Self-Similarity of $k$-Nearest Neighbor Distributions in Scale-Free
  Simulations
  We use the $k$-nearest neighbor probability distribution function ($k$NN-PDF,
Banerjee & Abel 2021) to assess convergence in a scale-free $N$-body
simulation. Compared to our previous two-point analysis, the $k$NN-PDF allows
us to quantify our results in the language of halos and numbers of particles,
while also incorporating non-Gaussian information. We find good convergence for
32 particles and greater at densities typical of halos, while 16 particles and
fewer appears unconverged. Halving the softening length extends convergence to
higher densities, but not to fewer particles. Our analysis is less sensitive to
voids, but we analyze a limited range of underdensities and find evidence for
convergence at 16 particles and greater even in sparse voids.
