DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16

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.

Universal covering spaces

Definition

A universal covering space of $B$ is a covering map $p : \tilde{B} \to B$ whose total space $\tilde{B}$ is simply connected (Covering maps, evenly covered neighbourhoods, fibres, sheets, and trivial coverings, Simply connected topological spaces).

Depends on

Dependency tree · 2 levels

Sources