False statementConstruction: Literature-sourcedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-26

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.

FALSE: every 2-homogeneous action is 2-transitive

Statement

Every $2$ -homogeneous action is $2$ -transitive.

Facts & Assumptions

Given: The square-affine action of $G$ on $F_{7}$ from The square-affine group of F_7 is 2-homogeneous but not 2-transitive.

[L1]

That action is $2$ -homogeneous but not $2$ -transitive (The square-affine group of F_7 is 2-homogeneous but not 2-transitive).

Refutation

technique · direct

1.1

By [L1], the square-affine action satisfies the hypothesis of the statement and fails its conclusion.

2.1

Therefore the statement is false.

step 1.1∎

Depends on

The square-affine group of F_7 is 2-homogeneous but not 2-transitive

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

P. J. Cameron, Permutation Groups, Chapter 2 (standard reference, not scraped)