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OpenAI reports: Kadison’s similarity conjecture

OpenAI reports that every bounded complex-linear unital homomorphism from a unital complex C*-algebra to operators on a Hilbert space is conjugate by a bounded invertible operator to a *-homomorphism.

Sources for this record

What was already known

Known results for nuclear algebras and other restricted classes do not establish the unrestricted bounded-representation target. The required similarity concerns one operator for the whole representation.

What changed and why it matters

Removes the stated restrictions from the bounded unital C*-algebra similarity target.

The AI contribution

OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.

Limitations

The theorem assumes a bounded unital complex-linear homomorphism. It is not a statement about arbitrary unbounded maps or an a priori uniform condition-number bound. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.

Accessible artifact / proof

The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.

Correction and publication history

2026-10-11 · publication

Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.

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