The cuplength lower bound for Rouquier dimension of wrapped Fukaya categories

Let $M$ be a smooth manifold, and let $\operatorname{Cuplength}(M)$ denote the cuplength of $H^*(M;k)$ for any field $k$. Let $\mathcal C(M)$ denote the wrapped Fukaya category associated to $M$. Cuplength conjecture.

$$\operatorname{Cuplength}(M)\leq \operatorname{Rdim}(\mathcal C(M)).$$

This conjecture proposes that cuplength gives a lower bound for Rouquier dimension, strengthening the paper's lower bound for generation by the cotangent fiber. The source gives no resolution.