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.

Deck transformations and the deck-transformation group of a covering

Definition

For a covering $p : E \to B$ , a deck transformation is an isomorphism $h : E \to E$ over $B$ , so $p \circ h = p$ (Maps and isomorphisms of covering spaces over a fixed base). Deck transformations form the deck group $Deck (p)$ under composition, and this group acts on $E$ by evaluation (Group and abelian group, Left group actions, transitive actions, and faithful actions).

Depends on

Dependency tree · 2 levels

Sources