The $\nu$-conjecture relating $\mathbf g$- and denominator vectors

Assume $B$ is acyclic. Let $\nu:V\to V^*$ and $\eta:V^*\to V$ be the mutually inverse maps defined from the bilinear forms $E$ and $F$ in the source. For a cluster variable $x$, let $\mathbf g(x)$ and $\mathbf d(x)$ denote its $\mathbf g$-vector and denominator vector. The $\nu$-conjecture. If $x$ is a cluster variable not contained in the initial seed, then $\mathbf g(x)=\nu(\mathbf d(x))$; equivalently, $\mathbf d(x)=\eta(\mathbf g(x))$. The source says this holds for finite Cartan type and is easily verified when $n=2$, but leaves the general acyclic case open.