Spin Singularities: Clifford Kaleidoscopes and Particle Masses

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 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.