MV-basis cluster conjecture for the unipotent coordinate ring

Let $G$ be a semisimple group, let $N$ be its maximal unipotent subgroup, and let $\mathbb C[N]$ be the coordinate ring equipped with its cluster-algebra structure. A cluster monomial is a product of cluster variables belonging to one cluster, and a basis element is $g$-pointed in a cluster when it has the corresponding pointed expansion there.

MV-basis cluster conjecture. The MV basis for $\mathbb C[N]$ contains all cluster monomials. Moreover, every element of the MV basis is $g$-pointed in each cluster.

This would imply that the MV and dual semicanonical bases agree for ${\mathbf{SL}}_5$, which is not known in the supplied text. The conjecture is proved for certain clusters, but remains open in general.