Source authenticated

Szabo's Conjecture A on equivariant Jiang-Su stability, in the unital stably finite case

Theorem 1.1: for $A$ simple, separable, unital, infinite-dimensional, nuclear, stably finite and $\mathcal Z$ -stable, every action $\alpha$ of a countable discrete amenable group is cocycle conjugate to $\alpha\otimes\mathrm{id}_{\mathcal Z}$ , with no restriction on how $\alpha$ acts on the trace simplex, and including finite groups and trivial actions. It does not treat nonunital algebras, and stably infinite (purely infinite) algebras are not part of this theorem.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Oct 5, 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: Szabo's Conjecture A on equivariant Jiang-Su stability, in the unital stably finite case · Szabo's Conjecture A, unital stably finite case

Confidence: Not scored

Registry verification: unreviewed · announcement · partial

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Szabo's Conjecture A on equivariant Jiang-Su stability, in the unital stably finite case

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against Conjecture A. It proves the conclusion for every action of a countable discrete amenable group on a simple separable unital infinite-dimensional nuclear stably finite $\mathcal Z$ -stable algebra, with no condition on traces or outerness. The manuscript itself says nonunital algebras, which Conjecture A includes, are beyond its scope; purely infinite algebras are also not covered by this theorem. The proof was not refereed and is not formalised.

Source ↗

Szabo's Conjecture A on equivariant Jiang-Su stability, in the unital stably finite case

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Szabo, Equivariant property (SI) revisited (2021)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Lineage and corrections

Szabo's Conjecture A on equivariant Jiang-Su stability, in the unital stably finite case parent of this event

This event attributed to Unreleased internal OpenAI model

VibeMathed record: Szabo's Conjecture A on equivariant Jiang-Su stability, in the unital stably finite case evidence for this event

Szabo, Equivariant property (SI) revisited (2021) evidence for this event

Szabo's Conjecture A on equivariant Jiang-Su stability, in the unital stably finite case evidence for this event

Act on this frontier

Verify, challenge, or extend the result.

Help verify Open canonical problem Explore evidence graph