Bogomolov conjecture for Drinfeld modules

Let $\phi:A\rightarrow K\{\tau\}$ be a Drinfeld module of generic characteristic with $\operatorname{End}_{K^{\operatorname{sep}}}(\phi)=A$, and let $X$ be an irreducible $K^{\operatorname{sep}}$-subvariety of $\mathbb{G}_a^g$, where $g\geq 1$. For each $n\geq 1$, define

$$X_n:=\{x\in X(K^{\operatorname{sep}})\mid \operatorname{\widehat{h}}(x)<\frac{1}{n}\}.$$

Bogomolov conjecture. If $X_n$ is Zariski dense in $X$ for every $n\geq 1$, then $X$ is a torsion subvariety of $\mathbb{G}_a^g$. This is presented as a consequence of the proposed small-height equidistribution statement and is the Drinfeld-module analogue of the Bogomolov conjecture.