OpenAI reports equivariant Jiang–Su stability for amenable actions

Every action of a countable discrete amenable group on a simple, separable, unital, infinite-dimensional, nuclear, stably finite, Jiang–Su-stable complex C∗-algebra absorbs the trivial Jiang–Su action up to cocycle conjugacy, with no condition on its action on traces.

Sources for this record

What was already known

Szabó conjectured automatic equivariant Jiang–Su stability for amenable actions. Earlier positive results required restrictions such as finitely many extreme-trace rays; the full unital stably finite case remained open.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Major

Proves the unital stably finite case of Szabó’s conjecture for arbitrary amenable actions.

Limitations

The nonunital case is outside the paper. The linked Lean note checks tracial real-rank and uniform-property-Gamma comparison results in a companion paper, not equivariant absorption.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.

Read this published revision