Lowest-entropy conjecture for generalized cylindrical shrinkers

Let $M^n_t\subset\mathbb R^N$ be a self-shrinking solution of mean curvature flow, and let $\lambda$ denote its entropy. For $n\leq 4$, consider the round generalized cylinders

$$\mathbb S^k_{\sqrt{2k}}\times\mathbb R^{n-k}.$$

Lowest-entropy conjecture for generalized cylinders. For any codimension and $n\leq 4$, the round generalized cylinders $\mathbb S^k_{\sqrt{2k}}\times\mathbb R^{n-k}$ are the shrinkers with the lowest entropy.

The claim concerns the entropy-minimizing self-shrinkers in dimensions at most four, including higher-codimension shrinkers. The source presents it as a conjecture and provides no resolution here.