Fomin–Zelevinsky sign-coherence conjecture for g-vectors

Let $\mathcal A(\Sigma)$ be a cluster algebra with principal coefficients at $\Sigma=(X,Y,B)$, where $B$ is an $n\times n$ sign-skew-symmetric integer matrix. For a cluster $X'$ and $x\in X'$, write $\mathbf g(x)$ for the $\mathbf g$-vector of $x$. Fomin–Zelevinsky's sign-coherence conjecture. For any cluster $X'$ of $\mathcal A(\Sigma)$, the vectors $\mathbf g(x)$ for $x\in X'$ are sign-coherent: for every coordinate $i$, the $i$-th coordinates of all these vectors are either all non-negative or all non-positive. This conjecture has been proved in the skew-symmetrizable case, while the paper establishes it for acyclic sign-skew-symmetric cluster algebras.