Polynomiality conjecture for deformed F-polynomials

Let $Q$ be a framed quiver and let $v_1,v_2,\ldots$ be a mutation sequence. Polynomiality conjecture for deformed $F$-polynomials. The deformed $F$-polynomial $S_n$ is a polynomial; equivalently, none of its monomial terms has a negative exponent. The source presents this as one of three conjectures about deformed $F$-polynomials and gives no resolution.