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Robert's trace-cone question: does the cone of extended traces classify W-stabilized separable nuclear C*-algebras?

Theorem 1.1: if $A,B$ are separable nuclear complex C*-algebras and $T(A)\cong T(B)$ as topological cones, then $A\otimes\mathcal W\otimes\mathcal K\cong B\otimes\mathcal W\otimes\mathcal K$ , and the isomorphism can be chosen to induce the given cone map. No density condition on finite domains of the weights and no UCT is assumed. It does not classify algebras without the $\mathcal W\otimes\mathcal K$ stabilization, and does not determine the range of the invariant.

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Prior state unknown→proved

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Occurred: Sep 25, 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: Robert's trace-cone question: does the cone of extended traces classify W-stabilized separable nuclear C*-algebras? · Robert's trace-cone classification question

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VibeMathed record: Robert's trace-cone question: does the cone of extended traces classify W-stabilized separable nuclear C*-algebras?

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No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against Robert's question in the Schafhauser-Tikuisis-White formulation, which keeps every extended trace including the ideal weights. The theorem assumes only separability and nuclearity, allows arbitrary ideal structure and both finite and infinite subquotients, and needs no UCT. The 7 October 2026 update added the supporting Comparator challenge TraceIdealTransportSupport (read here, with lean/docs/301.md): a trace-cone equivalence induces an order isomorphism of closed ideals carrying finiteness and zero ideals, and closed ideals correspond to additive idempotent traces. The classification itself is outside it, so the entry stays unreviewed. The proof combines existence and uniqueness theorems with an approximate intertwining; it was not refereed here.