Flapan–Macrì–O'Grady–Saccà conjecture on the semiorthogonal decomposition of the Fano eightfold

Let $F$ be the Fano eightfold obtained as a fixed locus in $X$, let $\mathcal{D}$ be a K3 category, and suppose that $X=(M_{\sigma}(h),v)$ is a moduli space of objects on $\mathcal{D}$ with polarization $v$. Let $K=M_{\sigma}(v)$ be the associated hyperkähler fourfold, called strange dual to $X$.

Flapan–Macrì–O'Grady–Saccà conjecture. The Fano eightfold $F$ admits the semiorthogonal decomposition

$$\operatorname{D}(F)=\langle \operatorname{D}(K),\operatorname{D},\operatorname{D},\operatorname{D},\mathcal{O},\mathcal{O}(1),\mathcal{O}(2)\rangle.$$

Here the three occurrences of $\operatorname{D}$ denote the K3-category components specified in the source. The conjecture proposes a categorical structure for $F$ analogous to the known semiorthogonal decomposition for the LLSvS eightfold; the supplied text does not state whether it has been resolved.