Understanding the trans-Neptunian Solar system; Reconciling the results of serendipitous stellar occultations and the inferences from the cratering record.

The most pristine remnants of the Solar system's planet formation epoch orbit the Sun beyond Neptune, the small bodies of the trans-Neptunian object populations.  The bulk of the mass is in ~100 km objects, but objects at smaller sizes have undergone minimal collisional processing, with "New Horizons" recently revealing that ~20 km (486958) Arrokoth appears to be a primordial body, not a collisional fragment.  This indicates bodies at these sizes (and perhaps smaller) retain a record of how they were formed.  However, such bodies are impractical to find by optical surveys due to their very low brightnesses.  Their presence can be inferred from the observed cratering record of Pluto and Charon, and directly measured by serendipitous stellar occultations.  These two methods produce conflicting results, with occultations measuring roughly ten times the number of ~km bodies inferred from the cratering record.  We apply MCMC sampling to explore numerical evolutionary models of the outer Solar system to understand what formation conditions can reconcile the occultations and cratering observations.  We find that models where the initial size of bodies decreases with their semimajor axis of formation, and models where the surface density of bodies increases beyond the 2:1 mean-motion resonance with Neptune can produce both sets of observations.  We discuss the astrophysical plausibility of these solutions, and possible future observations tests of them.