Metric cone conjecture for the Ricci-flow limit of Kähler–Ricci shrinkers

Let $X$ be a Kähler–Ricci shrinker with bounded scalar curvature and maximal volume growth. Let $(Z_0,d^Z_0)$ be the metric boundary produced by the Ricci flow, and let $(Z_0^{\operatorname{reg}},g_0^Z)$ denote its regular part with the induced metric.

Metric cone conjecture. If the Kähler–Ricci shrinker has maximal volume growth, then $(Z_0,d^Z_0)$ is a metric cone and coincides with the metric completion of $(Z_0^{\operatorname{reg}},g_0^Z)$.

This conjecture predicts conical asymptotic geometry and identifies the metric limit with the completion of its regular Riemannian part. The supplied source gives no resolution status.