The arithmetically bi-algebraic conjecture for enlarged mixed Shimura varieties

Let $S$ be an algebraic variety over $\overline{\mathbb{Q}}$ whose uniformization $\mathcal{X}$ has a structure of algebraic variety over $\overline{\mathbb{Q}}$. Suppose that $Y$ is a subvariety of $S$ containing a Zariski dense subset of arithmetically bi-algebraic points. The arithmetically bi-algebraic conjecture. Then $Y$ is geometrically bi-algebraic. This conjecture is presented as a formulation unifying the Manin–Mumford and André–Oort conjectures through bi-algebraic systems; the supplied text does not state a resolution.