data</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-augmented-bar-complex-is-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-augmented-simplicial-chain-complex-of-a-simplex-is-contractible</loc>
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<loc>https://alphabetamath.cc/item/lem-the-bar-differential-is-group-equivariant-and-squares-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-basepoint-evaluation-of-the-stiefel-section-space-is-a-fibration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-basic-weyl-invariant-degree-sum-is-the-number-of-positive-roots</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-bass-serre-coset-graph-is-a-tree</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-bgg-augmentation-has-image-the-simple-module</loc>
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<loc>https://alphabetamath.cc/item/lem-the-bockstein-is-independent-of-lift-and-cocycle-representative</loc>
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<loc>https://alphabetamath.cc/item/lem-the-borel-weil-section-extends-from-the-big-cell-to-the-flag-variety</loc>
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<loc>https://alphabetamath.cc/item/lem-the-bott-partial-connection-is-well-defined-and-flat-in-leaf-directions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-boundary-subobject-factors-through-the-cycle-subobject</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-canonical-map-to-the-enveloping-algebra-is-a-lie-algebra-homomorphism-into-the-commutator-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-casimir-element-is-independent-of-dual-bases</loc>
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<loc>https://alphabetamath.cc/item/lem-the-casimir-operator-is-basis-independent-and-intertwining</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-cayley-graph-of-a-finite-group-with-a-finite-generating-set-is-a-finite-simple-graph</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-cellular-boundary-squares-to-zero</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-center-has-finite-dimensional-image-on-an-o-object</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-center-of-a-full-matrix-algebra-over-a-field-consists-of-the-scalar-matrices</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-central-action-on-the-deformed-antidominant-projective</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-central-reduction-of-usl2-is-simple-away-from-finite-dimensional-characters</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-change-of-projective-resolution-isomorphisms-are-natural</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-closed-disk-is-a-manifold-with-boundary</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-coefficients-of-the-formal-square-root-of-one-minus-four-x</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-cohomology-universal-coefficient-extension-map</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-coinvariant-algebra-is-a-gorenstein-algebra-with-one-dimensional-socle</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-cokernel-of-a-chain-map-is-computed-degreewise</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-columns-of-the-augmented-tensor-double-complex-are-exact</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-combed-geometric-decomposition-is-unique</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-comma-category-projection-strictly-creates-limits-preserved-by-the-functor</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-commutator-of-vector-field-derivations-is-a-derivation</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-commutator-pairing-is-nondegenerate</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-commutator-pairing-is-well-defined-biadditive-and-alternating</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-compact-leaf-produced-by-a-vanishing-cycle-bounds-a-reeb-component</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-complement-of-an-oriented-link-is-a-connected-smooth-three-manifold</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-composite-of-two-functions-is-a-function</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-constant-term-of-a-cyclotomic-polynomial</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-coordinate-components-of-the-oriented-area-vector-are-projected-jacobians</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-coordinate-flux-identity-for-a-simple-solid-region</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-covering-of-a-leaf-associated-to-the-holonomy-kernel-exists</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-cycle-boundary-diagram-associated-to-a-short-exact-sequence-of-complexes</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-cyclic-cover-deformation-retracts-onto-the-lifted-flower-and-spine</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-de-rham-and-smooth-singular-mayer-vietoris-diagram-commutes-away-from-connectors</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-de-rham-complex-and-pullback-extend-to-manifolds-with-boundary</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-de-rham-homotopy-formula-extends-to-boundary-manifolds</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-de-rham-map-commutes-with-mayer-vietoris-connectors</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-de-rham-map-is-an-isomorphism-on-convex-coordinate-domains</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-de-rham-mayer-vietoris-difference-map-is-surjective</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-de-rham-mayer-vietoris-sequence-is-exact-at-the-first-two-terms</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-deck-group-of-a-covering-acts-by-a-covering-space-action</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-deficiency-one-fox-calculus-determinant-rule</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-denominator-quotient-has-only-imaginary-cone-support</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-derivative-lift-of-a-smooth-self-map-to-the-orientation-double-cover</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-derivative-map-is-continuous</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-derived-couple-maps-are-well-defined</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-diagonal-map-is-an-embedding</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-diagonal-of-a-smooth-manifold-is-a-closed-embedded-submanifold</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-differential-annihilates-the-tangent-kernel-at-a-constrained-extremum</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-differential-descends-to-a-quotient-complex</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-differential-sends-derivations-to-derivations-and-is-linear</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-disk-bundle-of-a-smooth-vector-bundle-is-a-compact-manifold-with-boundary</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-divergence-and-curl-of-a-cross-product</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-domain-and-range-of-a-relation-are-sets</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-down-shift-creates-no-new-shattered-set</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-down-shift-preserves-the-number-of-sets</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-drinfeld-hopf-pairing-is-nondegenerate-in-each-root-degree</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-dual-representative-has-uniform-bmo-oscillation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-e-graph-and-the-bird-are-leaf-reducible</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-e-graph-and-the-bird-graph-are-wonderful</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-effacement-extension-commutes-with-connecting-morphisms</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-effacement-extension-is-independent-of-the-effacing-morphism</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-exact-couple-differential-squares-to-zero</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-ext-balance-isomorphism-is-independent-of-resolution-comparison-data</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-extended-time-dependent-field-has-a-global-time-one-flow</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-fibration-connecting-map-is-independent-of-lift-and-representative</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-filtered-differential-induces-d-r-on-the-r-page</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-first-four-band-comparison-is-a-compensated-band-stabilization</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-first-layer-relations-in-a-closed-moy-resolution-form-a-regular-sequence</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-first-serre-differential-is-the-cellular-boundary-with-local-coefficients</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-flow-definition-of-tensor-lie-derivative-is-local-and-well-defined</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-fock-pairing-matches-projective-simple-and-standard-costandard-pairings</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-fock-space-tail-estimates-give-q-adic-vanishing-and-finiteness</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-fork-noodle-pairing-detects-essential-intersections</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-fork-noodle-pairing-is-well-defined-and-equivariant</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-four-band-d-pair-case-is-a-markov-sequence</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-four-point-condition-implies-slim-triangles</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-frechet-derivative-is-unique</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-full-boundary-twist-acts-on-lkb-by-the-scalar-q-to-two-n-t-squared</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-full-group-c-star-seminorm-is-finite-and-separates-the-required-quotient</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-galois-automorphisms-are-algebraically-independent-over-an-infinite-base-field</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-generic-borel-half-and-opposite-half-form-a-dj-crossed-double</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-geodesic-spray-is-a-well-defined-smooth-vector-field-on-tm</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-geometric-half-twist-acts-on-the-lifted-edge-basis-by-the-burau-block</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-gns-null-space-is-translation-invariant</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-gns-translation-action-is-unitary-and-strongly-continuous</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-goursat-majorant-equation-has-a-convergent-positive-power-series-solution</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-graph-notions-agree-with-the-published-finite-graph-theory</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-graph-of-a-continuous-map-into-a-hausdorff-space-is-closed</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-gromov-product-inequality-implies-the-four-point-condition</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-group-ring-is-free-over-a-subgroup-ring</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-harmonic-complement-of-the-coinvariant-algebra</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-hecke-bar-involution-is-well-defined</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-hecke-generators-satisfy-the-artin-relations-and-are-units</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-hecke-tower-is-free-over-the-previous-level</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-hom-cochain-differential-squares-to-zero</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-hom-complex-differential-squares-to-zero</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-homotopy-effect-of-a-surgery-killing-a-relative-class-below-the-middle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-horseshoe-kernel-fits-a-short-exact-sequence</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-identity-of-a-finite-dimensional-algebra-decomposes-into-primitive-central-idempotents</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-immersion-condition-is-open-in-the-weak-topology-for-compact-sources</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-imprimitivity-reconstruction-map-is-isometric-and-intertwining</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-induced-action-is-strongly-continuous</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-induced-action-is-unitary</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-induced-cohomology-map-is-independent-of-the-injective-comparison-extension</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-induced-homology-map-is-independent-of-the-comparison-lift</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-induced-inner-product-is-independent-of-coset-representatives</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-inhomogeneous-group-cochain-differential-squares-to-zero</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-interior-of-an-attached-cell-embeds-openly-in-its-closure</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-intersection-of-a-nonempty-set-is-a-set</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-interval-homotopy-operator-is-coordinate-independent</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-invariant-exterior-derivative-formula-is-c-infinity-multilinear</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-invariant-vector-and-covector-of-the-unreduced-burau</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-invariants-functor-for-n-sends-injectives-to-q-acyclic-modules</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-inverse-of-one-plus-the-generator-in-a-truncated-mod-two-polynomial-ring</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-k-topology-is-hausdorff-and-not-regular</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-kac-moody-denominator-is-weyl-skew</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-kernel-of-a-chain-map-is-computed-degreewise</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-kernel-of-a-function-is-an-equivalence-relation</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-khovanov-seidel-algebra-has-the-four-m-plus-one-path-basis</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-khovanov-seidel-curve-complex-is-a-complex-and-is-invariant-under-normal-form-moves</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-koszul-hochschild-comparison-respects-crossing-differentials-and-trigradings</