F-polynomial maximal-monomial conjecture

Fix a positive integer $n$, an $n$-regular tree $\mathbb{T}_n$, a vertex $t_0\in\mathbb{T}_n$, and a skew-symmetrizable integer matrix $B=(b_{i,j})$. For each $t\in\mathbb{T}_n$ and $\ell=1,\dots,n$, let $F_{\ell;t}^{B;t_0}\in\mathbb{Z}[u_1,\dots,u_n]$ be the associated $F$-polynomial. F-polynomial maximal-monomial conjecture. Each polynomial $F_{\ell;t}^{B;t_0}$ has a unique monomial of maximal degree. Furthermore, this monomial has coefficient $1$, and it is divisible by all the other occurring monomials. The source says this is equivalent to the constant-term conjecture, but gives no resolution status.