DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedaudited 2026-09-07

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.

Smooth maps between manifolds with boundary

Definition

A continuous map $f : M \to N$ is smooth if, for every pair of boundary charts around $p$ and $f (p)$ , the coordinate representative $ψ \circ f \circ φ^{- 1}$ is smooth on a relatively open subset of a half-space in the local-extension sense.

Smooth maps between manifolds with boundary

Definition

Depends on

Dependency tree · 2 levels

Sources