The integrality conjecture for special points on Shimura subvarieties

Let $k$ be a number field, let $S$ be a finite set of places of $k$ including all the archimedean places, and let $X$ be a special subvariety of a Shimura variety, defined over $k$. Let $D$ be a nonzero effective divisor on $X$. The Shimura-integrality conjecture. If at least one irreducible component of $D$ is not special, then

$$\{P\in X(\overline{k}):P\text{ is special and }S\text{-integral on }X\text{ relative to }D\}$$

is not Zariski dense in $X$. This is the Shimura-variety analogue of the preceding integrality conjectures and an integrality form of the André–Oort philosophy; it remains open as stated.