Angenent-Daskalopoulos-Sesum uniqueness conjecture for symmetric ancient ovals

Let an ancient oval be an ancient compact noncollapsed mean curvature flow that is not self-similar, and let $1\leq k\leq n$. An ancient oval is $\mathrm{O}(k)\times \mathrm{O}(n+1-k)$-symmetric if it is invariant under this product of orthogonal groups. Angenent-Daskalopoulos-Sesum's conjecture. $\mathrm{O}(k)\times \mathrm{O}(n+1-k)$-symmetric ancient ovals are unique up to time-shift and parabolic dilation. Ancient ovals are important as potential singularity models in mean-convex mean curvature flows and in the study of singularities. The analogous uniqueness statement is known under uniform two-convexity, while this general symmetric case is presented as a conjecture.