Maximal-monomial conjecture for $F$-polynomials

An $F$-polynomial is the polynomial in the initial coefficient variables obtained from a cluster variable by specializing the initial cluster variables to $1$. Maximal-monomial conjecture for $F$-polynomials. Each $F$-polynomial has a unique monomial of maximal degree; this monomial has coefficient $1$ and is divisible by all other monomials in the $F$-polynomial. The source relates this claim to the constant-term conjecture and records finite Cartan type as a case where it holds; no general resolution is stated.