DefinitionDefinition: AI-adaptedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-31

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.

Local and global frames of a vector bundle

Definition

Let $π : E \to M$ be a smooth rank- $r$ vector bundle and let $U \subseteq M$ be open.

A tuple of smooth local sections $(s_{1}, \dots, s_{r})$ on $U$ is a local frame when, for every $p \in U$ , the vectors $s_{1} (p), \dots, s_{r} (p)$ form a basis of the fibre $E_{p}$ .

When $U = M$ , the same data are called a global frame.

Local and global frames of a vector bundle

Definition

Depends on

Dependency tree · 2 levels

Sources