Conjecture on curvature critical points under curve-shortening flow

Let $\Gamma$ be a generic plane curve evolving under the curve-shortening flow, and let $\kappa$ denote its signed curvature. Write $n_\kappa(t)$ for the number of critical points of $\kappa$ at time $t$, and let $U$ be the reference point used for the critical-point trajectories. Curvature critical-point conjecture. The function $n_\kappa(t)$ decreases monotonically, and at the maximal time $t_{\max}$ one has

$$n_\kappa(t_{\max})=4,$$

with the four remaining trajectories meeting at right angles at $U$. This is proposed in the paper as a conjecture because monotonicity has not been proved; the paper suggests it on the basis of numerical evidence.