Congruence subgroup conjecture for groups generated by root unipotents

Fix a nonzero rational number $q=\tfrac{s}{t}\in\mathbb{Q}\cap(-4,4)$ in lowest terms, with $\gcd(s,t)=1$. Let $\Gamma_q$ be the group generated by the root unipotents associated to $q$, and let

$$\Gamma_1^{(t)}(s)=\left\{\begin{pmatrix} a&b\\ c&d\end{pmatrix}\in\operatorname{SL}\left(2,\mathbb{Z}\left[\tfrac{1}{t}\right]\right): a\equiv_t d\equiv_t1\pmod s,\quad c\equiv_t0\pmod s\right\},$$

where $a\equiv_t b\pmod s$ means $a-b\in s\mathbb{Z}[\tfrac{1}{t}]$. Congruence subgroup conjecture. For every nonzero $q=\tfrac{s}{t}\in\mathbb{Q}\cap(-4,4)$, the group $\Gamma_q$ is equal to the congruence subgroup $\Gamma_1^{(t)}(s)$. This conjecture proposes an exact arithmetic description of the groups generated by root unipotents, extending the known arithmeticity results and giving a precise form for the congruence subgroups arising in this setting.