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-kronecker-pairing-is-independent-of-cocycle-and-cycle-representatives</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-kunneth-cross-product-map-is-well-defined-and-natural</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-kunneth-tor-map</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-l1-involution-is-isometric-and-reverses-convolution</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-laurent-polynomial-ring-is-noetherian-and-a-unique-factorisation-domain</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-lefschetz-operator-factors-through-deleted-bott-samelsons</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-left-derived-connecting-map-is-independent-of-the-horseshoe-resolution-and-lifts</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-level-one-vector-representation-has-a-perfect-crystal-with-lower-global-basis</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-limit-map-of-a-compact-hausdorff-space-is-an-ultrafilter-algebra</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-local-affine-hecke-socle-argument-for-residue-translations</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-local-intersection-sign-of-the-graph-and-diagonal</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-loop-residue-form-is-alternating</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-loop-residue-form-satisfies-the-lie-two-cocycle-identity</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-lusztig-integral-form-is-stable-under-bar-and-contravariant-duality</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-mapping-cone-differential-squares-to-zero</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-mapping-cylinder-differential-squares-to-zero</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-markov-trace-of-an-inverse-hecke-generator</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-mayer-vietoris-connector-is-independent-of-small-chain-decomposition</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-minimal-rouquier-differential-supplies-weak-lefschetz-injectivity</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-minimal-sparsity-parameter-drops-below-the-target</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-minus-one-specialization-of-three-strand-burau-has-kernel-generated-by-delta-to-the-fourth</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-multilinear-monomials-of-bounded-degree-are-independent-on-the-cube</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-negative-half-is-separated-by-iterated-skew-derivations</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-nilpotent-central-fiber-is-a-reduced-integral-domain</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-node-count-is-the-level-one-cartan-pairing</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-nondegenerate-integral-specialization-has-a-quantum-casimir</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-norm-of-a-positive-element-is-the-supremum-of-state-values</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-normal-model-map-is-a-foliated-local-diffeomorphism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-normal-model-map-restricts-to-a-diffeomorphism-onto-a-saturated-neighbourhood</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-obstacle-admissible-set-is-closed-convex-and-weakly-closed</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-one-step-generator-map-is-a-functorial-monomorphism</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-open-sets-induced-by-an-ultrafilter-algebra-form-a-topology</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-open-star-criterion-produces-a-simplicial-map</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-order-p-automorphism-of-a-cyclic-group-of-order-p-squared</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-order-topology-on-an-ordinal</loc>
<lastmod>2026-08-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-orientable-double-cover-of-a-smooth-manifold</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-oriented-boundary-loop-represents-the-ordered-product-of-the-standard-meridians</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-orthogonal-complement-of-a-subspace-under-the-standard-form</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-oscillating-zigzag-curve</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-parabolic-hecke-modules-have-standard-bases-actions-and-compatible-bars</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-parabolic-highest-weight-truncation-factors-through-the-cyclotomic-quotient</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-parabolic-semi-regular-duality-and-reverse-column-label-map</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-partial-alternating-sum-of-a-binomial-row</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-planar-forgetful-map-has-a-continuous-section</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-plane-or-disc-alternative-gives-contractibility</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-point-motion-boundary-map-is-a-well-defined-homomorphism</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-pointwise-norm-is-smooth-off-the-zero-vector</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-positive-braid-monoid-is-left-and-right-cancellative</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-power-set-of-a-set-is-a-set</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-preconnecting-arrow-annihilates-boundaries</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-preferred-lift-of-a-half-twist-shifts-the-bigrading</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-prime-five-vertex-graphs-are-exactly-the-bull-five-cycle-five-vertex-path-and-its-complement</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-primitive-pi-cap-block-embeds-and-gives-the-global-reeb-model</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-principal-ultrafilter-and-ultrafilter-flattening-maps-are-natural</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-prism-triangulation-has-the-stated-oriented-boundary</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-product-of-an-indexed-family-is-a-set</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-product-of-two-absolutely-continuous-functions-is-absolutely-continuous</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-punctured-disk-is-path-connected-locally-path-connected-and-semilocally-simply-connected</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-q-antisymmetrizer-determines-the-finite-q-wedge-kernel</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-q-wedge-relations-coincide-with-the-type-a-energy-braiding-kernel</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-quotient-is-an-induced-subgraph-on-a-transversal</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-rank-one-soergel-bimodule-square-splits</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-realization-of-a-simplicial-map-is-continuous-and-functorial</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-reduced-burau-module-is-free-of-rank-n-minus-one</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-relative-connecting-map-is-independent-of-lift-and-representative</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-remaining-closure-koszul-complex-is-the-diagonal-hochschild-complex</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-riemannian-volume-density-is-coordinate-independent</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-round-circle-and-its-reflection-are-not-isotopic-embeddings-in-the-plane</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-rows-of-the-augmented-tensor-double-complex-are-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-rth-differential-squares-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-second-four-band-comparison-is-a-compensated-band-destabilization</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-second-fundamental-form-is-a-symmetric-normal-bundle-valued-two-tensor</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-second-homotopy-group-of-so-three-vanishes</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-serre-quotient-has-weyl-symmetry-and-no-residual-kac-moody-kernel</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-set-of-functions-between-two-sets-is-a-set</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-shifted-differential-squares-to-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-shifted-integrable-character-numerator-is-weyl-skew</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-simplicial-augmentation-is-a-chain-map</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-singular-coboundary-squares-to-zero</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-skeletal-telescope-projects-by-a-homotopy-equivalence-of-pairs</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-smooth-structure-on-g-mod-h-is-independent-of-the-local-complement</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-square-map-is-well-defined-and-refines-the-commutator-pairing</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-stabilizer-action-on-an-imprimitivity-fiber-is-unitary</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-stable-elementary-subgroup-is-normal-and-contains-the-commutator-subgroup</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-stable-homotopy-colimit-is-independent-of-the-chosen-cofinal-tail</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-standard-flower-is-a-deformation-retract-with-free-meridian-basis</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-standard-form-of-two-incidence-vectors-is-the-intersection-size</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-standard-stem-system-cuts-the-punctured-disk-open-to-a-disk</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-star-antiautomorphism-of-the-type-a-hecke-algebra</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-star-expansion-of-a-forest-containing-a-long-path-contains-the-corresponding-cycle</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-star-expansion-of-k-three-contains-the-hatted-five-cycle</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-star-expansion-of-the-four-vertex-path-contains-induced-c-six-and-c-seven</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-stokes-integrand-identity-on-a-c2-patch</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-substituted-set-is-a-module</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-sum-of-triangularly-disjoint-graded-ideals-is-disjoint-from-h</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-target-inclusion-in-a-cellular-mapping-cylinder-is-simple</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-tautological-one-form-is-intrinsic-and-smooth</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-tensor-total-differential-is-well-defined-and-squares-to-zero</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-three-cone-calculation-for-a-composite-chain-map</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-total-cartan-eilenberg-complex-computes-the-derived-composite</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-total-differential-squares-to-zero</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-totient-of-a-gcd-and-of-a-least-common-multiple</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-trefoil-does-not-bound-a-smooth-proper-disk-in-the-four-ball</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-two-filtrations-have-e-two-pages-rpg-rqf-and-the-derived-composite-edge</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-two-hom-double-complex-differentials-commute-before-signing</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-type-a-diagrammatic-relations-hold-for-soergel-bimodules</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-the-type-a-standard-character-is-multiplicative</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-underlying-set-functor-on-rings-strictly-creates-split-coequalizers</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-union-of-two-compatible-smooth-atlases-is-a-smooth-atlas</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-universal-coefficient-edge-map-for-homology-is-well-defined</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-universal-coefficient-tor-obstruction-map-for-homology</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-unordered-two-point-punctured-plane-has-an-equivariant-two-dimensional-cell-model</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-vacuum-projective-is-a-highest-weight-generator</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-weak-smooth-topology-is-independent-of-the-chosen-atlas</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-wedge-product-is-alternating-and-bilinear</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-weighted-area-form-is-sl2-r-invariant</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-the-weighted-discrete-series-space-is-a-hilbert-space</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-theorem-of-the-square-and-mumford-homomorphism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-theta-n-connected-sum-operation-is-well-defined</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-thin-quadrilaterals-in-a-hyperbolic-space</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-this-homeomorphism-sends-the-cantor-set-onto-a-set-of-lebesgue-measure-one</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-thom-class-of-a-disk-bundle-pairs-with-the-base-generator</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-thom-disk-sphere-quotient-identifies-relative-and-reduced-cohomology</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-thom-isomorphism-extends-over-a-finite-numerable-trivializing-cover</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-thom-isomorphisms-glue-over-two-trivializing-opens</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-thom-space-is-independent-of-the-bundle-metric-up-to-canonical-homeomorphism</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-connected-graph-has-a-contractible-edge</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-connected-kuratowski-free-is-planar</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-dimensional-laplace-spherical-harmonic-addition-theorem</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-dimensional-scattering-kernel-is-square-integrable</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-mod-four-prime-dividing-two-square-sum</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-sat-to-binary-constraint-graph</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