  A theory for kinetic arrest in isotropic systems of repulsive,
radially-interacting particles is presented that predicts exponents for the
scaling of various macroscopic quantities near the rigidity transition that are
in agreement with simulations, including the non-trivial shear exponent. Both
statics and dynamics are treated in a simplified, one-particle level
description, and coupled via the assumption that kinetic arrest occurs on the
boundary between mechanically stable and unstable regions of the static
parameter diagram. This suggests the arrested states observed in simulations
are at (or near) an elastic buckling transition. Some additional numerical
evidence to confirm the scaling of microscopic quantities is also provided.
