  We present the methodology for deriving accurate and reliable cosmological
constraints from non-linear scales (<50Mpc/h) with k-th nearest neighbor (kNN)
statistics. We detail our methods for choosing robust minimum scale cuts and
validating galaxy-halo connection models. Using cross-validation, we identify
the galaxy-halo model that ensures both good fits and unbiased predictions
across diverse summary statistics. We demonstrate that we can model kNNs
effectively down to transverse scales of rp ~ 3Mpc/h and achieve precise and
unbiased constraints on the matter density and clustering amplitude, leading to
a 2% constraint on sigma_8. Our simulation-based model pipeline is resilient to
varied model systematics, spanning simulation codes, halo finding, and
cosmology priors. We demonstrate the effectiveness of this approach through an
application to the Beyond-2p mock challenge. We propose further explorations to
test more complex galaxy-halo connection models and tackle potential
observational systematics.
