Categorification conjecture for the m-tensor quiver Schur algebra

For positive integers $r_1,\dots,r_m$ with $l=r_1+\cdots+r_m$, let $S_n(\mathbf{r})$ be the $p$-DG $m$-tensor quiver Schur algebra

$$S_n(\mathbf{r}):={\operatorname{END}}_{\mathrm{NH}_n^l}\left(\bigoplus_{\lambda\in \mathcal{P}_n^{\mathbf{r}}}e_\lambda G(\lambda)\right),$$

and let $\mathcal{D}^c(S_n(\mathbf{r}))$ denote its compact derived category. Write $V_{r_i}$ for the corresponding $\mathbb{O}_p$-module and $\dot{U}_{\mathbb{O}_p}(\mathfrak{sl}_2)$ for the idempotented quantum group. The categorification conjecture. The compact derived category $\mathcal{D}^c(S_n(\mathbf{r}))$ categorifies the weight $l-2n$ subspace in the $m$-fold tensor product representation

$$V_{r_1}\otimes_{\mathbb{O}_p}V_{r_2}\otimes_{\mathbb{O}_p}\cdots\otimes_{\mathbb{O}_p} V_{r_m}$$

of $\dot{U}_{\mathbb{O}_p}(\mathfrak{sl}_2)$. This is the proposed categorification arising from the categorical action on the $p$-DG module categories of the $m$-tensor quiver Schur algebras; the excerpt provides no evidence that the conjecture has been proved or refuted.