Conjecture on nodal Enriques surface summands

The paper considers the Artin--Mumford example, the variety $V_{10}$ with $10$ singular points, a double covering of a quadric ramified in an octic with $20$ nodal singular points, and a double solid ramified in a sextic with $35$ singular points. Nodal-Enriques-summand conjecture. The derived categories $D^b(X)$ of these examples contain the category of a nodal Enriques surface as a direct summand. This conjecture is motivated by their common strictly unipotent Landau--Ginzburg monodromy and the resulting similarities in Hochschild homology; it is not proved in the source.