-series-necessity-for-truncated-means-and-variances</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-simply-connected-models-are-inequivalent</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-three-slope-inequality-for-convex-functions</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-thue-small-representatives</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-tight-borel-gaussian-law-has-separable-support</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-tikhonov-bias-converges-for-minimum-norm-solution</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-tikhonov-data-residual-continuity-monotonicity-and-limits</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-tikhonov-source-condition-bias-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-time-along-ode-solution-derivative-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-time-at-least-input-length-permits-complete-input-reading</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-time-bounds-imply-space-bounds</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-time-controlled-self-reference-for-nondeterministic-machines</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-time-diagonal-language-respects-its-budget</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-time-penalisation-moves-a-doubling-variables-maximum-away-from-the-terminal-boundary</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-time-translation-acts-freely-on-nonconstant-trajectories</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-toeplitz-matrix-has-displacement-rank-at-most-two</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-top-cohomology-vanishes-above-canonical-ample-threshold</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-top-exterior-power-detects-subspace-stabilizers</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-topological-group-translations-and-inversion</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-topological-vector-space-translation-scaling-and-absorption</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-topologists-sine-curve-is-connected</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-toponogov-distance-support-inequality</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-tor-with-the-trivial-module-is-computed-by-the-weak-bgg-resolution</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-torsion-is-c-infinity-bilinear-and-skew-symmetric</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-torsion-quotient-invertible-sheaves-effective-divisor</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-torus-rational-modules-and-gradings</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-total-boundedness-passes-to-dense-uniform-extensions</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-total-fractions-split-over-hypersurface-branches</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-total-oracle-functional-has-computable-use-bound</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-total-soundness-follows-by-union-bound</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-total-transform-strict-plus-exceptional-multiplicity</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<loc>https://alphabetamath.cc/item/lem-total-variation-coupling-and-kernel-contraction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-total-variation-half-l1-formula-on-a-countable-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-total-variation-seminorm-laws</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-totally-bounded-basic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-totally-bounded-uniformities-equal-their-samuel-uniformity</loc>
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<loc>https://alphabetamath.cc/item/lem-tournament-cycle-insertion</loc>
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<loc>https://alphabetamath.cc/item/lem-trace-commutes-with-smooth-boundary-cutoffs-and-charts</loc>
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<loc>https://alphabetamath.cc/item/lem-trace-form-nondegeneracy-characterizes-semisimple-finite-dimensional-algebras</loc>
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<loc>https://alphabetamath.cc/item/lem-trace-form-of-a-faithful-representation-of-a-semisimple-lie-algebra-is-nondegenerate</loc>
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<loc>https://alphabetamath.cc/item/lem-trace-norm-of-hilbert-exterior-powers</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trace-of-a-holomorphic-one-form-under-a-nonconstant-map-to-the-sphere</loc>
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<loc>https://alphabetamath.cc/item/lem-trace-of-an-idempotent-is-the-dimension-of-its-image</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trace-of-commutators-of-square-matrices-is-zero</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trace-pairing-for-a-finite-separable-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trace-riccati-inequality</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tracial-hilbert-module-dimension-and-finite-corners</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tracial-standard-form-and-normal-functional-vectors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transcendence-basis-exchange</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transfer-cycle-decomposition-formula</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transfer-is-a-homomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transfer-is-independent-of-the-transversal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transfinite-iteration-of-the-generator-extension-preserves-monomorphisms-and-factorizes-small-source-maps</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transgression-between-two-connections-is-exact</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transgression-kernel-is-the-image-of-restriction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transitive-p-group-permutation-modules-have-point-stabilizer-vertices</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transitive-subgroups-of-s-four-and-the-resolvent-action</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transitive-zf-models-have-correct-proof-codes</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transitivity-of-module-finiteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-translates-of-a-block-form-a-g-invariant-partition-of-its-orbit</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-translation-estimate-for-w-one-p-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-translation-invariant-locally-finite-borel-measure-on-rd</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-translations-preserve-compactly-supported-continuous-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transport-characteristics-depend-c-one-on-initial-position</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transport-equation-along-a-characteristic</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transport-lattice-spectral-measure-to-torus</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transpose-is-bounded-and-has-the-same-norm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transpose-lower-bound-gives-image-ball-density</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transpose-range-membership-by-domination</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transpose-reverses-composition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transposition-class-sum-acts-on-a-specht-module-by-total-content</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transversal-wide-blocks-in-structural-comb-partitions-yields-a-pure-blockade</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transversality-is-equivalent-to-surjectivity-on-the-normal-quotient</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transverse-complementary-spheres-have-product-charts</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transverse-holonomy-transport-is-well-defined-and-equivariant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transverse-hybrid-event-time-error</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transverse-hyperplane-selects-unique-local-branch-point</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-transverse-shapovalov-pairing-on-a-generic-hyperplane</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tree-cones-give-uniform-two-side-control</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tree-predecessors-and-common-extensions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tree-schreier-generators-are-freely-independent</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-triangle-extrema-and-real-tree-tripod-rules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-triangle-inequality-finite</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-triangular-borel-maps-scale-euclidean-volume</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-triangular-independence-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-triangular-information-averages</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-triangulated-k-zero-shifts-and-exact-functors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trigonalizable-iff-invariant-flags</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trigonometric-characters-are-orthonormal</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trigonometric-identities-machin-and-range-reduction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trimming-a-self-regular-set-of-high-density</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trimming-a-self-regular-set-of-low-density</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-triple-cubic-rational-surface-branch-reduces-in-two-steps</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-triple-massey-expression-is-closed</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trivial-action-on-standard-meridians-fixes-the-stem-arc-system-up-to-isotopy</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trivial-c1-holonomy-gives-a-saturated-product-neighbourhood</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trivial-circuit-constraint-system-is-a-weak-assignment-tester</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-trivial-fundamental-group-implies-null-homology-for-plane-domains</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trivial-simplicial-fibration-fibres-products-and-contraction</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trivial-words-in-a-recursively-presented-group-are-recursively-enumerable</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncated-cg-iterates-are-krylov-vectors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncated-integrals-of-rational-powers</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncated-modified-flow-matches-map</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncated-perron-kernel</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncated-plane-local-length</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncated-riesz-kernel-potential-bounded-on-lp</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncated-svd-bias-and-data-noise-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncated-wave-cone-geometry-and-frustum-presentation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-truncation-triangles-are-essentially-unique-and-functorial</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trust-region-cauchy-decrease</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trust-region-ratio-accuracy-for-small-radii</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-trust-region-subproblem-optimality-and-hard-case</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tseitin-transformation-is-linear-size-and-equisatisfiable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tt-star-reduces-extension-to-convolution-with-surface-measure-transform</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tube-lemma-for-a-compact-factor</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tube-lemma-for-a-compact-metric-factor</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-tubular-charts-realize-a-prescribed-normal-identification</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-turan-graph-edge-count-and-balance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-turing-reducibility-is-a-preorder</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-turing-step-coding-is-primitive-recursive</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-twisted-boundaries-square-to-zero-and-are-independent-of-lift-bases</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/lem-twisted-product-is-a-group-iff-the-factor-set-is-a-two-cocycle</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-twisting-sheaf-projective-space-ample</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-two-affine-double-cover-cohomology</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-two-and-three-by-three-nonsingular-dyadic-system-solvable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-two-block-admm-energy-and-objective-estimates</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-two-by-two-delta-complex-for-a-double-tower</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-two-cell-hat-and-quadratic-functions-lie-in-h10</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-two-colour-ramsey-arrow-recursion</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-common-diagonalizations-are-related-by-a-base-isomorphism-and-a-measurable-field-of-unitaries</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-compact-cover-sweeps-for-function-lattices</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-cyclotomic-shears-give-a-periodic-integrable-based-sl-two-chain</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-dimensional-numerical-range-is-convex</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-dimensional-tame-symbol-reciprocity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-disjoint-circles-in-s-two-cobound-an-annulus</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-disk-complement-in-a-homotopy-sphere-is-an-h-cobordism-in-dimensions-at-least-six</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-distinct-minimal-normal-subgroups-of-a-primitive-group-are-regular</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-dyadic-cubes-are-nested-or-disjoint</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-essentially-different-two-square-representations-factor-an-odd-integer</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-extensions-with-the-same-ext-class-are-equivalent</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-