Non-degeneracy conjecture for cyclic quiver potentials

Let $C(W_n^I)$ be the potential associated with the cyclic quiver construction, for parameters $m,n\in\mathbb{Z}_n$. Non-degeneracy conjecture. For any $m,n\in\mathbb{Z}_n$, the potential $C(W_n^I)$ is non-degenerated. The claim generalizes the known non-degeneracy of the corresponding Labardini potentials for triangulations of a once-punctured disk with six marked points, a sphere with four punctures, and a sphere with five punctures. Its status beyond these cases is not established in the supplied source.