Integer-basis conjecture for denominator vectors

Assume $B$ is acyclic. Let $\mathrm{Ex}_0(B)$ be the vertices of the exchange graph, let $I(v)$ index the cluster at $v$, and let $\mathbf d(x)$ denote the denominator vector of a cluster variable $x$. Integer-basis conjecture for denominator vectors. For each $v\in\mathrm{Ex}_0(B)$, the vectors $\{\mathbf d(x^v_e):e\in I(v)\}$ form a $\mathbb Z$-basis for the weight lattice. The source derives this as one of several consequences of preceding conjectures and later proves it for finite Cartan type; no general resolution is stated.