Nonexistence of exotic ancient ovals

Let $M_t\subset\mathbb{R}^{n+1}$ be an ancient oval whose tangent flow at $-\infty$ is $\mathbb{R}^{k}\times S^{n-k}$. A $k$-oval is an ancient oval with this tangent flow whose higher-order asymptotics around the cylinder exhibit quadratic bending in every cylindrical direction. Nonexistence of exotic ovals. Any ancient oval in $\mathbb{R}^{n+1}$ whose tangent flow at $-\infty$ is $\mathbb{R}^{k}\times S^{n-k}$ is a $k$-oval. Bamler and Lai have answered this conjecture affirmatively, so it is now a theorem; consequently, there are no ancient ovals with the specified cylindrical tangent flow that fall outside the $k$-oval class.