DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-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.

Cover-small singular chains

Definition

If $U$ is a family of subsets whose interiors cover $X$ , let $C_{n}^{U} (X; G)$ be the subgroup generated by singular $n$ -simplices whose images lie in one member of $U$ . Faces remain in that member, so these groups form the cover-small singular-chain subcomplex.

Cover-small singular chains

Definition

Depends on

Dependency tree · 2 levels

Sources