  Nondominated sorting is a combinatorial algorithm that sorts points in
Euclidean space into layers according to a partial order. It was recently shown
that nondominated sorting of random points has a Hamilton-Jacobi equation
continuum limit. The original proof relies on a continuum variational problem.
In this paper, we give a new proof using a direct verification argument that
completely avoids the variational interpretation. We believe this proof is new
in the homogenization literature, and may be generalized to apply to other
stochastic homogenization problems for which there is no obvious underlying
variational principle.
