Rigidity conjecture for super-exponentially decaying cylindrical flows

Let $\mathcal{M}$ be a rescaled mean curvature flow in $\mathbb{R}^{n+1}$ without boundary. The source distinguishes asymptotic cases for such flows, including a case of super-exponential decay, denoted there by case

$$of Theorem$$

. Super-exponential rigidity conjecture. If this super-exponential decay case holds, then $\mathcal{M}$ coincides with some low spherical flow. The claim is motivated by unique-continuation heuristics: super-exponential decay should force the perturbation from the spherical model to vanish identically. The source presents this as plausible but does not establish it.