McMullen's expansion conjecture for arithmetic Veech groups

For a translation surface in the stratum $\mathcal{H}(2)$, the associated Veech group is arithmetic when its orbit gives rise to the graphs under consideration. McMullen's expansion conjecture. The family of graphs associated to arithmetic Veech groups in $\mathcal{H}(2)$ is an expander family. Equivalently, the spectral gaps of the arithmetic Veech groups possess a uniform lower bound. This conjecture connects effective density near Teichmüller curves with uniform spectral expansion; the source does not state whether it has been resolved.