Generic-variable basis conjecture for acyclic cluster algebras

Let $Q$ be an acyclic quiver. Let $\mathcal A(Q)$ be its acyclic cluster algebra and let $\mathcal G(Q)$ be the set of generic variables associated with $Q$. Generic-variable basis conjecture. The set $\mathcal G(Q)$ is a $\mathbb{Z}$-basis of $\mathcal A(Q)$. This is the paper's proposed general construction of integral bases for acyclic cluster algebras; the introduction explains that generic variables contain the cluster monomials and coincide with them exactly when $Q$ is a Dynkin quiver.