LemmaStatement: Literature-sourcedProof: AI-adaptedprecheck passjudge 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 coordinate morphisms well defined

A same-degree homogeneous tuple $F_{0}, \dots, F_{m}$ having no common zero on $X$ defines a projective morphism $X \to P_{k}^{m}$ .

Given: Such a tuple, of common degree $d$ .

1.1givenalgebra

Rescaling $a$ by $λ$ rescales every $F_{i} (a)$ by $λ^{d}$ , so the target class is representative-independent.

2.1step 1.1algebra

On $D_{+} (y_{j})$ the coordinate functions are $F_{i} / F_{j}$ , regular equal-degree fractions wherever $F_{j} \neq 0$ .

3.1step 2.1∎

The target standard opens cover the image and the ratios agree on overlaps, so the local maps glue to a morphism.

Depends on