OpenAI · 291-02 · 2026-09-23 · Operator algebras
Cuntz comparison and Jiang–Su absorption
preprints/Cuntz-comparison-and-Jiang-Su-absorption-September-23-2026
Family 291. Toms–Winter and equivariant Jiang–Su stability.
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
Proves equivariant Jiang–Su stability for every countable discrete amenable group action on a simple separable unital infinite-dimensional nuclear stably finite Jiang–Su-stable -algebra, resolving this case of Szabó's conjecture without restrictions on trace dynamics. The family also proves the unital Toms–Winter conjecture, equating strict comparison, finite nuclear dimension and Jiang–Su stability in the simple separable unital infinite-dimensional nuclear setting.
We prove that strict comparison in the extended-functional sense implies Jiang–Su absorption for separable simple nuclear non-elementary C∗-algebras. This resolves the corresponding implication of the Toms–Winter regularity problem, including nonunital algebras and allowing unbounded traces. More generally, every separable nuclear C∗-algebra whose Cuntz semigroup is almost unperforated and fully almost divisible absorbs the Jiang–Su algebra.
Preprint source and Lean scope
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A Lean scope note is stored for family 291, but it does not name this preprint. It names 291-04. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.