Ilmanen's multiplicity-one conjecture for mean curvature flow

Consider the mean curvature flow of embedded hypersurfaces, and let a blowup limit mean a limit obtained by parabolic rescaling near a singularity, counted with its varifold multiplicity. Ilmanen's multiplicity-one conjecture. For the mean curvature flow of embedded hypersurfaces all blowup limits have multiplicity one. The conjecture is proved in $\mathbb{R}^3$, while the source identifies it as open in $\mathbb{R}^d$ for $d\geq4$ and notes that higher-dimensional cases require new ideas.