finite-linear-subdivisions-have-a-common-simplicial-refinement</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-functions-are-equal-exactly-when-they-agree-at-every-point</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-noncommuting-elements-of-an-extraspecial-p-group-generate-a-subgroup-of-order-p-cubed</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-omitted-values-rule-out-an-essential-singularity</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-open-cover-cech-complex</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-open-cover-small-chains-are-the-sum-of-the-two-singular-subcomplexes</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-point-interpolation-for-a-separating-real-function-lattice</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-point-interpolation-in-a-separating-real-function-algebra</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-points-avoiding-a-finite-set-lie-in-a-common-embedded-ball</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-query-pcps-and-constraint-graphs-are-equivalent</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-relative-cell-layers-have-free-group-ring-homotopy-bases</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-sample-u-statistic-degenerate-remainder-order</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-sample-u-statistic-hoeffding-decomposition</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-sample-u-statistic-projections-well-defined</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-scale-gradient-decomposition-for-h01</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-sided-mills-bounds-for-standard-normal-tail</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-sided-scaled-householder-similarity-error</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-sided-stationary-extension-preserves-rho-mixing</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-sided-unitary-equivalence-errors-accumulate-for-pencil</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-signs-detect-an-operator-increment</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-simulation-summary-covariance-is-singular-in-two-dimensions</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-square-representations-of-prime-powers</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-stage-finite-design-variance-identities</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-stage-rosenbrock-local-defect-and-residual-error</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-two-torsion-and-uniqueness-of-plane-cubic-group-law</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-character-recursion-under-simple-soergel-tensoring</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-graph-bimodule-extension-vanishing</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-hecke-permutation-modules-have-semistandard-murphy-bases-and-specht-filtrations</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-hecke-standard-basis-for-soergel-comparison</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-kazhdan-lusztig-basis-has-elementary-triangular-bar-properties</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-modular-root-interval-essential-subset-basis-and-count</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-nilpotent-orbit-closures-are-normal-via-chain-varieties</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-reduced-words-are-connected-by-braid-moves</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-soergel-frobenius-biadjunction</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-soergel-generators-are-finite-free-on-both-sides</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-soergel-special-hom-formula</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-support-filtration-multiplicities-are-intrinsic</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-tableau-central-summands-are-single-linkage-blocks</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-a-top-support-layers-are-controlled-by-reflection-localization</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-i-factor-fields-admit-measurable-irreducible-multiplicity-splittings</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-s-h-prior-draws-are-l2-densities</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-type-s-posterior-preliminary-contraction</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-typical-degrees-in-a-regular-pair</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ula-fixed-step-gaussian-kernel-exponential-drift</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ula-pathwise-kl-error-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ula-potential-coercivity-from-radial-drift</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ula-uniform-exponential-moments-and-invariant-laws</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ultra-tight-multisets-admit-column-potentials</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ultrafilter-cluster-points-are-limits</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ultrafilter-prime</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ultrafilter-pushforward-is-an-ultrafilter-and-is-functorial</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-ultrafilters-on-totally-bounded-uniform-spaces-are-cauchy</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-unbounded-adjoint-is-well-defined-and-closed</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-unbounded-pvm-integral-is-well-defined-and-closed</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-unbounded-stationary-fibres-yield-a-partition</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uncorrelated-joint-banach-gaussians-are-independent</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uncorrelated-jointly-gaussian-blocks-are-independent</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uncountable-almost-disjoint-family-on-natural-numbers</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uncountable-analytic-splitting</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uncountable-club-guessing-at-a-double-successor</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uncountable-delta-system-for-finite-sets</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-undeformed-lefschetz-and-hodge-riemann-restrict-to-soergel-summands</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-unequal-parameter-hecke-standard-basis-and-bar-triangularity</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-cdf-order-and-quantile-coverage</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-closure-of-a-general-real-function-algebra-is-a-lattice</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-closure-of-a-real-function-algebra-is-a-lattice</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-convergence-implies-pointwise-convergence-real-functions</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-convergence-in-the-uniform-metric</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-convergence-uniformity-is-finer-than-pointwise</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-convexity-gives-unique-asymptotic-centers</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-empirical-bayes-marginal-score-bound</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-ergodicity-controls-uniform-mixing</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-filling-data-give-a-uniform-slimness-bound</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-integral-error-bound</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-interval-poincare-inequality</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-laurent-approximation-through-bundle-automorphisms</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-law-on-finite-subset-families</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-limits-linear-combinations</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-metric-on-a-function-space</loc>
<lastmod>2026-08-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-null-g-delta-capture-functions</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-product-limit-under-boundedness</loc>
<lastmod>2026-08-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-right-censoring-risk-set-convergence</loc>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-sine-integral-bound-and-dirichlet-value</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniform-tail-control-for-dominated-improper-multiple-integrals</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniformizable-spaces-are-completely-regular</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniformizable-spaces-are-regular</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-uniformizer-differential-is-a-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-uniformly-convergent-sequences-form-equicontinuous-families</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-union-of-a-chain-of-dominated-extensions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-union-of-chain-of-filters</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-union-of-two-meeting-modules-is-a-module</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unions-and-intersections-of-small-families</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unions-of-components-and-of-anticomponents-are-modules</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unipotent-and-diagonalizable-intersection-is-trivial</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unipotent-invariants-are-exact-over-c</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unipotent-representation-criterion</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unique-parsing-of-set-coded-syntax</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unique-subgroup-of-order-p-forces-cyclicity</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-uniqueness-of-a-multivariate-exponential-transform</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-uniqueness-of-an-extended-complete-field-absolute-value</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-uniqueness-of-stable-clifford-hopf-decomposition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-uniqueness-of-the-complex-derivative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-uniqueness-of-the-total-derivative</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-uniqueness-of-twists-on-the-projective-line</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unisolvent-dofs-define-reference-interpolant</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-circle-is-a-compact-metrizable-topological-group</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-cube-h01-separability-and-l2-compactness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-disc-estimate-for-weierstrass-elementary-factors</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-interval-circle-is-a-nonempty-compact-metric-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-interval-functions-extend-over-evaluation-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-interval-is-standard-borel</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-interval-lebesgue-gauss-data-valid</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-logarithms-lie-in-the-product-formula-hyperplane</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unit-sphere-is-lebesgue-null</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unitary-intertwiners-preserve-direct-integral-fiber-dimension</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unitary-intertwiners-preserve-fiber-multiplicity-over-a-standard-borel-base</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unitary-invariant-subspaces-have-invariant-orthogonal-complements</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unitary-matrix-coefficients-are-bounded-and-uniformly-continuous</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unitary-similarity-error-accumulation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-units-and-powers-of-the-laurent-polynomial-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-units-of-z</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-univariate-trimmed-mean-total-and-measurable</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-central-extension-is-unique-up-to-unique-isomorphism</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-complex-flag-bundle-is-bt-n</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-cover-cellular-boundary-and-lifted-maps-are-right-group-ring-linear</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-cyclotomic-hecke-canonical-trace-is-perfect-and-symmetric</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-cyclotomic-hecke-ordered-monomials-form-a-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-family-and-hilbert-polynomial-strata</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-hyperplane-relative-weak-lefschetz-and-maximal-pullback-subobjects</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-martin-lof-test-exists</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-metric-trajectory-projection-is-fredholm</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-mod-two-class-detects-admissible-composites-in-the-strict-range</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-net-cluster-points-are-limits</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-nondegenerate-affine-hecke-ordered-monomials-form-a-basis</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-oriented-sphere-bundle-has-bso-n-minus-one-total-space</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-pcf-sequences-have-strong-increase-and-exact-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-property-of-a-contraction</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-universal-real-thom-spaces-are-r-minus-one-connected</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universal-weyl-c-star-algebra-is-well-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-universally-closed-valuative-existence-quasicompact</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-unmodified-integral-torus-has-a-quantum-binomial-basis</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-unordered-pair-equality</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-unreduced-burau-matrices-satisfy-the-artin-relations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unshifted-elliptic-equation-is-an-identity-minus-compact-equation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unstable-orientations-induce-trajectory-moduli-orientations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unsuspended-a-infinity-identities-are-tensor-codifferentials</