LemmaStatement: Literature-sourcedProof: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-06

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.

Alternating universal property

Statement

Alternating bilinear maps A×A→B factor uniquely through ∧²A.

Proof

Given: Let $b : A \times A \to B$ be alternating and bilinear.

1.1

The tensor universal property gives a unique map $A \otimes A \to B$ carrying $a \otimes a^{'}$ to $b (a, a^{'})$ .

given

2.1

Because $b (a, a) = 0$ , it kills the defining subgroup and factors uniquely through $⋀^{2} A$ .

step 1.1algebra∎

Depends on

Used by

Universal coefficients split naturally False statement
Multiplier of an abelian group Theorem

Dependency tree · two levels

7 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

Clara Löh, Group Cohomology (standard reference, not scraped)