Backwards uniqueness conjecture past singularities for mean curvature flow in R^3

Let $M^i\subset\mathbb{R}^3$, $i=1,2$, be two smooth, connected, compact hypersurfaces in $\mathbb{R}^3$. Denote by $M^i_t$ the outermost mean curvature flows emanating from $M^i$. Suppose that $t_0$ is strictly prior to the extinction time of $M^1_t$ and that $M^1_{t_0}=M^2_{t_0}$. Backwards uniqueness conjecture. Then

$$M^1_t\equiv M^2_t,\qquad \forall t\in[0,t_0].$$

This conjecture asks whether outermost weak mean curvature flows are uniquely determined backwards from a common time before extinction, even when the flows may have passed through singularities. The paper's results substantiate the conjecture for asymptotically conical singularities, while the general question, including cylindrical singularities, remains open.