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-untwisted-hall-product-finiteness</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-unweighted-good-lambda-local-estimate-for-maximal-truncations</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-upper-half-plane-sum-phase-between</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-upper-semicontinuous-functions-are-borel-and-circle-integrals-are-defined</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-upper-unitriangular-central-series</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-upper-unitriangular-coordinate-ring-is-coconnected</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-urysohn-sits-between-hausdorff-and-regular-plus-t1</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-valence-boundary-arc-computation</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-valuation-ring-is-local</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-value-of-a-state-at-a-self-adjoint-element-lies-between-the-spectral-bounds</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-van-der-corput-oscillatory-integral-estimate</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-van-kampen-factorization-invariance</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-van-kampen-homotopy-grid</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-compactly-supported-h1-on-opens-implies-c-soft</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-gradient-and-time-derivative-imply-constancy-on-convex-sets</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-ideal-is-radical</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-ideal-of-a-reduced-hypersurface-germ</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-of-negative-laurent-coefficients-on-a-hartogs-figure</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-relative-homotopy-extends-a-homotopy-inverse-over-successive-cells</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-set-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-set-of-a-finite-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-set-of-an-arbitrary-sum</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-set-reverses-inclusions</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-sets-detect-radicals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-tail-control-implies-small-truncated-second-moment</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-torsion-allows-algebraic-diagonalization-by-simple-handle-moves</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vanishing-viscosity-families-are-locally-precompact-in-lone</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variable-base-cotensor-corner-and-path-objects</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variable-coefficient-flux-stencil-second-order-consistency</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variable-degree-polynomial-spaces-are-h1-conforming</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variable-radius-injectivity-for-normal-addition</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variable-step-adams-lagrange-weights</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variable-step-bdf2-increment-ratio-recurrence</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variable-step-bdf2-interpolation-and-local-defect</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variance-and-covariance-identities-for-random-variables</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variance-and-covariance-identities</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variance-sensitive-bounded-empirical-process-concentration</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variation-additive-on-subintervals</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variation-function-and-jordan-identities</loc>
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<loc>https://alphabetamath.cc/item/lem-variation-of-constants-integral-is-continuous-for-lone-time-forcing</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-variety-equations-dimension-bound</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-variety-ideal-galois-connection</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vc-set-covering-entropy</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vector-bundle-chow-homotopy-invariance</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vector-bundle-p1-extension-splits</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vector-bundle-p1-has-maximal-degree-line-subbundle</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-vector-bundle-p1-maximal-line-quotient-locally-free</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vector-bundle-transition-functions-satisfy-the-cocycle-identities</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-vector-field-index-is-independent-of-chart-ball-and-trivialization</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-vector-newton-correction-error-under-lipschitz-jacobian</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-vector-operations-are-continuous-in-a-normed-space</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vector-space-elementary-consequences</loc>
<lastmod>2026-08-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vector-valued-continuous-curve-space-is-complete</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-verma-embedding-implies-strong-linkage</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-verma-filtered-objects-are-acyclic-for-n-minus-coinvariants</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-verma-flag-multiplicities-are-independent-of-the-flag</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-verma-self-extensions-in-category-o-split</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-verma-sign-sum-over-bruhat-intervals</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-veronese-map-well-defined-closed-immersion</loc>
<lastmod>2026-09-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vertex-and-edge-stabilizers-and-their-incidence-inclusions</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vertex-connectivity-at-most-edge-connectivity</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vertex-operator-series-for-padded-schur-functions</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-vertical-composition-of-natural-transformations-is-natural</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-very-ample-implies-ample</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-viete-finite-cosine-product-and-nested-radicals</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-viral-divisive-finite-family-yields-weak-viral</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-virtual-weyl-combinations-detect-q-schur-block-separation</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-viscosity-initial-trace-is-enforced-by-upper-and-lower-barriers</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-viscosity-testing-by-first-order-jets</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-viscous-approximations-obey-uniform-linfinity-and-energy-bounds</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-viscous-scalar-laws-contract-spatial-translates-in-lone</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-volume-chirality-and-clifford-hopf-clutching</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-volume-far-field-map-is-bounded</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-volume-integral-operator-well-defined-and-bounded</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-von-mangoldt-explicit-formula-residues</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-voronoi-vertex-empty-circle</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-w-one-p-is-reflexive</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-w-one-two-is-a-hilbert-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-w1-is-finite-on-probability-measures-with-finite-first-moment</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wall-crossing-compositions-produce-the-projective-with-the-top-standard-label</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wall-crossing-functors-act-on-standard-modules-by-the-two-step-extension</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wall-crossing-functors-act-on-the-grothendieck-group-by-right-multiplication-by-one-plus-s</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wall-signature-and-rt-cap-reference-correction</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wallis-integrals-recurrence-and-squeeze</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-walsh-hadamard-code-has-distance-one-half</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-water-filling-optimal-allocation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wave-formulas-attain-the-cauchy-data</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wave-packet-model-dominates-the-linearised-carleson-operator</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wavelet-product-prior-is-l2-valued</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-and-strong-additivity-of-orthogonal-projections</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-beltrami-factorization-in-holder-coordinates</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-bgg-base-case-for-the-trivial-module</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-bialgebra-source-and-target-bases</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-closedness-keeps-the-direct-method-limit-admissible</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-containment-implies-kernel-inclusion</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-containment-of-the-trivial-representation-and-almost-invariant-vectors</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-derivative-is-independent-of-lp-representatives</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-derivative-linearity-locality-and-commutation</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-derivatives-are-polynomial-fourier-multipliers</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-derivatives-are-unique-almost-everywhere</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-divergence-form-equations-are-invariant-under-c-two-boundary-charts</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-equation-for-a-first-derivative-includes-coefficient-commutators</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-equivalences-glue-along-a-common-connected-cw-subcomplex</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-equivalences-of-pairs-induce-isomorphisms-on-relative-homotopy</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-harmonic-limits-on-riemann-surfaces</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-hausdorff-diagonals-and-closed-quotients</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-homotopy-equivalences-induce-integral-homology-isomorphisms-without-choice</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-join-classifying-model-is-a-cw-k-g-one</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-leibniz-rule-with-a-smooth-factor</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-limit-of-uniformly-bounded-difference-quotients-is-the-weak-derivative</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-local-subharmonic-peak-function-implies-regularity</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-lower-semicontinuity-of-the-sobolev-norm</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-lq-thresholded-covariance-expected-risk</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-lq-thresholded-covariance-row-sum</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-partial-derivatives-lower-sobolev-order</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-product-rule-for-bounded-sobolev-functions</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-solution-of-a-degree-zero-divisor-and-logarithmic-derivative-identity</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-sparsity-is-a-bound-on-the-edge-density</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weak-stability-of-sobolev-derivatives</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weakly-singular-fractional-gronwall</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wedge-monomials-in-a-dual-basis-form-a-basis</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wedge-with-a-closed-form-preserves-exactness-classes</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weierstrass-j-invariant-of-the-legendre-normal-form</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weierstrass-low-frequency-difference-quotient-bound</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weierstrass-p-degree-two-and-half-periods</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weierstrass-probe-points</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weierstrass-quotient-is-a-finite-module</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weierstrass-tail-difference-quotient-bound</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weight-is-well-defined</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weight-norm-bound-for-finite-dimensional-simple-modules</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weight-subsets-with-equal-root-sums-are-unique</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-collection-in-lower-central-coordinates</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-continuous-path-space-is-complete</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-coordinate-boxes-give-matching-growth-bounds</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-drift-minorization-gives-contraction-and-invariant-law</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-fourier-images-of-schwartz-functions-are-dense-in-ltwo</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-good-lambda-inequality-for-maximal-truncations</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
<loc>https://alphabetamath.cc/item/lem-weighted-maximal-function-is-weak-type-one-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/lem-weighted-maximal-weak-bound-for-a-one</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-weighted-morrey-estimate-on-smooth-pseudoconvex-domains</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-weighted-network-energy-kernel-and-mass-balance</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-overlapping-block-moment-and-covariance-limits</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-pinsker-inequality-for-probability-laws</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-total-variation-space-is-complete</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weighted-von-mangoldt-harmonic-estimate</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weissinger-fixed-point-criterion</loc>
