Remark: Family 294. A counterexample to Kaplansky's quasitrace conjecture

Disproves Kaplansky's quasitrace conjecture by constructing a separable unital complex $C^{\ast }$-algebra admitting normalized $2$-quasitraces, all of which are nonadditive. As a consequence, two unital simple stably finite $C^{\ast }$-algebras can have a properly infinite minimal tensor product, with one factor $C_r^{\ast }({\mathbb{F}}_2)$.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.