OpenAI reports trace-cone classification after Razak–Jacelon stabilization

For separable nuclear complex C∗-algebras A and B, any isomorphism between their topological cones of all extended lower-semicontinuous tracial weights is realized by an isomorphism A⊗W⊗K ≅ B⊗W⊗K, where W is the Razak–Jacelon algebra and K the compact operators.

Sources for this record

What was already known

Trace-based classification after W stabilization was known in simple or otherwise restricted cases. Robert asked whether the full topological cone classified separable nuclear algebras without ideal-structure or dense-finiteness restrictions.

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

Answers Robert’s trace-cone classification question for arbitrary ideal structures.

Limitations

The linked Lean note checks transport of ideals by a trace-cone equivalence, not construction or uniqueness of the stabilized algebra isomorphism.

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