Finiteness conjecture for high-degree arithmetic points in strata

Let $\textnormal{S}_{\alpha}$ be a stratum of abelian differentials up to scaling. An arithmetic point has a degree, and points of degree at least $3$ are those whose arithmetic degree is at least $3$. Finiteness conjecture for high-degree arithmetic points. Any stratum $\textnormal{S}_{\alpha}$ contains only finitely many arithmetic points of degree at least $3$.

The statement is presented as the core of a broader Zilber–Pink conjecture for atypical intersections in strata of abelian differentials. Earlier results in the paper concern arithmetic points and invariant linear subvarieties, but the asserted finiteness remains open.