Ultraproduct normal-subgroup conjecture for higher-rank arithmetic groups

Let $\Gamma$ be the arithmetic group specified by the local-to-global conjecture above, fix a non-principal ultrafilter $\mathcal{N}$ on the natural numbers, and let $O^*$ and $K^*$ be the corresponding $\mathcal{N}$-ultrapowers of $O$ and $K$. Ultraproduct normal-subgroup conjecture. For every $g\in\mathbf{G}(O^*)$ such that the normal subgroup of $\mathbf{G}(K^*)$ generated by $g$ is all of $\mathbf{G}(K^*)$, the normal subgroup of $\mathbf{G}(O^*)$ generated by $g$ contains a finite-index subgroup of a principal congruence subgroup. This is stated as a weaker analogue of the local-to-global conjecture, resembling Margulis' normal subgroup theorem; its resolution is not supplied.