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.

Equivalence of n-fold extensions

Definition

For two $n$ -fold extensions with the same endpoints, begin with chain maps between their displayed exact sequences that are the identity on $N$ and $M$ . Their reflexive, symmetric, and transitive closure is called equivalence of $n$ -fold extensions. For $n > 1$ , this generated relation does not require one isomorphism of all middle terms.

Equivalence of n-fold extensions

Definition

Depends on

Dependency tree · 2 levels

Sources