The quiver and mutation conjecture for rank two Lie groups

Let $G$ be a semisimple, simply connected, complex Lie group. A quiver $Q_G$ is a quiver associated with $G$, and $\mu_G^{\operatorname{rot}}$ and $\mu_G^{\operatorname{flip}}$ are quiver mutations. The maps and spaces in Theorems~ and are those defined in the surrounding construction, and $\mathcal M$ denotes the map occurring there.

Quiver and mutation conjecture. For every semisimple, simply connected, complex Lie group $G$, there exists a quiver $Q_G$ and quiver mutations $\mu_G^{\operatorname{rot}}$ and $\mu_G^{\operatorname{flip}}$ such that Theorems~ and hold. The map $\mathcal M$ should be a composition of minor coordinates and a monomial map.

This conjecture proposes a uniform quiver-mutation description of the rotation and flip maps for configurations associated with rank two Lie groups. The supplied text gives no resolution status or evidence that the assertion has been proved or disproved.