Derived-category identification for the blowup of a nodal quartic double solid

Let $V$ and $W$ be four-dimensional vector spaces, let $s:W\subset S^2V^\vee$ be a generic embedding, and let $D\subset\mathbb{P}(W)\cong\mathbb{P}^3$ be the associated quartic symmetroid. Let $D'$ be its K3 resolution, let $\iota$ be the fixed-point-free involution induced by transposition, and set $S=D'/\iota$. Let $X$ be the nodal quartic double solid ramified over $D$, let $X'$ be the blowup of $X$ at its nodes, and let $\mathcal{A}_{X'}\subset D^b(X')$ be the subcategory defined in the cited corollary. Derived-category identification conjecture. One has

$$\mathcal{A}_{X'}\cong D^b(S).$$

The assertion identifies the residual component of the derived category of the algebraic resolution $X'$ with the derived category of the associated nodal Enriques surface. It is the categorical counterpart of the relationship between quartic symmetroids, Artin–Mumford quartic double solids, and Enriques surfaces; the source provides no resolution status.