The curve-quiver potential conjecture for crepant resolutions of abelian quotient singularities

Let $G$ be a finite abelian subgroup of $\operatorname{SL}_3(\mathbb{C})$, and let $Q$ be the curve quiver for a crepant resolution of $\mathbb{C}^3/G$. A minimal potential on $Q$ is a potential satisfying the minimality condition used for curve quivers. Curve-quiver potential conjecture. There is a unique minimal potential $W$ on $Q$ such that the quivers with potential mutation-equivalent to $(Q,W)$ naturally biject with crepant resolutions of $\mathbb{C}^3/G$ in such a way that mutation in a node corresponds to flopping the associated curve. This conjecture seeks to extend the correspondence between quiver-with-potential mutations and flops beyond the polyhedral case to finite abelian subgroups of $\operatorname{SL}_3(\mathbb{C})$; its status is not determined by the supplied source context.