Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
On a finite counting space, Minkowski agrees with the published finite theorem for
Under the finite counting-measure identification of is the space of counting measure, the integral Minkowski inequality of Minkowski's inequality for integrals, including becomes the published finite-sum theorem Minkowski's inequality for finite sums and real exponent p greater than one for real on the same coordinates. The integral theorem's and clauses also specialize to the corresponding elementary finite-sum inequalities, but those endpoints are outside the cited theorem's statement. This is an agreement seam, not a second construction.
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Sources
- Richard L. Wheeden and Antoni Zygmund, Measure and Integral, Chapter 8 (standard reference, not scraped)