The denominator-vector formula from F-polynomials

Fix $B^0,t_0,\ell,t$ such that the cluster variable $x_{\ell;t}$ is not in the initial cluster at $t_0$, and write its denominator vector as $\mathbf{d}_{\ell;t}^{B^0;t_0}=(d_1,\dots,d_n)$. Let $F_{\ell;t}^{B^0;t_0}$ be its $F$-polynomial and let $\operatorname{Trop}(u_1,\dots,u_n)$ denote tropical specialization. Denominator-vector F-polynomial conjecture.

$$u_1^{-d_1}\cdots u_n^{-d_n}=F_{\ell;t}^{B^0;t_0}|_{\operatorname{Trop}(u_1,\dots,u_n)}(u_1^{-1},\dots,u_n^{-1}).$$

This is equivalent, under the proposition stated immediately before it, to the single-$F$-polynomial formula for the $\mathbf{g}$-vector. It is proved in the bipartite case and remains open in general.