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.
Absolute-continuity conventions and hierarchy agreement
The convention used below is exactly the finite disjoint-interval condition in Absolute continuity on a compact interval, including degenerate intervals. The published hierarchy implies Lipschitz, Lipschitz implies absolutely continuous, and absolutely continuous implies continuous and bounded variation gives on a compact interval. None of these inclusions is silently reversed here.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
15 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Christopher Heil, Absolute Continuity and the Banach--Zaretsky Theorem, §§3.2--3.3 (standard reference, not scraped)