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.
Why the middle nine lemma needs a zero composite
Remark
In the middle-row variant, exactness is not even a meaningful target until the middle row is first known to be a complex. That is the role of the zero-composite hypothesis in Nine lemma variants by which rows are assumed exact: it is not a technical afterthought, but the condition that allows the phrase "the middle row is short exact" to make literal sense.
Depends on
Used by
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Sources
- Charles A. Weibel, An Introduction to Homological Algebra, Exercise 1.3.2 (standard reference, not scraped)
- Saunders Mac Lane, Categories for the Working Mathematician, Exercise VIII.4.5 (standard reference, not scraped)