Log Yau–Tian–Donaldson conjecture for cscK cone metrics

Let $X$ be a polarized variety with polarization $L_X$, let $D$ be a divisor, and fix a cone angle along $D$. A cscK cone metric is a Kähler cone metric on $(X,D)$ with constant scalar curvature. Log Yau–Tian–Donaldson conjecture. The pair $((X,L_X);D)$ admits a cscK cone metric if and only if it is log $K$-polystable. This is the conical analogue of the Yau–Tian–Donaldson correspondence, relating constant-scalar-curvature Kähler cone metrics to logarithmic algebraic stability; the source does not state its resolution.