Non-abelian generalization of the G-infinity theorem for k-dependent groups

Let $T$ be a $k$-dependent theory, let $A$ be a small parameter set, and let $G$ be a type-definable group over $A$. Let $\mathcal{M} \supseteq A$ be a small model and let $\bar{b}_1, \ldots, \bar{b}_{k-1}$ be finite tuples such that $(\mathcal{M},A,\bar{b}_1,\ldots,\bar{b}_{k-1})$ are in a generic position. The theorem cited in the statement provides a set $C \subseteq \mathcal{M}$ with $|C| \leq \beth_2(|T|+|A|)$ and an equality describing $G^{\infty}$ for abelian $G$. Non-abelian G-infinity conjecture. The same conclusion holds for arbitrary $k$-dependent groups, without assuming that $G$ is abelian. The conjecture proposes extending the stated $G^{\infty}$ intersection formula from type-definable abelian groups to arbitrary $k$-dependent groups.