<lastmod>2026-08-21T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-well-definedness-of-the-simple-integral</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-well-founded-borel-code-evaluation</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-well-order-comparability</loc>
<lastmod>2026-08-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-well-order-rigid</loc>
<lastmod>2026-07-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-alternants-are-skew-invariant</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-alternation-extracts-a-dominant-highest-weight-coefficient</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/lem-weyl-anti-invariants-are-divisible-by-the-discriminant</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-coinvariant-hilbert-series-has-order-w-dimension</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-denominator-and-anti-invariant-orbit-sum-basis</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-eigenvalue-singular-value-inequalities</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-invariant-cartan-polynomials-extend-to-g-invariants</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-length-parity-is-multiplicative</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-orbit-sums-form-a-basis-of-finite-weyl-invariants</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-weyl-orthogonality-identifies-the-highest-weight-character-numerator</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-white-noise-is-borel-gaussian-on-negative-sobolev-space</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whitehead-classes-are-represented-by-invertible-matrices</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whitney-decomposition-of-proper-open-subsets-of-euclidean-space</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whitney-disk-framing-obstruction-can-be-corrected-under-the-standard-high-dimensional-hypotheses</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whitney-normal-tubes-have-submersive-radius-and-bounded-stratumwise-lifts</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whitney-stratifications-admit-compatible-control-data</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whitney-sum-coalgebra-is-well-defined-on-stable-thom-cohomology</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whitney-trick-realizes-algebraic-middle-handle-cancellation-geometrically</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whitney-type-ball-cover-of-a-proper-open-set</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-whole-space-maximum-principle-under-gaussian-growth</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wide-gaussian-matrix-has-full-row-rank-almost-surely</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wide-gaussian-pseudoinverse-frobenius-moments</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wide-gaussian-pseudoinverse-spectral-moments-and-tail</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wide-pullbacks-compute-intersections-independently-of-representatives</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wielandt-sylow-binomial-valuation</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wilson-inverse-pairing</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-winding-number-is-locally-constant-via-integral-estimate</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-winding-number-jumps-by-one-across-a-regular-planar-arc</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/lem-witt-central-cocycles-are-cubic</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-witt-cubic-cocycle-is-a-2-cocycle</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wolfe-step-lower-bound-from-the-descent-angle</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wolfe-steps-give-positive-bfgs-curvature</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-word-length-is-well-defined-and-satisfies-the-length-laws</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-word-mirror-involution-of-a-klr-algebra-and-the-quantum-star</loc>
<lastmod>2026-10-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-word-reversal-transposes-the-insertion-tableau</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-words-satisfy-the-free-monoid-universal-property</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wreath-double-power-coefficient-symmetry</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-wronskian-of-two-jacobi-fields-is-constant</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-x-plus-the-cantor-function-is-a-homeomorphism-from-zero-one-onto-zero-two</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-x-squared-plus-one-is-irreducible-over-the-reals</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-xd-finite-matrix-exponential-series</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-xd-geometric-poisson-tail-bound</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-xd-uniformized-matrix-is-stochastic</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-xxz-open-chain-local-matrix-satisfies-temperley-lieb</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yamada-vogel-reducing-moves-lower-bad-seifert-circle-complexity</loc>
<lastmod>2026-10-03T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yangian-fundamental-evaluation-intertwiner</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yangian-gl2-one-root-bethe-cancellation</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yangian-periodic-monodromy-satisfies-rtt</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yangian-rtt-component-commutator-form</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yangian-rtt-spectral-rescaling</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yext-exact-sequences-in-both-variables</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yext-zero-splice-factorization</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yoneda-evaluation-bijection</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yoneda-splicing-is-well-defined-on-equivalence-classes</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yosida-approximants-are-bounded-and-converge-on-the-domain</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-yosida-resolvent-converges-strongly-to-the-identity</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-young-partition-sum-estimate-rational</loc>
<lastmod>2026-08-11T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-young-permutation-module-is-induced-from-the-trivial-character</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zariski-closed-set-axioms</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zariski-lemma-localised-polynomial-ring-not-field</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zariski-lemma-one-variable-localisation-not-finite</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zariski-lemma-transcendence-basis-reduction</loc>
<lastmod>2026-09-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-and-one-handles-can-be-eliminated-in-a-simply-connected-h-cobordism</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-at-identity-induction-restriction-for-a-frobenius-complement</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-boundary-piecewise-affine-functions-lie-in-h1zero</loc>
<lastmod>2026-10-18T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-covariance-multivariate-trimmed-mean-exact</loc>
<lastmod>2026-10-14T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-determinant-matrix-has-nonzero-kernel-vector</loc>
<lastmod>2026-10-17T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-dimensional-classical-variety-finite</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-dimensional-projective-scheme-has-finite-local-charts</loc>
<lastmod>2026-09-27T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-divisor-annihilator-contained-in-associated-prime</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-extension-from-w-one-p-zero</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-free-entire-function-of-exponential-type-is-an-exponential</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-in-a-localised-module</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-integral-compactly-supported-top-forms-on-euclidean-space-have-compactly-supported-primitives</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-length-sets-are-removable-for-continuous-analytic-functions</loc>
<lastmod>2026-10-08T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-locus-ideal-closure</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-locus-of-an-ideal-equals-zero-locus-of-its-radical</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-long-run-variance-gives-degenerate-clt</loc>
<lastmod>2026-10-15T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-of-a-real-analytic-function-is-isolated-or-locally-identical</loc>
<lastmod>2026-07-31T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-scheme-of-line-bundle-section</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-section-gysin-and-excess-vector-subbundle</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-section-proves-injectivity-of-the-thom-unit-orbit</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-set-propagation-for-a-nonnegative-holder-weak-solution</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
<priority>0.5</priority>
</url>
<url>
<loc>https://alphabetamath.cc/item/lem-zero-set-ultrafilters-and-stone-cech-points</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
<priority>0.5</priority>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/rem-novikov-conclusions-do-not-extend-to-arbitrary-codimension-or-noncompact-manifolds</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-nullity-and-nowhere-density-remain-independent-for-lebesgue-measure</loc>
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<loc>https://alphabetamath.cc/item/rem-objectwise-double-dual-isomorphisms-do-not-supply-a-pivotal-structure</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-omega-one-and-the-cost-of-choice</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-omega-one-strongly-compact-normal-moore-refinement</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-onan-scott-eight-type-and-five-type-conventions</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-open-mapping-theorem-via-argument-principle</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-optional-stopping-requires-a-passage-to-the-limit-hypothesis</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-oracle-and-promise-conventions-are-distinct</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-ordinal-versus-cardinal-exponentiation</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-orientation-and-notation-conventions-for-ends-coends-and-twisted-arrows</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-paley-wiener-and-microlocal-analysis</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-paracompactness-choice-and-convention-ledger</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-pe26-conditioning-and-work-are-separate</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-permutation-statistics-conventions</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-pincus-transfer-interface-and-preservation-limits</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-pivotal-and-spherical-structures-vary-by-monoidal-automorphisms-of-the-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-plane-harmonic-theory-is-owned-by-complex-analysis</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-plane-star-shaped-and-convex-dictionary</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-pointwise-and-integral-constraints-have-different-regularity-tests</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-polar-coordinates-recover-the-published-ball-volume-and-gaussian-formulas</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-polynomial-identity-bounds-for-sum-check</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-polynomials-are-not-polynomial-functions</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-positive-square-root-and-covariance-matrices</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-preprojective-coha-and-nakajima-action-source-boundaries</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-probability-characteristic-function-normalization</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-products-need-scheme-fibre-products</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-proj-does-not-recover-graded-ring-literally</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-projective-coordinate-ring-not-function-ring</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-projective-modules-are-flat-is-supplied-by-mod-three</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-projective-representations-and-the-schur-multiplier</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-projective-versus-proper</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-proof-cost-and-complex-analysis-interface-for-hardy-uncertainty</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-proof-cost-of-the-carleson-hunt-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-proper-cohomology-finiteness-needs-coherence</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-proper-not-topologically-compact-over-arbitrary-field</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-properness-can-replace-compactness-only-when-the-intersection-trace-is-compact</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-properties-can-change-after-field-extension</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-qa-20-higher-order-formula-proof-obligations</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-qa-32-bqp-pp-pspace-proof-obligations</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/rem-qa-35-private-coin-lower-bound-unresolved</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-qa-nonabelian-hidden-subgroup-scope</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-qa-number-theoretic-extension-scope</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-quadratic-variation-depends-on-the-approximating-partitions-without-regularity</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-quasi-and-weak-hopf-extensions-change-different-axioms</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-quotient-sheaf-versus-representing-scheme</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-r-native-topology-scope</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-ramsey-and-erdos-rado-orientation</