ExampleConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedjudge 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.

Normalizing an inhomogeneous cochain

Example

If $z : G \to M$ is a $1$ -cocycle, then $z (1) = 0$ , so it is already normalized.

Verification

Given: A $1$ -cocycle $z$ , so $z (g h) = z (g) + g z (h)$ .

1.1given

Set $g = h = 1$ to get $z (1) = z (1) + z (1)$ .

2.1step 1.1∎

Subtracting $z (1)$ gives $z (1) = 0$ . Thus the normalized representative is $z$ itself.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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

Weibel, Appendix 6.5.5 (standard reference, not scraped)