Díaz–Park sharpness conjecture for fusion systems

Let $S$ be a finite $p$-group, let $\mathcal{F}$ be a fusion system over $S$, and let $M=(M_{*},M^{*})$ be a Mackey functor over $\mathcal{F}$ on $\mathbb{F}_{p}$. Write $\mathcal{O}(\mathcal{F}^{c})$ for the centric fusion orbit category, and let $M^{*}\downarrow_{\mathcal{O}(\mathcal{F}^{c})}^{\mathcal{O}(\mathcal{F})}$ denote the restriction of the contravariant part of $M$ to this subcategory. Díaz–Park's sharpness conjecture. The higher limits vanish:

$$\operatorname{lim}^{n}_{\mathcal{O}(\mathcal{F}^{c})}\left(M^{*}\downarrow_{\mathcal{O}(\mathcal{F}^{c})}^{\mathcal{O}(\mathcal{F})}\right)=0$$

for every $n\geq 1$. This generalizes the vanishing of higher limits of cohomology functors over centric fusion orbit categories, and would establish sharpness for the associated homology decomposition. The conjecture remains unresolved and has been the subject of recent research.