Generation conjecture for compactly supported autoequivalences

Let $Y$ be the surface, let $D\subset Y$ be the boundary divisor, let $U=Y\setminus D$, and let $Z$ be the union of all $(-2)$ curves in $Y$. Write $Z'=Z\cap U$, let $\bar{Q}$ be the image of $Q$ in $\operatorname{Pic}(U)$, let $\operatorname{Aut}(Y,D;\mathrm{pt})$ be the automorphisms of $Y$ fixing $D$ pointwise, and let $\mathrm{Br}_{Z'}$ denote the subgroup defined in the source. Compact-auto-equivalence generation conjecture. The group $\operatorname{Auteq}_cD(U)$ is generated by $\bar{Q}$, $\operatorname{Aut}(Y,D;\mathrm{pt})$, and $\mathrm{Br}_{Z'}$. The source gives no resolution for this formulation.