ExampleConstruction: Literature-sourcedVerification: AI-adaptedjudge 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 closure parabola

Example

For the parabola $A = V (y - x^{2}) \subseteq A_{k}^{2}$ , use homogeneous coordinates $[Z : X : Y]$ . Its homogenization is $Y Z - X^{2}$ , so ${\overline{A}}^{p r o j} = V_{+} (Y Z - X^{2})$ . The $Z = 1$ chart is $y = x^{2}$ . At infinity $Z = 0$ , the equation gives $X = 0$ , leaving exactly $[0 : 0 : 1]$ .

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, Chapter 6 (standard reference, not scraped)
Michael Artin, Algebraic Geometry, Chapter 3 (standard reference, not scraped)