Mean-curvature blow-up conjecture for embedded flows in dimensions at most six

Let $M_t$ be a closed smooth embedded mean curvature flow in $\mathbb{R}^{n+1}$, with $n dleq 6$, and suppose the flow develops a first finite singular time. Mean-curvature blow-up conjecture. The mean curvature blows up at the first finite singular time. The source describes this as a weaker conjecture, conditional on the smooth-blowup and multiplicity-one conjectures in dimensions at most six, and does not report a resolution.