DefinitionDefinition: AI-adaptedProof: Not applicablejudge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17

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.

Perfect fields: every irreducible polynomial is separable

Definition

A field $F$ (Field) is perfect when every nonconstant irreducible polynomial in $F [x]$ is separable (Repeated roots in extension fields and separable polynomials).

Depends on

Dependency tree · 2 levels

Sources