Fomin–Zelevinsky's conjecture on constant terms of F-polynomials

Let $\Sigma$ be a cluster algebra with principal coefficients, and let $F(x)$ denote the $F$-polynomial of a cluster variable $x$, obtained by evaluating its Laurent expansion at the initial cluster variables $x_1,\ldots,x_n$ equal to $1$. Fomin–Zelevinsky's conjecture. Each $F$-polynomial has constant term $1$. This conjecture is stated for cluster algebras with principal coefficients and concerns the normalization shared by all their $F$-polynomials; the supplied text gives no resolution status.