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.

Oriented smooth manifolds and oriented charts

Definition

An orientation of an $n$ -manifold is a smooth choice of a ray in $\det T_{p} M$ for every $p$ . For $n > 0$ , a chart is oriented when its coordinate frame is in that ray. For $n = 0$ , the datum is a sign at each point; the unique empty frame does not encode both choices.

Oriented smooth manifolds and oriented charts

Definition

Depends on

Dependency tree · 2 levels

Sources