The Manin–Mumford conjecture for Drinfeld modules

Let $K$ be a function field of transcendence degree $1$ over $\mathbb{F}_p$, and let $\phi:A\rightarrow K\{\tau\}$ be a Drinfeld module. Let $n\ge 1$ and let $X$ be an irreducible $K^{\operatorname{alg}}$-subvariety of $\mathbb{G}_a^n$. The torsion points for $\phi$ are points of $\mathbb{G}_a^n(K^{\operatorname{alg}})$ whose coordinates are torsion points for the diagonal action. Manin–Mumford conjecture for Drinfeld modules. If the set of torsion points $P\in\mathbb{G}_a^n(K^{\operatorname{alg}})$ for $\phi$ is dense in $X$, then there exist a torsion point $\overline{\gamma}\in\phi_{\operatorname{tor}}^n$ and a $K^{\operatorname{alg}}$-subvariety $Y\subset\mathbb{G}_a^n$, invariant under a nonzero endomorphism of $\phi$, such that

$$X=\overline{\gamma}+Y.$$

This is presented as a weak form of the Bogomolov conjecture. The examples in the supplied context indicate that, in finite characteristic, invariance under an endomorphism is the sharp conclusion, while the source suggests a stronger formulation may hold in generic characteristic; no resolution of this stated conjecture is supplied.