The saturation conjecture for F-polynomials of cluster monomials

Let $F_M$ denote the $F$-polynomial associated with a representation, and call its support saturated if every lattice point in the Newton polytope of $F_M$ has a nonzero coefficient. The saturation conjecture. The support of the $F$-polynomial of a cluster monomial in any cluster algebra is saturated. Saturation is proved for rigid representations of acyclic quivers, but the conjecture concerns cluster monomials in arbitrary cluster algebras.