Choda–Dykema conjecture on purely infinite reduced free products

Let $(A,\varphi)$ and $(B,\psi)$ be nontrivial $C^*$-probability spaces inducing faithful GNS representations. Form their reduced free product $(A,\varphi)*(B,\psi)$. Choda–Dykema conjecture. If $(A,\varphi)*(B,\psi)$ is simple and at least one of $\varphi$ or $\psi$ is nontracial, then $(A,\varphi)*(B,\psi)$ is purely infinite and simple. This conjecture predicts pure infiniteness for simple reduced free products whenever one of the input states is nontracial; the source presents it as a conjecture of Choda and Dykema, and no resolution is supplied here.