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.

Closed immersions of schemes

Definition

A morphism $i : Z \to X$ is a closed immersion if its underlying map is a homeomorphism onto a closed subset and the morphism $O_{X} \to i_{*} O_{Z}$ is surjective.

Depends on

Dependency tree · 2 levels

Sources

The Stacks Project, Morphisms of Schemes, Definition 2.1