DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-06

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.

projective algebraic set

Definition

For homogeneous $T \subseteq k [x_{0}, \dots, x_{n}]$ , let $V_{+} (T) = {[a] \in P_{k}^{n} : F (a) = 0 for all F \in T}$ . A projective algebraic set is a set $V_{+} (T)$ ; write $V_{+} (J)$ for a homogeneous ideal. By convention $V_{+} (\emptyset) = P_{k}^{n}$ and $V_{+} ((x_{0}, \dots, x_{n})) = \emptyset$ .

projective algebraic set

Definition

Depends on

Dependency tree · 2 levels

Sources