Domain-of-attraction characterization of free stable laws

Let $\mathcal{M}_k$ be the class of measures used in the paper, let $\mu\in\mathcal{M}_k$ be nontrivial, and let $\nu$ be the limiting law under consideration. The free domain of attraction of $\nu$ is the collection of measures whose normalized free convolutions converge to $\nu$.

Domain-of-attraction conjecture. Assume that $\mu\in\mathcal{M}_k$ is not a point mass. Then $\nu$ is $\boxplus$-stable if and only if the free domain of attraction of $\nu$ is not empty.

This proposes an exact characterization of free stable laws by nonemptiness of their free domains of attraction. The supplied text does not state whether the conjecture has been resolved.