Staticity conjecture for noncollapsed ancient Ricci flows with Ricci-flat tangent cones

Let $(M,g_t)_{t\in(-\infty,0]}$ be a noncollapsed ancient Ricci flow with bounded curvature within each compact time interval. Suppose

$$\operatorname{Ric}_{g_t}\ge 0$$

on $M\times(-\infty,0]$, and suppose every tangent flow at infinity is a Ricci-flat cone. The staticity conjecture. The metric $g_t$ is a static Ricci-flat metric with positive asymptotic volume ratio, that is, $g_t$ is independent of $t$ and $\operatorname{AVR}(M,g_t)>0$. This conjecture is proposed in the setting of a dichotomy for noncollapsed ancient Ricci flows with nonnegative Ricci curvature: such flows are expected to be static Ricci-flat when all tangent flows at infinity are Ricci-flat cones. The general assertion remains open.