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.

Interior and boundary of a manifold with boundary

Definition

Let $p$ lie in an $n$ -manifold with boundary. If $n > 0$ , call $p$ a provisional boundary point if a boundary-chart image has last coordinate $0$ , and an interior point if it has last coordinate $> 0$ . If $n = 0$ , declare every point interior and no point a provisional boundary point. Write these sets as $\partial M$ and $Int M$ ; chart independence is proved below.

Interior and boundary of a manifold with boundary

Definition

Depends on

Dependency tree · 2 levels

Sources