DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-03

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.

Principal ideal domain

An integral domain $R$ is a principal ideal domain (PID) if every ideal $I ⊴ R$ is principal: there is an $a \in R$ with $I = (a)$ .

The domain hypothesis is part of the term. A ring in which all ideals are principal but which has zero divisors is not called a PID here.

Depends on