Title: Categorification of sign-skew-symmetric cluster algebras and some conjectures on g-vectors,
Abstract: Using the unfolding method given in \cite{HL}, we prove the conjectures on
sign-coherence and a recurrence formula respectively of ${\bf g}$-vectors for
acyclic sign-skew-symmetric cluster algebras. As a following consequence, the
conjecture is affirmed in the same case which states that the ${\bf g}$-vectors
of any cluster form a basis of $\mathbb Z^n$. Also, the additive
categorification of an acyclic sign-skew-symmetric cluster algebra $\mathcal
A(\Sigma)$ is given, which is realized as $(\mathcal C^{\widetilde Q},\Gamma)$
for a Frobenius $2$-Calabi-Yau category $\mathcal C^{\widetilde Q}$ constructed
from an unfolding $(Q,\Gamma)$ of the acyclic exchange matrix $B$ of $\mathcal
A(\Sigma)$.