Berkovich skeleton complement conjecture for virtual open disks

Let $K$ be a complete discrete valued field with equal characteristic $0$, and let $\mathcal{X}$ be a smooth proper integral variety of dimension $n$ over $K$. Write $\mathcal{X}^{\textsf{an}}$ for its Berkovich analytification, let $\textsf{Sk}^{\textsf{ess}}(\mathcal{X}^{\textsf{an}})$ denote its essential skeleton, and call an open subset a virtual open disk when it is a Berkovich virtual open disk of relative dimension $1$. Berkovich skeleton complement conjecture. For every point $x\in\mathcal{X}^{\textsf{an}}$, $x$ is contained in an open virtual disk if and only if $x$ is not contained in $\textsf{Sk}^{\textsf{ess}}(\mathcal{X}^{\textsf{an}})$. The authors prove this when $\mathcal{X}$ admits a strictly semistable model with semiample canonical class; the general case remains open.