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Research / Oct 6, 2026

Thompson's group F is nonamenable

Can the mathematical statement in Thompson's group F is nonamenable be proved and verified machine-checked in Lean?

Model / AI: OpenAI (unreleased)

machine-checked (formal proof)self-reported (formal proof)
Oct 6, 2026

Lean formalization in OpenAI math repository (Result 248)

Model / AI: OpenAI (unreleased)

machine-checked (formal proof)self-reported (formal proof)

OpenAI's internal frontier model proved and formalized in Lean the main result of 'Thompson's group F is nonamenable'. We prove that Thompson's group F is nonamenable. This confirms Geoghegan's conjecture and resolves the amenability problem for F.

Source read 2026-10-08. Cataloged from OpenAI's formalization.yaml (Family 248). The Lean development was not rebuilt locally.