Minimality conjecture for categorical resolutions

Let $Y$ be a singular variety, and let a categorical resolution of $Y$ correspond to a Lefschetz decomposition of $4D^b(\mathit{Z})4D$, where $\mathit{Z}$ is the exceptional divisor in the resolution considered in the paper. A Lefschetz decomposition is minimal when it is strict and minimal with respect to the partial ordering by inclusion of strict Lefschetz decompositions. Minimality conjecture. The categorical resolution of $Y$ is minimal if and only if the corresponding Lefschetz decomposition is minimal with respect to this partial ordering. This makes minimality of the categorical resolution accessible through the Lefschetz decomposition; the source gives no evidence that the conjecture has been resolved.