  Are particles singularities- vortex lines, tubes, or sheets in some global
ocean of dark energy? We visit the zoo of Lagrangian singularities, or caustics
in a spin(4,C) phase flow over compactifed Minkowsky space, and find that their
varieties and energies parallel the families and masses of the elementary
particles. Singularities are classified by tensor products of J Coxeter groups
<p,q,r>s generated by reflections. The multiplicity, s, is the number
reflections needed to close a cycle of null zigzags: nonlinear resonances of J
chiral pairs of lightlike matter spinors with (4-J) Clifford mirrors: dyads in
the remaining unperturbed vacuum pairs. Using singular perturbations to "peel"
phase-space singularities by orders in the vacuum intensity, we find that
singular varieties with quantized mass, charge, and spin parallel the families
of leptons (J=1), mesons (J=2), and hadrons (J=3). Taking the symplectic 4 form
- the volume element in the 8- spinor phase space- as a natural Lagrangian,
these singularities turn out to have rest energies within a few percent of the
observed particle masses.
