The homotopy-colimit conjecture for the varieties X_C

Let $\mathcal{C}$ be the poset of faces and let $X_C$ be the associated varieties, with the derived categories $D^b(X_C)$ forming the corresponding diagram. Homotopy-colimit conjecture. The homotopy colimit

$$\underrightarrow{\operatorname{holim}}^{\mathrm{Mrt}}_{C\in\mathcal{C}} D^b(X_C)$$

is identified with $D^b(Z)$. This is part of the proposed categorical description of the geometry encoded by the perverse schober, but the supplied text gives no evidence that the assertion has been proved or disproved.