OpenAI · 301-01 · 2026-09-25 · Operator algebras
The trace cone classifies Razak–Jacelon stabilizations
preprints/The-trace-cone-classifies-Razak-Jacelon-stabilizations-September-25-2026
Family 301. Classification by trace cones after Razak–Jacelon stabilization.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Classifies separable nuclear complex -algebras after tensoring with the Razak–Jacelon algebra and the compact operators, using their full topological cones of extended lower-semicontinuous tracial weights. This answers Robert’s trace-cone question, including algebras with arbitrary ideal structure and both finite and infinite subquotients.
We prove that the canonical topological cone of all extended lower-semicontinuous tracial weights determines a separable nuclear C∗-algebra after tensoring with the Razak–Jacelon algebra and the compact operators, answering Robert's trace-cone classification question positively. The isomorphism realizes the prescribed cone map, with arbitrary ideal structure and without a density assumption on the finite domains of the weights.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 301: Trace cones and Razak–Jacelon stabilization. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.