# Representation stability hypothesis adapter

Family 251: Amenability, unitarizability, and strong Ulam stability. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Distinguish amenability, unitarizability and strong operator-norm Ulam stability for the specified groups and Hilbert representations.

## Applicability and commercial boundary

Potentially infinite Hilbert spaces and uniform boundedness matter; the result is not a finite numerical conditioning guarantee.

## 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

Extract quantitative constants and finite restricted representations.

## 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).

[Unitarizability implies amenability for discrete groups](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026/paper.pdf).