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.

Determinant-line orientations of finite-dimensional real vector spaces

Definition

For a finite-dimensional real vector space $V$ , an orientation is a positive ray in the one-dimensional determinant line $\det V = Λ^{\dim V} V$ . If $\dim V = 0$ , $\det V = R$ still has the two rays $R_{> 0}$ and $R_{< 0}$ .

Determinant-line orientations of finite-dimensional real vector spaces

Definition

Depends on

Dependency tree · 2 levels

Sources