Bridgeland stability conjecture for the Kuznetsov component of a singular cubic sevenfold

Let $Y=Y^{\mathsf{sing}}$ be the singular cubic $7$-fold considered in the paper, and let

$$\operatorname{\mathcal{K}\mkern-1mu\mathit{u}}(Y)$$

be its Kuznetsov component.

Bridgeland stability conjecture. The category $\operatorname{\mathcal{K}\mkern-1mu\mathit{u}}(Y)$ admits a Bridgeland stability condition.

The context identifies this category with a categorical resolution related to a smooth Calabi--Yau threefold and to a category of Clifford modules over a stacky curve. It suggests that methods used for related singular cubic varieties may construct such stability conditions, but the supplied text does not state that this has been achieved.