The associahedron conjecture for finite-type mutation matrices

Let $\mathcal{A}(\widetilde{\sf M})$ be a finite-type cluster algebra with principal coefficients and possibly cyclic initial seed $(\widetilde{\sf M},\mathbf{x},\mathbf{y})$. Define the $\widetilde{\sf M}$-associahedron as the Minkowski sum of the Newton polytopes of all $F$-polynomials of $\mathcal{A}(\widetilde{\sf M})$:

$$\sum \operatorname{Newton}({{\sf F}(\mathbf{y})})\subset V.$$

Associahedron conjecture. All $\widetilde{\sf M}$-associahedra of a given finite type have the same combinatorial type, meaning that they have the same face lattice. In particular, their duals realize the cluster complex. This conjecture proposes that the resulting Minkowski-sum realization is independent, up to combinatorial type, of the finite-type initial mutation matrix; the source gives no resolution status.