DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge 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.

The diagonal morphism

Definition

For $X \to S$ , the diagonal morphism is the unique $Δ_{X / S} : X \to X \times_{S} X$ satisfying ${pr}_{1} Δ_{X / S} = {id}_{X} = {pr}_{2} Δ_{X / S}$ . It exists by Existence of all scheme fibre products. For any test scheme $T$ , it takes an $S$ -morphism $a : T \to X$ to the compatible pair $(a, a)$ .

The diagonal morphism

Definition

Depends on

Dependency tree · 2 levels

Sources