The unique maximal-monomial conjecture for F-polynomials

Fix $B^0,t_0,t$, and let $F_{\ell;t}^{B^0;t_0}(y_1,\dots,y_n)$ be the associated $F$-polynomial. Unique maximal-monomial conjecture. Each such polynomial has a unique monomial of maximal degree; that monomial has coefficient $1$ and is divisible by every other monomial occurring in the polynomial. This is presented as an equivalent formulation of the constant-term-one conjecture after applying the stated inversion relation for $F$-polynomials. It remains open in general.