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The spatial Kadison-Kastler problem for close separable C*-algebras

Theorem 1.1: for every $\varepsilon>0$ there are unital norm-separable C*-algebras $A,B$ on a separable Hilbert space with $\mathrm{KK}(A,B)<\varepsilon$ and $A''=B''$ but no unitary with $uAu^*=B$ . The construction uses sequence algebras over a deformation of the free-group regular representation (Pytlik-Szwarc family) and a tensor-norm obstruction. It does not show $A$ and $B$ are non-isomorphic, imposes no nuclearity (the CSSWW positive theorem needs it), and does not affect von Neumann algebras.

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Prior state unknown→disproved

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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: The spatial Kadison-Kastler problem for close separable C*-algebras · Separable C*-algebra Kadison-Kastler

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VibeMathed record: The spatial Kadison-Kastler problem for close separable C*-algebras

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No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against the separable spatial question as the paper states it. It claims, for every $\varepsilon>0$ , unital norm-separable C*-algebras on a separable Hilbert space with common identity, Kadison-Kastler distance below $\varepsilon$ and equal bicommutants, that are not unitarily conjugate. Proof not refereed; not formalized. The paper says it gives no abstract non-isomorphism and no von Neumann counterexample.

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The spatial Kadison-Kastler problem for close separable C*-algebras

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Universal strong Kadison-Kastler stability

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Universal strong Kadison-Kastler stability evidence for this event

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