The unified Mordell–Lang conjecture for uniformizable T-modules

Let $\mathcal{A}=(\mathbb{G}_{a}^{m},\Phi)$ be a uniformizable $T$-module such that there exists $i\in\mathbb{N}\setminus\{0\}$ for which the leading coefficient matrix of $\Phi(T^{i})$ is invertible. Let $X$ be an algebraic subvariety of $\mathbb{G}_{a}^{m}$, let $\Gamma$ be a finitely generated subgroup of $\mathcal{A}(\overline{k})$, and let $\overline{\Gamma}$ be the object defined in Statement 1. A torsion subvariety is a translate of a sub-$T$-module by a torsion point. Unified conjecture. There exist finitely many torsion subvarieties $\overline{\gamma}_{1}+\mathcal{B}_{1},\ldots,\overline{\gamma}_{s}+\mathcal{B}_{s}$ of $\mathcal{A}$ such that

$$X\cap\overline{\Gamma}=\bigcup_{1\leq i\leq s}(\overline{\gamma}_{i}+\mathcal{B}_{i}\cap\overline{\Gamma}).$$

The authors propose this as a modification of Denis' statement after explaining that their examples refute the earlier formulations. They note that it would imply Ghioca's conjecture for powers of Drinfeld modules; the source does not prove the unified assertion.