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-rapl-carries-no-size-hypothesis</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-raw-versus-usual-filtration-in-the-strong-markov-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-real-and-complex-normed-space-convention</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-real-arithmetic-graph-versus-rounded-execution</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-real-banach-spaces-require-complexification-for-analyticity</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-real-exponents-deferred</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-real-hp-is-quasi-banach-below-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-rearrangement-in-higher-dimensions</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-reciprocal-root-convention-for-recurrences</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-reebless-and-taut-are-not-equivalent-without-extra-hypotheses</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-regular-homotopy-allows-self-intersections-but-never-rank-drop</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-regularity-estimates-do-not-create-boundary-compatibility</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-rellich-is-a-strictly-subcritical-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-representation-theory-of-noncompact-real-reductive-groups</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-resolution-higher-dimension-not-claimed</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-resolution-of-singularities-conventions</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-riemann-integral-choice-ledger</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-riemann-sphere-one-point-compactification</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-riemann-stieltjes-conventions-and-scope</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-riesz-representation-name-split</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-riesz-thorin-supplied-by-measure-theory</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-rigidity-alone-does-not-make-a-tensor-category</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-ring-form-of-the-de-rham-theorem-needs-the-singular-cup-product</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-rmk-functional-analysis-uses</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-rn-conventions-and-scope</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-rnp-is-not-the-scalar-radon-nikodym-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-routes-to-the-catalan-count</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-roydens-vitali-route-is-a-third-proof</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-rsk-longest-increasing-subsequence-consequences-remain-rg11-owned</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-sauer-shelah-uses-no-linear-algebra</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-scalar-de-giorgi-theory-does-not-transfer-verbatim-to-systems</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-schatten-p-classes</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/rem-schwarz-reflection-as-analytic-continuation</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-sections-not-determined-by-single-stalk</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-self-adjoint-extensions-and-deficiency-indices</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-semantic-ctm-versus-formal-relative-consistency</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/rem-separability-is-essential-for-finite-integral-closure</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-separate-regularity-and-joint-continuity-in-the-real-and-complex-cases</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/rem-sharp-degree-thresholds-wait-for-duality</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-shoenfield-absoluteness-scope-orientation</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-sieve-pigeonhole-and-double-counting-conventions</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-sign-patterns-in-the-four-square-identity</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-signature-is-not-defined-geometrically-by-zero-in-other-dimensions</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-simple-groups-as-composition-factors</loc>
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<url>
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<url>
<loc>https://alphabetamath.cc/item/rem-strictification-gives-equivalence-and-never-isomorphism</loc>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<url>
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<loc>https://alphabetamath.cc/item/rem-two-results-called-mazurs-lemma</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-two-routes-to-every-dual-statement</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-two-senses-of-regularity-for-lebesgue-measure</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-tychonoff-choice-strengths</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-unbracketed-tensor-strings-are-not-yet-defined</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-uncertainty-principles-measure-different-notions-of-localisation</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-uniform-convergence-agrees-with-the-later-uniform-topology</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-universality-is-the-construction-independence-principle</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-urysohn-implies-dmc-open-status</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-valuative-criterion-quantifies-all-valuation-rings</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-value-functions-and-hamilton-jacobi-bellman-equations</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-vanishing-primary-double-point-and-characteristic-obstructions-do-not-classify-embeddings</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-wave-poisson-formula-is-not-the-harmonic-poisson-kernel</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-weak-derivatives-are-distributional-derivatives-with-function-values</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-weak-harnack-exponent-has-a-coefficient-and-dimension-dependent-upper-range</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-weighted-endpoints-are-not-obtained-by-setting-p-equal-one</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-weil-pullback-not-automatic</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-weyl-kac-products-are-formal-not-analytic-identities-here</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-what-is-needed-before-a-trace-can-be-written</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-what-is-not-developed-here</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-what-is-not-proved-about-change-of-base</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-what-the-diagonal-criterion-gives-and-what-it-costs</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-what-the-library-does-and-does-not-prove-about-cfsg</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-what-the-subtraction-rule-does-not-say</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-where-a-choice-principle-would-be-needed</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-where-the-archimedean-hypothesis-is-needed</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-which-axiom-each-construction-uses</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-which-side-the-word-left-refers-to</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/rem-whitehead-group-construction-remains-at-owned</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-why-completeness-alone-is-not-enough-for-an-adjoint</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-why-separation-replaces-unrestricted-comprehension</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/rem-why-the-diagram-lemmas-are-not-proved-by-the-embedding-theorem</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-why-the-enriched-generalisation-cannot-stop-at-conical-limits</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-why-the-five-lemma-asks-for-isomorphisms-in-the-middle</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-why-the-middle-nine-lemma-needs-a-zero-composite</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-why-this-library-takes-unit-counit-as-the-definition</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/rem-wiener-lemma-is-developed-on-the-fourier-analysis-track</loc>
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<url>
<loc>https://alphabetamath.cc/item/rem-zero-dimensional-morse-convention</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/rem-zero-times-infinity-convention-for-pointwise-products</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-banach-space-is-reflexive-iff-its-dual-is-reflexive</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-based-root-system-is-determined-up-to-isomorphism-by-its-cartan-matrix</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-bernstein-set-has-inner-measure-zero-and-full-outer-measure-in-every-interval</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-bipartite-graph-with-bounded-a-degree-has-a-large-comb-or-a-small-b-side</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-bounded-above-acyclic-complex-of-injective-objects-is-contractible-when-its-cycle-monomorphisms-split</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-bounded-above-complex-of-projectives-is-homotopically-projective</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-bounded-below-acyclic-complex-of-projective-objects-is-contractible-when-its-cycle-epimorphisms-split</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-bounded-below-complex-of-injectives-is-homotopically-injective</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-bounded-partition-into-weakly-restricted-sets</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-bounded-projective-bimodule-complex-defines-a-derived-tensor-functor</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-braided-rigid-category-has-a-drinfeld-morphism</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-cartesian-square-induces-an-isomorphism-on-the-kernels-of-its-parallel-legs</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-cartesian-square-over-an-epimorphism-is-also-cocartesian</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-category-enriched-in-a-preorder-is-a-preorder-and-one-enriched-in-sets-is-an-ordinary-category</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-category-enriched-in-abelian-groups-is-exactly-a-preadditive-category</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-category-enriched-in-categories-is-exactly-a-small-object-strict-two-category-with-small-homs</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-category-enriched-in-the-two-element-lattice-is-a-preordered-set</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-category-is-tensored-exactly-when-every-covariant-hom-has-a-left-enriched-adjoint</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-category-with-finite-biproducts-is-enriched-in-commutative-monoids</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-category-with-finite-products-is-monoidal</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-central-product-of-extraspecial-p-groups-is-extraspecial</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-chain-homotopy-equivalence-is-a-quasi-isomorphism</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-chain-map-induces-a-well-defined-map-on-homology</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-chain-map-is-a-homotopy-equivalence-exactly-when-its-cone-is-contractible</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-chain-map-is-a-quasi-isomorphism-exactly-when-its-cone-is-acyclic</loc>
<lastmod>2026-09-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-chosen-family-of-ends-assembles-into-a-functor-of-the-parameters</loc>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-closed-monoidal-category-has-its-tensor-cocontinuous-in-each-variable</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-closed-monoidal-category-is-enriched-in-itself</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-coend-is-a-colimit-weighted-by-the-hom-bifunctor</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-commuting-square-with-monic-legs-is-a-pullback-exactly-when-the-induced-morphism-to-the-intersection-is-an-isomorphism</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-compact-hausdorff-space-is-regular-and-normal</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-complete-local-isometry-is-a-covering-map</loc>
<lastmod>2026-10-02T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-complete-locally-small-category-with-a-jointly-weakly-initial-set-has-an-initial-object</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-complete-locally-small-category-with-a-small-coseparating-set-and-all-subobject-intersections-has-an-initial-object</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-complex-is-exact-at-n-exactly-when-its-nth-homology-is-zero</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-complex-linear-operator-comes-from-a-real-operator-exactly-when-it-commutes-with-the-chosen-conjugation</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-composite-of-a-quotient-and-a-subobject-inclusion-is-the-canonical-factorisation</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-conical-limit-is-stronger-than-a-limit-in-the-underlying-category</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-connected-covering-space-of-a-connected-lie-group-carries-a-unique-lifted-lie-group-structure</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-continuous-functor-preserves-ends-and-a-cocontinuous-functor-preserves-coends</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-coproduct-of-projectives-is-projective-and-a-product-of-injectives-is-injective</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-cycle-and-a-forest-complement-have-the-erdos-hajnal-property</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-decomposable-wedge-is-nonzero-exactly-for-independent-vectors</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-deformation-retract-is-a-homotopy-equivalence</loc>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-direct-summand-of-a-projective-is-projective</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-distribution-with-zero-derivatives-on-a-connected-open-set-is-constant</loc>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-distributive-law-makes-the-composite-a-monad</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-divergence-free-c1-field-on-a-star-shaped-open-set-has-a-vector-potential</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-dual-object-in-the-endofunctor-category-is-an-adjoint-functor</loc>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-family-natural-in-the-parameter-factors-through-the-parametrised-end</loc>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-filtered-complex-produces-an-exact-couple</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-finitary-monad-on-a-complete-cocomplete-locally-small-category-has-complete-and-cocomplete-algebras</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-finite-cw-homotopy-equivalence-is-simple-if-and-only-if-its-whitehead-torsion-vanishes</loc>
