DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-12

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.

A principal open subset of a classical affine variety

Definition

Let $X$ be a classical affine variety over an algebraically closed field $k$ , and let $\overline{f} \in k [X]$ . The principal open subset determined by $\overline{f}$ is $D_{X} (\overline{f}) : = {x \in X : \overline{f} (x) \neq 0} .$

If $f \in k [x_{1}, \dots, x_{n}]$ is any representative of $\overline{f}$ , then $D_{X} (\overline{f})$ depends only on the class $\overline{f}$ , not on the chosen representative. Its boundary cases are $D_{X} (0) = \emptyset and D_{X} (1) = X .$

A principal open subset of a classical affine variety

Definition

Depends on

Dependency tree · 2 levels

Sources