The $\mathbb{Z}$-special-point characterization conjecture

Let $(G,X,\Gamma)$ be a real Shimura datum and let $W\subset S_\Gamma$ be an algebraic subvariety. The $\mathbb{Z}$-special-point characterization conjecture. The subvariety $W$ contains a Zariski dense set of $\mathbb{Z}$-special points if and only if it is special and arithmetic. This is the proposed non-arithmetic analogue of the André–Oort characterization and is stronger than the later CM-point special case; the source gives no proof or resolution.