Polystable reduction conjecture over valuation rings

Let ${\mathcal O}$ be a height-one valuation ring with algebraically closed fraction field $K$, and let $X$ be a flat ${\mathcal O}$-scheme of finite type whose generic fiber $X_\eta$ is smooth. A modification $Y\to X$ is a proper birational morphism that is an isomorphism over the generic fiber.

Polystable reduction conjecture. There exists a modification $Y\to X$ such that $Y_\eta=X_\eta$ and $Y$ is polystable over ${\mathcal O}$.

Polystable schemes are, étale locally, products of semistable schemes. This conjecture asserts that polystable modification provides the appropriate form of semistable reduction over arbitrary height-one valuation rings, where semistable modification may fail to exist when the value group has rational rank greater than one. The source attributes the conjecture to Abramovich and Karu and to Temkin; its resolution is not specified here.