The rigid polystable reduction conjecture

Let $\mathcal{O}$ be a complete rank-$1$ valuation ring with algebraically closed fraction field $K$, and let $\mathcal{X}$ be a flat, topologically finitely presented formal $\mathcal{O}$-scheme whose adic generic fiber $\mathcal{X}_K$ is smooth.

Rigid polystable reduction conjecture. There is a rig-isomorphism $\mathcal{X}'\to\mathcal{X}$ such that $\mathcal{X}'$ is polystable.

This conjecture would give a polystable model after a rig-isomorphism for every formal model satisfying the stated hypotheses. In the source, it is presented as a stronger polystable reduction statement for rigid-analytic spaces; the supplied material gives no resolution status.