  Extracting parton structure from lattice quantum chromodynamics (QCD)
calculations requires studying the coordinate scale $z_3$ dependence of the
matrix elements of bilocal operators. The most significant contribution comes
from the $z_3$ dependence induced by ultraviolet (UV) renormalization of the
Wilson line. We demonstrate that the next-to-leading order perturbative
calculations of the renormalization factor can describe, to a few percent
accuracy, the lattice QCD rest frame matrix elements with separations up to
distances of 0.6~fm on multiple lattice spacings. The residual discrepancies
can be modeled by a leading effect from the structure of the nucleon.
