Quasi-homogeneity conjecture for contraction algebra potentials

Let $Y\to X$ be a 3-dimensional flopping contraction with contraction algebra $\Lambda(Y,\Phi)$.

Quasi-homogeneity conjecture. The threefold $X$ is quasi-homogeneous if and only if the potential $\Phi$ is quasi-homogeneous. The source introduces this as a conjectural relation between quasi-homogeneous hypersurface singularities and quasi-hogeneous potentials; no resolution is stated.