André–Oort conjecture for meromorphic strata in genus zero

Let $\mathcal H(\mu)$ be a stratum of meromorphic differentials in genus zero, and let $S\subseteq\mathcal H(\mu)$ be an algebraic variety containing a Zariski-dense set of arithmetic points, where an arithmetic point is a $\overline{\mathbb Q}$-bi-algebraic point. The residue map assigns to a differential its residues at the marked poles.

André–Oort conjecture in genus zero. The variety $S$ is $\overline{\mathbb Q}$-bi-algebraic. Furthermore, if not all residues are identically zero on $S$, then the fibers of the residue map are affine-linear bi-algebraic varieties.

This is the genus-zero analogue of the André–Oort conjecture for holomorphic strata, adapted to account for residues in meromorphic strata. The source does not state a resolution of this conjecture.