ExampleConstruction: Literature-sourcedVerification: 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.

The quadratic Veronese image of P1 is a plane conic

Example

The quadratic Veronese map is $[s : t] \mapsto [s^{2} : s t : t^{2}] = [Z_{0} : Z_{1} : Z_{2}]$ . Its image has equation $Z_{0} Z_{2} - Z_{1}^{2} = 0$ . The line $a Z_{0} + b Z_{1} + c Z_{2} = 0$ pulls back to the binary quadratic $a s^{2} + b s t + c t^{2} = 0$ , illustrating the hyperplane-section correspondence.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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--6.24 (standard reference, not scraped)