Chuang–Miyachi's Koszul duality conjecture for affine category O blocks

Let $e,\ell,m>0$, let $\nu\in\mathbb{Z}^{\ell}(m)$, and let $\mathcal{O}^{\nu}_{\mu,a}$ denote the block defined by

$$\mathcal{O}_{\mu,a}^{\nu}=\mathcal{O}^{\nu}_{\mu}(n),\qquad n=\Bigl\langle a\delta+\sum_{p=1}^{\ell}\omega_{\nu_p}-\mu:\hat\rho_e\Bigr\rangle,$$

with $a\in\mathbb{N}$. Chuang–Miyachi's conjecture. The blocks $\mathcal{O}^{\nu}_{\mu,a}$ and $\mathcal{O}^{\mu}_{\nu,a}$ are Koszul and are Koszul dual to each other. This predicts a symmetry exchanging the affine parameters $e$ and $\ell$ at the level of block categories; the source provides no resolution status.