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.
FALSE: the middle nine lemma holds without assuming the composite is zero
Statement
The middle-row form of the nine lemma remains true even if no hypothesis is made that the middle row is a complex.
Facts & Assumptions
Given: The middle-row variant of the nine lemma.
The middle-row conclusion is stated only after assuming the middle row is a complex (Nine lemma variants by which rows are assumed exact).
That zero-composite hypothesis is load-bearing (Why the middle nine lemma needs a zero composite).
Refutation
By [L1], the theorem itself does not claim exactness of the middle row without first requiring that its composite vanish.
By [L2], without that hypothesis the middle row need not even be a complex, so the purported strengthening is false.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
10 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
- Charles A. Weibel, An Introduction to Homological Algebra, Exercise 1.3.2 (standard reference, not scraped)