Almost High Rank Conjecture for orbit closures of translation surfaces

Let $\mathcal{M}$ be an orbit closure of surfaces of genus $g$. Its rank is denoted by $\operatorname{rank}(\mathcal{M})$. Almost High Rank Conjecture. If

$$\operatorname{rank}(\mathcal{M})=\frac{g}{2}+\frac{1}{2},$$

then $\mathcal{M}$ is a locus of double covers of a component of a stratum of Abelian differentials, a locus of double covers of a hyperelliptic locus in a stratum of Abelian differentials, or the locus of all holonomy double covers of surfaces in a stratum of quadratic differentials. This conjecture proposes a classification of orbit closures at the boundary of the high-rank regime; the source presents it as a next step in the investigation, and no resolution is supplied.