# Amenability assumption evidence

Family 248: Thompson's group <i>F</i> is nonamenable. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Record the claimed nonamenability of Thompson group F for research workflows relying on amenability.

## Applicability and commercial boundary

This does not directly determine performance of a finite system or provide a practical amenability decider.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Inspect the proof, formal scope and an explicit witness representation.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Thompson's group F is nonamenable](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Thompsons-group-F-is-nonamenable-September-23-2026/paper.pdf).