Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness

What OpenAI claims

Disproves Kaplansky's quasitrace conjecture by constructing a separable unital complex C∗-algebra admitting normalized 2-quasitraces, all of which are nonadditive. As a consequence, two unital simple stably finite C∗-algebras can have a properly infinite minimal tensor product, with one factor C_r^*(𝔽₂). (Lean)

Paper

1. A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness

   23 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract 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 C_r^*(𝔽₂).

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.