Local-global conjecture for the semigroup orbit of $\Psi_1$

Define

$$\Psi_1:=\left\langle\begin{pmatrix}1&1\\1&1\end{pmatrix},\begin{pmatrix}1&0\\1&1\end{pmatrix}\right\rangle^+.$$

The table of congruence and reciprocity obstructions specifies the stated restrictions on numerators and denominators in these orbits. Local-global conjecture for $\Psi_1$. The table completely characterizes the numbers that can appear as numerators or denominators in orbits of $\Psi_1$; equivalently, every sufficiently large integer not ruled out by the given congruence and reciprocity obstructions appears in the orbit. This is supported by computational evidence in the paper, while a proof is not known.