DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedaudited 2026-09-07

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.

Cellular homology

Let $X$ be a CW complex, $G$ an abelian group, and $n \geq 0$ . The cellular homology of $X$ with coefficients in $G$ is $H_{n}^{c e l l} (X; G) = \ker d_{n} / im d_{n + 1}$ for the cellular groups of Oriented cellular chain group, with differentials defined in Cellular boundary from three consecutive skeleta. These maps form a chain complex by The cellular boundary squares to zero.

Depends on