André–Pink–Zannier conjecture for Hecke orbits

Let $S$ be a Shimura variety and let $V$ be an irreducible subvariety of $S$. André–Pink–Zannier conjecture. Suppose that the intersection of $V$ with a single Hecke orbit in $S$ is Zariski dense in $V$. Then $V$ is a weakly special subvariety of $S$. This concerns unlikely intersections with a single Hecke orbit and is described as a notable corollary of Zilber–Pink; the general status is not resolved in the supplied text.