ExampleConstruction: AI-generatedVerification: AI-adaptedPipeline-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.

A bidegree (2,3) Segre-Veronese embedding

Example

For $([s : t], [u : v]) \in P^{1} \times P^{1}$ , the bidegree $(2, 3)$ coordinates are the twelve products $s^{2 - i} t^{i} u^{3 - j} v^{j} (0 \leq i \leq 2, 0 \leq j \leq 3) .$ Scaling the two representatives by $λ, μ$ scales every coordinate by $λ^{2} μ^{3}$ . Up to the target coordinate permutation determined by the chosen Veronese monomial orderings, this is $σ \circ (ν_{1, 2} \times ν_{1, 3})$ , hence is the stated closed embedding.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

J. S. Milne, Algebraic Geometry, 6.23 and 6.26 (standard reference, not scraped)