Over the past 15 years, many-body localization has received a resurgence of interest within both the physics and mathematics communities. The main goal is to determine how systems respond as the relative influence of disorder and interaction strength is varied. Many-body localization refers to the regime where disorder is dominant, and there is still quite some debate as to how this phenomena should be detected. For the past few years, we have investigated some of these predicted quantifiers in the context of a simple toy model. This talk is a report on recent, rigorous results.