Cluster algebra conjecture for quantum cohomology of quiver critical loci

Let $(\mathbf{Q},\mathbf{W},\mathbf{v})$ be a quiver with potential and dimension vector, with associated quiver variety $X$ and superpotential, and let $Z$ be its critical locus; define $Z'$ similarly for the mutated quiver with potential $(\mathbf{Q}',\mathbf{W}',\mathbf{v}')$. Let $\mathcal{A}$ be the cluster algebra associated with $\mathbf{Q}$, let $\operatorname{QH}^{\mathrm{GW}}(Z)$ and $\operatorname{QH}^{\mathrm{GW}}(Z')$ denote the quantum cohomology rings, and let $t$ be an extra independent variable. Cluster algebra conjecture. The quantum cohomology rings of $Z$ and $Z'$ are naturally isomorphic. Moreover, there is an injective map of algebras

$$\psi:\mathcal{A}\to\operatorname{QH}^{\mathrm{GW}}(Z)[t]\cong\operatorname{QH}^{\mathrm{GW}}(Z')[t].$$

In particular, the cluster variables are sent to Chern polynomials $c_t(\mathcal{V})$ for certain tautological bundles $\mathcal{V}$ on $Z$. This conjecture proposes a direct relationship between cluster algebras and quantum cohomology in the setting of quiver varieties and their critical loci; the source provides no resolution status.