DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01

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.

Deleted resolutions

Definition

If $\dots \to P_{2} \to P_{1} \to P_{0} \overset{ε}{\to} A \to 0$ is a projective resolution of $A$ , its deleted projective resolution is the chain complex $\dots \to P_{2} \to P_{1} \to P_{0} \to 0,$ obtained by removing the resolved object $A$ and the augmentation.

Dually, if $0 \to A \to I^{0} \to I^{1} \to I^{2} \to \dots$ is an injective resolution, its deleted injective resolution is the cochain complex $0 \to I^{0} \to I^{1} \to I^{2} \to \dots,$ obtained by removing the coaugmentation from $A$ .

Deleted resolutions

Definition

Depends on

Dependency tree · 2 levels

Sources