Analytic properties of representation zeta functions of unipotent group schemes

Let $\mathcal{O}$ be the ring of integers of a number field $K$, and let $\mathbf{G}$ be a unipotent group scheme arising from a finitely generated free torsion-free $\mathcal{O}$-Lie lattice. Let $R$ be a ring which is a finitely generated torsion-free $\mathcal{O}$-module, and write $\alpha(\mathbf{G})$ for the abscissa of convergence of $\zeta_{\mathbf{G}(R)}(s)$. Unipotent-group analytic-properties conjecture. The abscissa $\alpha(\mathbf{G})$ is independent of $R$, and $\zeta_{\mathbf{G}(R)}(s)$ admits meromorphic continuation to

$$\operatorname{Re}(s)>\alpha(\mathbf{G})-\delta(\mathbf{G})$$

for some $\delta(\mathbf{G})>0$ independent of $K$. Existing results establish related statements for $\mathbf{G}(\mathcal{O})$, but the asserted uniformity for general $R$ remains open.