Ilmanen's smooth-blowup conjecture for embedded hypersurfaces

Let an embedded hypersurface evolve by mean curvature flow in $\mathbb{R}^{n+1}$, with $n dleq 6$, and consider blow-ups at singularities. Ilmanen's smooth-blowup conjecture. The blow-ups are smooth for embedded hypersurfaces in $\mathbb{R}^{n+1}$ up to $n dleq 6$. The source states that this conjecture remains open for $3 dleq n dleq 6$; if it holds together with the multiplicity-one conjecture in these dimensions, then the mean curvature must blow up at the first finite singular time for a closed smooth embedded flow.