The braid group and exchange graph conjecture for quivers with superpotential

Let $(Q,W)$ be a quiver with superpotential of degree $N$, and let $\Gamma$ be its associated Ginzburg differential graded algebra. Write $\operatorname{CT}(Q,W)$ for the cluster braid group and $\operatorname{ST}(Q,W)$ for the spherical twist group, and let $\operatorname{\mathcal{EG}}(\Gamma)$ and $\operatorname{\mathcal{CEG}}_{N-1}(\Gamma)$ denote the exchange graphs of hearts and cluster exchange graphs, respectively. General quiver-with-superpotential conjecture. For any quiver with superpotential $(Q,W)$ of degree $N$,

$$\operatorname{CT}(Q,W)\cong\operatorname{ST}(Q,W)$$

and $\operatorname{\mathcal{EG}}(\Gamma)$ is the universal cover of $\operatorname{\mathcal{CEG}}_{N-1}(\Gamma)$. In the Dynkin and decorated marked surface cases, analogous statements are established by the theorems preceding this conjecture; the general case remains open.