OpenAI · 294-01 · 2026-09-23 · Operator algebras
A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness
preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026
Family 294. A counterexample to Kaplansky's quasitrace conjecture.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Disproves Kaplansky's quasitrace conjecture by constructing a separable unital complex -algebra admitting normalized -quasitraces, all of which are nonadditive. As a consequence, two unital simple stably finite -algebras can have a properly infinite minimal tensor product, with one factor .
We refute Kaplansky's quasitrace conjecture by constructing a separable unital complex C∗-algebra that admits normalized 2-quasitraces but has no tracial state. As a consequence, we show that the minimal tensor product of two unital simple stably finite complex C∗-algebras can be properly infinite, even when one factor is the reduced free-group algebra .
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 294: Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.