Alphabeta Math
LemmaStatement: Literature-sourcedProof: AI-adaptedprecheck passaudited 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 regular function chart compatibility

Statement

On overlapping standard charts, equal-degree fractions define the same regular function exactly when their cross-products agree in S(X). Thus regularity is chart-independent.

Proof

Given: Equal-degree fractions G/H,G′/H′ with denominators nonzero at a common point.

1.1

G/H=G′/H′ is equivalent to GH′=G′H after multiplying by the nonzero product HH′.

givenalgebra
2.1

Dehomogenization in either chart turns this into the same equality of ordinary affine fractions.

step 1.1algebra
3.1

Therefore the affine descriptions agree exactly as stated.

step 2.1∎

Depends on

Used by

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