The random matrix strong convergence conjecture for tensor actions

Let $r\in\mathbb{N}$, let $\alpha\in\mathbb{C}[\mathbb{F}_r]\otimes\mathbb{C}[\mathbb{F}_r]$, and let $u$ be an $r$-tuple of free Haar unitaries. For almost every sequence of Haar-random tuples $U^{(N)}\in\mathcal{U}(\mathbb{M}_N(\mathbb{C})^r)$, define $(B\otimes C)\# A=BAC^T$. The random matrix strong convergence conjecture. One has

$$\sup_{R>0}\inf_{F\subset\mathbb{C}[\mathbb{F}_r]\ \mathrm{finite}}\limsup_{N\to\infty}\sup_{\substack{A\in\mathbb{M}_N(\mathbb{C}),\ \|A\|\leq R,\ \|A\|_2\leq1,\forall P\in F,\ \operatorname{tr}(A^*P(U^N))=0}}\left\|\alpha(U^{(N)}\otimes1_N,1_N\otimes(U^{(N)})^t)\# A\right\|_2 \leq\left\|\alpha(u\otimes1,1\otimes u^{-1})\right\|_{C^*_{\lambda}(\mathbb{F}_r)\otimes_{\min}C^*_{\lambda}(\mathbb{F}_r)}.$$

The estimate asserts that, after removing finitely many polynomial directions, the random tensor action has the expected limiting norm. The source states that this conjecture has since been resolved by several authors, so its status is solved.