Odaka's non-compact Yau–Tian–Donaldson conjecture

Let $((X,D),L)$ be a polarized dlt log Calabi–Yau pair with $\lfloor D\rfloor=\sum_iD_i$, $K_X+D\equiv0$, and $L$ ample on $X^{o}:=X\setminus\operatorname{Supp}(\lfloor D\rfloor)$. Non-compact Yau–Tian–Donaldson conjecture. (1) If $X^{o}$ admits a complete Ricci-flat weak Kähler metric $g$ whose volume growth dimension is at most $\dim_{\mathbb R}(X)=2\dim_{\mathbb C}(X)$ and whose Kähler class is $c_1(L)|_{X^{o}}$, then $(X^{o},L^{o})$ is weakly open K-polystable. (2) Such a metric, with any base point, is the pointed Gromov–Hausdorff limit of conical singular weak cscK metrics on polarized dlt log Calabi–Yau compactifications $((X,(1-\epsilon)D),L_\epsilon)$ as $\epsilon\to0$, with $c_1(L_\epsilon|_{X^{o}})\to c_1(L|_{X^{o}})$, if and only if $(X^{o},L^{o})$ is strongly open K-polystable. This is proposed as a metric-existence and correspondence principle; the source gives no resolution.