The Toms-Winter conjecture: strict comparison implies Jiang-Su stability for simple nuclear C*-algebras
Theorem 1.1: strict comparison implies for every separable simple nuclear non-elementary , unital or not. More generally (Theorem 1.2) every separable nuclear algebra whose Cuntz semigroup is almost unperforated and fully almost divisible is -stable, which answers the implication (iii) to (ii) of the nonsimple Toms-Winter problem (STW Problem LXXV) and the abstract Cuntz-semigroup question (STW Problem XXVI). Separability and nuclearity remain hypotheses; nonnuclear and non-separable algebras are not treated.
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Occurred: Sep 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The Toms-Winter conjecture: strict comparison implies Jiang-Su stability for simple nuclear C*-algebras · Toms-Winter conjecture
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Companion: Nuclear dimension and Jiang-Su stability without elementary subquotients evidence for this event
This event attributed to Unreleased internal OpenAI model
Companion: Tracial projection methods and uniform property Gamma (unital route) evidence for this event
Theorem 1.1: strict comparison implies for every separable simple nuclear non-elementary , unital or not. More generally (Theorem 1.2) every separable nuclear algebra whose Cuntz semigroup is almost unperforated and fully almost divisible is -stable, which answers the implication (iii) to (ii) of the nonsimple Toms-Winter problem (STW Problem LXXV) and the abstract Cuntz-semigroup question (STW Problem XXVI). Separability and nuclearity remain hypotheses; nonnuclear and non-separable algebras are not treated. parent of this event
The Toms-Winter conjecture: strict comparison implies Jiang-Su stability for simple nuclear C*-algebras evidence for this event
VibeMathed record: The Toms-Winter conjecture: strict comparison implies Jiang-Su stability for simple nuclear C*-algebras evidence for this event
The Toms-Winter conjecture: strict comparison implies Jiang-Su stability for simple nuclear C*-algebras parent of this event
Schafhauser-Tikuisis-White, Nuclear C*-algebras: 99 problems (Problem XXXVI) evidence for this event
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