Derived equivalence conjecture for the Lehn–Lehn–Sorger–van Straten eightfold

Let $Y$ be a cubic fourfold, let $Z$ be its associated symplectic eightfold, and suppose that $Y\in\mathcal C_d$ for some $d$ satisfying the relevant condition. Then $Z$ is isomorphic to a moduli space of Bridgeland-stable complexes on a K3 surface $S$. Let $\alpha\in\operatorname{Br}(Z)$ be the obstruction to the existence of a universal complex on $Z\times S$, and let $U\in D^b(Z\times S,\alpha\boxtimes 1)$ be a twisted universal complex. Since $Y$ is naturally embedded in $Z$ and $\operatorname{Br}(Y)=0$, the restriction $U|_{Y\times S}$ can be untwisted. Derived equivalence conjecture. The functor $\mathcal A\to D^b(S)$ induced by $U|_{Y\times S}$ is an equivalence. This is an approach to proving that the Kuznetsov component $\mathcal A$ of the cubic fourfold is equivalent to the derived category of a K3 surface under the stated discriminant condition; the parser supplied no evidence resolving this conjecture.