Generalized Mazur conjecture for simple abelian varieties over the algebraic numbers

Let $A$ be a simple abelian variety over $\overline{\mathbb{Q}}$ of dimension $g$, and let $\Gamma\subset A(\overline{\mathbb{Q}})$ be a subgroup of positive rank. Let $C$ be the closure of $\Gamma$ in $A(\mathbb{C})$ for the analytic topology, with real Lie-group dimension $\dim C$. Generalized Mazur conjecture. Either

$$\dim C=2g,$$

or $\dim C=g$ and there exist an abelian variety $A'$ over $K=\overline{\mathbb{Q}}\cap\mathbb{R}$ and an isogeny $v:A\longrightarrow A'\otimes_K\overline{\mathbb{Q}}$ such that $v(\Gamma)\subset A'(\mathbb{R})$. This is presented as a generalization of Mazur's conjecture for abelian varieties: failure of analytic density should be explained by descent to a real model. The source gives no resolution.