DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

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 reference-triangle Duffy map from a vertex

Let $S = [0, 1]^{2}$ and let $T = {(x, y) : 0 \leq y \leq x \leq 1}$ be the reference triangle. The vertex Duffy map is $D : S \to T$ , $D (r, s) = (r, r s)$ . Its image, inverse for $r > 0$ , and Jacobian determinant are verified in The reference-triangle Duffy map has the stated image and Jacobian ↗. The change-of-variables use and endpoint limit for weak singularities are proved in The Duffy map turns a vertex singularity into an integrable radial weight ↗.

Used by

Nothing. This result depends on no other item in the library.