Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-09
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.
The candidate domain of a rational map
Definition
For a rational-map class , define its candidate domain by It is open and nonempty because every representative domain is open and the class contains a representative. At this point the definition is only a union of domains; it asserts neither a glued map nor maximality.
Sources
Source comparison: Milne, Algebraic Geometry, v6.10, §5l p. 117. Conventions here distinguish arbitrary affine algebraic sets from nonempty irreducible varieties.