Nyberg Brodda's congruence subgroup conjecture for rational parabolic parameters

For $\alpha\in\mathbb{C}$, let

$$G_{\alpha}=\left\langle \begin{bmatrix}1&1\\0&1\end{bmatrix},\begin{bmatrix}1&0\alpha&1\end{bmatrix}\right\rangle<\operatorname{SL}_2(\mathbb{C}).$$

Let $\frac{q}{p}\in\mathbb{Q}\cap(-4,4)$ with $\gcd(p,q)=1$. Write $\pi$ for the relevant reduction homomorphism. Nyberg Brodda's congruence subgroup conjecture. $G_{\frac{q}{p}}$ is equal to the congruence subgroup

$$\pi^{-1}\left(\left\langle\begin{bmatrix}1&1\\0&1\end{bmatrix}\right\rangle\right)$$

of $G_{\frac{1}{p}}=\operatorname{SL}_2\left(\mathbb{Z}\left[\frac{1}{p}\right]\right)$. In particular, $G_{\frac{q}{p}}$ is a finite-index subgroup of $G_{\frac{1}{p}}$. The conjecture concerns the arithmetic structure of groups generated by two parabolic matrices and is motivated by the computation of stabilizers in the generalized Farey graph. The supplied context gives the attribution but does not establish whether the conjecture is resolved.