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 Segre image of P1 times P1 is a quadric surface

Example

For $([s : t], [u : v]) \in P^{1} \times P^{1}$ , Segre gives $[z_{00} : z_{01} : z_{10} : z_{11}] = [s u : s v : t u : t v] .$ The sole $2 \times 2$ minor is $z_{00} z_{11} - z_{01} z_{10}$ , so the image is the quadric surface $V_{+} (z_{00} z_{11} - z_{01} z_{10}) \subseteq P^{3}$ . On $z_{00} \neq 0$ , its inverse sends $[z]$ to $([z_{00} : z_{10}], [z_{00} : z_{01}])$ ; the other three charts give the analogous formulas.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

8 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, 6.26 (standard reference, not scraped)