Anderson–Kogan conjecture on cluster monomials in the MV basis

Let $N$ be the unipotent subgroup of $\operatorname{GL}_m$, and let $\mathbb{C}[N]$ have its cluster algebra structure. A cluster monomial is a product of cluster variables supported on a single cluster. The MV basis is a basis of $\mathbb{C}[N]$ consisting of Mirković–Vilonen basis elements.

Anderson–Kogan conjecture. The cluster monomials are contained in the MV basis.

This conjecture concerns the relationship between the cluster algebra structure on $\mathbb{C}[N]$ and the MV basis. The source presents it as motivated by evidence from the comparison of the MV, dual canonical, and dual semicanonical bases; its resolution is not specified here.