What was already known
The problem asks whether F admits an invariant mean, equivalently the relevant Følner behavior. Known structural facts about F do not decide that property.
What changed and why it matters
Resolves the longstanding amenability question for the specified Thompson group.
The AI contribution
OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.
Limitations
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. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.
Accessible artifact / proof
The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.
Correction and publication history
Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.
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