Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)
How 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.
Bounded-Lipschitz discrepancy for finite measures
Definition
For finite signed Borel measures on , define their bounded-Lipschitz discrepancy by
where the supremum is over all real functions on with supremum norm at most and Lipschitz constant at most . For a finite measure , the notation means . This discrepancy only tests bounded Lipschitz observables; it does not control an unbounded moment without a separate moment estimate.
Used by
- Continuous-size coagulation-fragmentation weak model Definition
- Fixed-pivot projection has first-order bounded-Lipschitz kernel quadrature error Lemma
- Weighted total variation bounds bounded-Lipschitz discrepancy Lemma
- Bounded-kernel measure solutions are stable in bounded-Lipschitz discrepancy Theorem
- Sectional forward Euler separates temporal, quadrature, and cutoff errors Theorem
- The unbounded fixed-pivot flow has first-order grid error Theorem
- Unbounded-grid fixed-pivot dynamics are globally well posed and stable Theorem
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Philippe Laurençot, Weak compactness techniques and coagulation equations, §§2–3 (standard reference, not scraped)