DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-07

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.

Affine open subschemes

Definition

For a scheme $X$ and an open set $U \subseteq X$ , the open subscheme $U$ means $(U, O_{X} ∣_{U})$ . It is an affine open subscheme when this restricted locally ringed space is affine; thus “affine open” always includes its restricted structure sheaf, not merely an open subset of $∣ X ∣$ .

Depends on

Dependency tree · 2 levels

Sources

The Stacks Project, Schemes, Definition 9.1 and Lemma 9.2