Quiver Hecke categorification conjecture for K-theoretic Coulomb branches

Let $\Gamma$ be an ADE root system, let $Q$ be an orientation of its Dynkin diagram, and let $\alpha=\sum_{i\in Q_0}n_i\alpha_i$ be a positive root. Set $G=\prod_{i\in Q_0}GL_{n_i}$ and $N=\bigoplus_{i\to j\in Q_1}\operatorname{Hom}(\mathbb{C}^{n_i},\mathbb{C}^{n_j})$. Let $C_{w,v}$ be the specified monoidal subcategory of finite-dimensional graded modules over the quiver Hecke algebra of affine type $\Gamma^{(1)}$, and let $\mathcal{KP}^{\eta}_{G,N}$ be the corresponding localized canonical-basis category. Quiver Hecke categorification conjecture. There is a monoidal functor

$$C_{w,v}\longrightarrow\mathcal{KP}^{\eta}_{G,N}$$

which takes distinct simples to distinct simples. In particular, the bases defined by the classes of simples in each category coincide, up to inverting certain classes of simples in $C_{w,v}$. This is proposed for quiver gauge theories whose Coulomb branches are related to open Richardson varieties and quiver Hecke algebra module categories; the source gives no resolution.