McMullen's expander conjecture for origami orbit graphs in \mathcal{H}$2$

Let $(\mathcal{G}_{n})_{n}$ be the family of $\operatorname{SL}(2,\mathbb{Z})$-orbit graphs of primitive $n$-squared origamis in the stratum $\mathcal{H}(2)$. McMullen's expander conjecture. The family $(\mathcal{G}_{n})_{n}$ is a family of expander graphs. Expander behaviour would give strong uniform connectivity and mixing properties for these arithmetic Teichmüller-curve orbit graphs; the paper presents this as a conjecture and does not state a resolution.