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.
Collapse at a page
Definition
A spectral sequence collapses at if every differential at every bidegree is zero for every r≥s. The specified transitions then identify with the stable page of Spectral sequence stabilization at a bidegree. One zero differential does not meet this definition. Pointwise stabilization with no uniform bound R(p,q) also does not imply collapse at any fixed page. We use the same definition with subscripts in the cohomological convention.
Source notes
Weibel, Chapter 5, §5.2 pp.122–125 and Definitions 5.4.2–4 pp.132–133; Sharifi, §4.1 pp.87–89 and Definition 4.2.1 p.90. The all-later-differentials convention follows Sharifi Definition 4.1.13; Weibel Definition 5.2.7 uses the narrower one-row/column terminology.