Weak cluster structure conjecture for punctured infinite type $fD$ cluster categories

Let $n\in\mathbb{N}_{>0}$, and let $\mathcal{C}(\mathbb{D}_{\overline{n,\infty}})$ be an infinite type $\mathbb{D}$ weak cluster category. A full subcategory is weakly cluster tilting if it is one of the weakly cluster tilting subcategories considered in this category. Weak cluster structure conjecture. The weakly cluster tilting subcategories of each weak cluster category $\mathcal{C}(\mathbb{D}_{\overline{n,\infty}})$ form a weak cluster structure. This is presented as the analogue of the preceding conjecture for the categories associated with the punctured disk; the required mutation computations are not supplied, so the assertion remains open.