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<loc>https://alphabetamath.cc/item/thm-a-finite-family-with-the-erdos-hajnal-property-is-viral</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-finite-group-is-abelian-iff-all-its-irreducible-complex-characters-have-degree-one</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-first-quadrant-filtered-complex-spectral-sequence-converges-to-filtered-homology</loc>
<lastmod>2026-09-12T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-five-and-symmetric-groups-from-degree-five-are-not-solvable</loc>
<lastmod>2026-08-13T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-flat-connection-admits-local-parallel-frames</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-forest-complement-and-its-star-expansion-have-the-erdos-hajnal-property</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-free-proper-action-makes-m-to-m-mod-g-a-principal-g-bundle</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-free-ultrafilter-on-n-is-not-lebesgue-measurable</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-full-subcategory-is-reflective-exactly-when-each-object-has-a-universal-arrow</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-function-is-a-bijection-exactly-when-it-has-a-two-sided-inverse</loc>
<lastmod>2026-08-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-functor-between-additive-categories-is-additive-exactly-when-it-preserves-finite-biproducts</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-generating-set-with-no-two-letter-relation-whose-cayley-graph-is-a-tree-is-a-free-basis</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-generator-detects-equality-of-subobjects</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-geodesic-does-not-minimize-past-its-first-conjugate-point</loc>
<lastmod>2026-09-30T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-grothendieck-abelian-category-has-functorial-injective-embeddings</loc>
<lastmod>2026-09-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-group-admits-a-universal-central-extension-iff-it-is-perfect</loc>
<lastmod>2026-09-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-homomorphism-from-a-connected-lie-group-is-determined-by-its-differential-at-the-identity</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-infinity-power-decay-characterisation</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-kan-extension-along-a-fully-faithful-functor-genuinely-extends-when-it-is-pointwise</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-lax-monoidal-functor-carries-monoid-objects-to-monoid-objects</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-lax-monoidal-functor-induces-a-change-of-base-on-enriched-categories</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-left-adjoint-exists-exactly-when-every-comma-category-has-an-initial-object</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-left-dual-of-an-object-has-that-object-as-a-right-dual</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-left-exact-functor-preserves-monomorphisms-and-a-right-exact-functor-preserves-epimorphisms</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-left-module-is-flat-exactly-when-tor-one-with-every-right-module-vanishes</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-left-or-right-exact-functor-between-abelian-categories-is-additive</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-length-minimizing-piecewise-smooth-curve-is-a-constant-speed-geodesic-up-to-reparametrization</loc>
<lastmod>2026-09-13T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-linear-continuum-is-connected</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-lipschitz-function-after-an-absolutely-continuous-function-is-absolutely-continuous</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-locally-cartesian-closed-category-has-pullbacks-and-with-a-terminal-object-all-finite-limits</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-locally-cartesian-closed-category-with-a-terminal-object-is-cartesian-closed</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-locally-compact-hausdorff-space-is-completely-regular</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-locally-finite-sum-of-smooth-functions-is-smooth</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-locally-small-abelian-category-with-a-generator-is-well-powered</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-long-blockade-without-a-large-pure-pair-contains-a-rainbow-forest-or-complement</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-long-blockade-yields-a-wide-cograph-pattern-subblockade-or-a-rainbow-forest</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-modular-partition-its-quotient-and-its-parts-determine-the-graph</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-module-valued-coend-is-a-quotient-of-a-direct-sum-by-the-dinaturality-submodule</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-monad-morphism-induces-restriction-of-algebras-and-a-comparison-of-free-algebras</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-monadic-functor-is-conservative</loc>
<lastmod>2026-08-17T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-monoid-object-in-the-endofunctor-category-is-exactly-a-monad</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-monoidal-category-equivalent-to-a-strict-one-satisfies-coherence</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-morphism-factors-uniquely-through-its-coimage</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-morphism-factors-uniquely-through-its-image</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-morphism-of-chain-maps-induces-a-chain-map-of-cones</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-natural-transformation-induces-a-morphism-of-ends-and-of-coends</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-nonzero-abelian-category-cannot-satisfy-both-ab5-and-ab5-star</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-one-object-preadditive-category-is-the-same-thing-as-a-ring</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-plus-b-is-the-unique-minimum-norm-least-squares-solution</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-pointwise-right-adjoint-extends-uniquely-to-a-functor</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-poset-with-finite-meets-is-a-strict-monoidal-category</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-positive-smooth-density-defines-a-locally-finite-radon-measure</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-power-is-a-product-of-copies-and-a-copower-is-a-coproduct-of-copies</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-presheaf-category-on-a-small-category-is-cartesian-closed</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-prime-power-conjugacy-class-forces-a-proper-nontrivial-normal-subgroup</loc>
<lastmod>2026-08-30T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-process-law-on-cylinder-space-is-determined-by-finite-dimensional-distributions</loc>
<lastmod>2026-09-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-projective-generator-detects-isomorphisms</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-quasi-isometric-embedding-with-coarsely-dense-image-admits-a-quasi-inverse</loc>
<lastmod>2026-09-23T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-real-basis-complexifies-to-a-complex-basis</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-real-l-one-density-defines-a-finite-signed-measure-with-its-canonical-hahn-and-jordan-data</loc>
<lastmod>2026-09-09T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-reflective-inclusion-creates-all-limits</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-reflective-subcategory-has-every-colimit-the-ambient-category-has</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-regular-level-set-is-an-embedded-submanifold</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-ribbon-object-defines-a-unique-framed-tangle-evaluation-functor</loc>
<lastmod>2026-10-06T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-riemannian-manifold-is-flat-iff-it-is-locally-isometric-to-euclidean-space</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-riemannian-metric-has-a-unique-levi-civita-connection-on-the-cotangent-bundle</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-right-enriched-adjoint-preserves-weighted-limits</loc>
<lastmod>2026-09-05T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-right-module-is-flat-exactly-when-tor-one-with-every-left-module-vanishes</loc>
<lastmod>2026-09-10T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-semiadditive-category-is-preadditive-exactly-when-every-morphism-has-an-additive-inverse</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-separating-set-is-equivalently-a-jointly-faithful-family-of-representables</loc>
<lastmod>2026-08-16T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-set-valued-coend-is-a-quotient-of-a-coproduct-by-the-dinaturality-relation</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-set-weighted-limit-is-a-limit-over-a-category-of-elements</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-short-exact-sequence-is-a-kernel-cokernel-pair</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-simple-graph-is-a-tree-exactly-when-every-two-vertices-are-joined-by-a-unique-path</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-small-product-of-abelian-categories-is-abelian</loc>
<lastmod>2026-08-28T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-space-is-perfectly-normal-iff-it-is-normal-and-every-closed-set-is-a-zero-set</loc>
<lastmod>2026-07-29T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-sphere-has-a-nowhere-zero-tangent-vector-field-iff-its-dimension-is-odd</loc>
<lastmod>2026-09-07T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-split-coequalizer-is-a-coequalizer-and-is-absolute</loc>
<lastmod>2026-08-24T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-splitting-of-an-idempotent-is-simultaneously-an-equalizer-and-a-coequalizer-and-is-unique-up-to-unique-isomorphism</loc>
<lastmod>2026-08-27T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-square-is-cartesian-exactly-when-a-short-sequence-is-exact</loc>
<lastmod>2026-08-29T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-stopped-martingale-is-a-martingale</loc>
<lastmod>2026-09-14T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-subobject-classifier-represents-the-subobject-functor</loc>
<lastmod>2026-09-01T00:00:00.000Z</lastmod>
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<url>
<loc>https://alphabetamath.cc/item/thm-a-supercompact-cardinal-can-be-forced-to-give-pfa</loc>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-tau-critical-graph-with-a-large-low-degree-induced-subgraph-has-a-rooted-stable-tooth-comb</loc>
<lastmod>2026-08-31T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-transitive-subgroup-of-s-p-containing-a-transposition-is-s-p</loc>
<lastmod>2026-08-26T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-transverse-banach-bundle-section-has-a-split-zero-submanifold</loc>
<lastmod>2026-09-22T00:00:00.000Z</lastmod>
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</url>
<url>
<loc>https://alphabetamath.cc/item/thm-a-twist-on-a-braided-rigid-category-is-the-same-thing-as-a-pivotal-structure-of-drinfeld-type</loc>
<lastmod>2026-09-04T00:00:00.000Z</lastmod>
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</url>
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<loc>https://alphabetamath.cc/item/thm-qa-relative-probability-guarantee</loc>
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<loc>https://alphabetamath.cc/item/thm-qa-shor-factoring-cost</loc>
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<loc>https://alphabetamath.cc/item/thm-qa-truncated-qft-gate-count</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-axis-rotation-pauli-formula</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-basic-rewrite-correct-and-terminating</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-binary-pauli-quotient-isomorphism</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-bitstring-index-is-bijection</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-bloch-coordinate-existence-and-uniqueness</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-bqtisp-to-ptisp-simulation</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-channel-composition-hybrid-bound</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-channel-diamond-norm-one</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-channel-tensor-error-bound</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-channels-compose-and-tensor</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-choi-trace-preservation-condition</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-circuit-inverse-reversal</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-circuit-pattern-equivalence-and-universality</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-circuit-simulated-by-adaptive-pattern</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-classical-distance-correction-and-erasure-radius</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-one-qubit-euler-decomposition</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-pauli-commutator-is-symplectic-pairing</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-planar-surface-code-iid-z-memory-bound</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-probabilistic-polynomial-time-hierarchy</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-projective-conditional-state</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-projective-measurement-outcome-law</loc>
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<loc>https://alphabetamath.cc/item/thm-qc-purification-existence-and-unitary-equivalence</loc>
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