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 degree-d Veronese map

Definition

Fix $d \geq 1$ and an ordering $M_{0}, \dots, M_{N}$ of all degree- $d$ monomials in $x_{0}, \dots, x_{n}$ , where $N = (\binom{n + d}{d}) - 1$ . The degree- $d$ Veronese map is $ν_{n, d} : P_{k}^{n} ⟶ P_{k}^{N}, [x] ⟼ [M_{0} (x) : \dots : M_{N} (x)] .$

Depends on

Dependency tree · 2 levels

Sources

J. S. Milne, Algebraic Geometry, 6.23