OpenAI reports: Nonamenability of Thompson’s group F
OpenAI reports that Thompson’s group F, viewed as a discrete group, is nonamenable.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06Nonamenability of Thompson’s group F
The problem asks whether F admits an invariant mean, equivalently the relevant Følner behavior.
Progress records 1
Understand the problem ↓1 record · How we rate progress
Understanding the problem
Read the background
The problem asks whether F admits an invariant mean, equivalently the relevant Følner behavior. Known structural facts about F do not decide that property.
The claim concerns Thompson’s group F, not other Thompson groups, and an abstract nonamenability result is not an efficient membership or word-problem algorithm.
Why it matters
If correct, resolves the longstanding amenability question for the specified Thompson group.
What counts as progress
A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.
What to watch for
- Assess the precise statement and assumptions before comparing results.
- The claim concerns Thompson’s group F, not other Thompson groups, and an abstract nonamenability result is not an efficient membership or word-problem algorithm.
- Track independent assessments, dependencies, corrections, and withdrawals separately from importance.
Background review: 2026-10-11. Selected sources:
Website timeline
Publication dates and editorial changes.