Conjecture on bimodules of maximal amenable subalgebras of free group factors

Let $t\in(1,\infty]$ and let $N\subseteq L(\mathbb{F}_{t})$ be a maximal amenable von Neumann subalgebra. Regard the following as $N$-$N$ bimodules, where $L^{2}(N)\otimes L^{2}(N)$ is taken with infinitely many copies: The maximal-amenable bimodule conjecture.

$$L^{2}(L(\mathbb{F}_{t}))\ominus L^{2}(N)\leq [L^{2}(N)\otimes L^{2}(N)]^{\oplus\infty}.$$

This conjecture proposes that the part of the standard bimodule of the free group factor orthogonal to a maximal amenable subalgebra is contained in infinitely many copies of the coarse $N$-$N$ bimodule. It is motivated by the authors' results on free Araki–Woods and free group factors; the excerpt does not state whether it has been proved or disproved.