DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-21

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 regular locus of a square-dimensional $C^{1}$ map

Definition

Let $n \geq 1$ , let $U \subseteq R^{n}$ be open, and let $f : U \to R^{n}$ be $C^{1}$ in the sense of Continuously differentiable maps, local inverses, and local diffeomorphisms. A point $a \in U$ is regular when the linear map $D f (a)$ is invertible (Invertible Euclidean linear maps). The regular locus is

$Reg (f) : = {a \in U : D f (a) is invertible} .$

Its complement in $U$ is the singular locus of $f$ .

Depends on

Dependency tree · 2 levels

Sources