Poincaré-type cscK metric and relative K-polystability conjecture

Let $X$ be a polarized variety with polarization $L_X$, and let $D$ be a divisor. A metric on $X\setminus D$ is said to be of Poincaré type when it has the prescribed Poincaré asymptotics near $D$. Poincaré-type stability conjecture. The pair $((X,L_X);D)$ has a cscK, or more generally extremal Kähler, metric of Poincaré type if and only if it is relatively K-polystable for angle $0$. This is presented as an expected equivalence between existence of distinguished Kähler metrics and algebro-geometric stability; the source does not state its resolution.