Root conjecture for c-vectors of cluster algebras

Let $B$ be a skew-symmetrizable matrix, let $A(B)$ be its associated symmetrizable Cartan matrix, and let $\Delta(A(B))$ be the corresponding root system. A root is identified with a nonzero integer vector whose components are either all non-negative or all non-positive.

Root conjecture. Every $c$-vector of the cluster algebra $\mathcal{A}_\bullet(B)$ is a root of $\Delta(A(B))$.

This conjecture is a refinement of sign-coherence and is motivated by the relationship among cluster algebras, path algebras, and Kac–Moody algebras. The source explains that the corresponding extension of Kac's theorem to valued quivers had not yet been fully achieved; no resolution status is supplied here.