The RoCK core block conjecture for the map eta

Let $\Lambda$ be a dominant weight, let $\boldsymbol{\kappa}$ be the associated charge, let $\omega$ and $\beta$ be weights, and let $\Lambda_+^{\boldsymbol{\kappa}}(\omega)$ denote the corresponding block. Write $e$ for the quantum characteristic, $\theta$ for the relevant parameter, $\operatorname{ht}(\beta)$ for the height of $\beta$, and $\operatorname{cap}_\delta^\theta(\omega,\boldsymbol{\kappa})$ for the associated capacity. Let $\eta_{\omega,\beta}^\Lambda$ be the map from the tensor product of the relevant KLR algebras to the block algebra.

RoCK core block conjecture. If $\Lambda_+^{\boldsymbol{\kappa}}(\omega)$ is a $\theta$-RoCK core block with $\operatorname{ht}(\beta) \leq e \cdot \operatorname{cap}_\delta^\theta(\omega,\boldsymbol{\kappa})$, then the map $\eta_{\omega,\beta}^\Lambda$ is an isomorphism.

The claim concerns the tensor-product structure of KLR algebras associated with RoCK core blocks. The supplied text does not state whether this conjectural formulation is resolved beyond the cited surrounding results.