DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-11

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.

A free group action has no nonidentity element fixing a point

A left action of a group $G$ on a set $X$ (Left group actions, transitive actions, and faithful actions) is free when

$g \cdot x = x ⟹ g = e$

for every $g \in G$ and $x \in X$ . Equivalently, no nonidentity element of $G$ fixes any point of $X$ .

Depends on