The Mirković–Vilonen basis and cluster pointedness

We prove that the Mirković–Vilonen basis of $\mathbb{C}[N]$ contains every cluster monomial and that each of its elements is $g$-pointed in every cluster, where $N$ is a maximal unipotent subgroup of a complex semisimple group. This resolves Conjecture 6.6 in Kamnitzer’s ICM 2022 survey.