Uniqueness conjecture for compact convex ancient G-flows

Let $G$ be the curvature function defining the flow, and consider convex ancient $G$-flows that are noncollapsing, uniformly two-convex, and compact. Uniqueness conjecture. Up to parabolic rescalings and rigid motions of the ambient space, there is a unique such flow. This solution is the ancient oval constructed by Lu, also studied by Risa and Sinestrari. The conjecture is motivated by the classification results available for related curvature flows, but its resolution is not established in the supplied source.