Fomin–Zelevinsky sign-coherence conjecture for c- and d-vectors

Let $B$ be any skew-symmetrizable matrix. The $c$-vectors and $d$-vectors of the principal-coefficients cluster algebra $\mathcal{A}_\bullet(B)$ are defined by the coefficient and cluster-variable mutation recurrences, respectively.

Sign-coherence conjecture. (i) Any $c$-vector of $\mathcal{A}_\bullet(B)$ is a nonzero vector, and its components are either all non-negative or all non-positive. (ii) Any non-initial $d$-vector of $\mathcal{A}_\bullet(B)$ is a nonzero vector, and its components are all nonnegative.

These sign properties are fundamental to the structure theory of cluster algebras. The source attributes the two parts to conjectures of Fomin and Zelevinsky; no resolution status is supplied here.