DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-12

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.

A reduced affine k-algebra

Let $k$ be a field. A reduced affine $k$ -algebra is a commutative $k$ -algebra $A$ that is of finite type over $k$ and reduced.

Equivalently, $A$ is a finitely generated commutative $k$ -algebra with no nonzero nilpotent elements.

Depends on