André–Pink–Zannier conjecture for Shimura varieties

Let $S$ be a Shimura variety and let $obreak\boldsymbol{\Xi} obreak\to S$ be a \subset of the generalised Hecke orbit of a point in $S$. Write $obreak\boldsymbol{\bar{\Xi}} obreak$ for the union in $S$ of the generalised Hecke orbits of the points of $obreak\boldsymbol{\Xi} obreak$; a subvariety is $obreak\boldsymbol{\bar{\Xi}} obreak$-special if it is weakly special and contains a point of $obreak\boldsymbol{\bar{\Xi}} obreak$. André–Pink–Zannier conjecture for $S$. The Zariski closure of $obreak\boldsymbol{\Xi} obreak$ is a finite union of $obreak\boldsymbol{\bar{\Xi}} obreak$-special subvarieties. Equivalently, any subvariety $V$ of $S$ contains only finitely many maximal $obreak\boldsymbol{\bar{\Xi}} obreak$-special subvarieties. The statement is presented as the Shimura-variety André–Pink–Zannier conjecture; the supplied text gives no resolution for this formulation.