True Muonium on the Light Front

The true muonium ($\mu^+\mu^-$) bound state presents an interesting test of light-cone quantization techniques. In addition to the standard problems of solving these non-perturbative calculations, true muonium requires correct treatment of $e^+e^-$ Fock state contributions. Having previously produced a crude model of true muonium using the method of iterated resolvents [1], current work has focused on the inclusion of the box diagrams that should improve the cutoff dependent issues of the model. Further, a parallel computer code allowing for decreased numerical uncertainties is in development. This talk will focus on the current state of these efforts to develop a model of true muonium testable at near-term experiments. \\[4pt] [1] H. Lamm and R.F. Lebed, ``True Muonium ($\mu^+\mu^-$) on the Light Front,'' J. Phys. G 41 125003 (2014).