Formal Statement of the Chaoiton Existence Theorem in Lean 4

We study a classical field theory over flat (3+1)-dimensional Minkowski space defined by two coupled covariant vector fields, Aμ and Jμ, each subject to the Lorenz constraint, with a nonlinear coupling f(JμJμ†). We call this the Ouroboros system, motivated by its mutual-confinement structure. Prior numerical searches for static solitons found no stable solutions across a wide parameter range, consistent with Derrick-type scaling arguments. We show that oscillatory (time-periodic) solutions — chaoitons — do exist and are stable in the variational sense. Numerical scans over 1280 parameter combinations identify 62 stable chaoiton families, with positive energy, finite conserved charge, and nonzero angular momentum. The angular-momentum-to-charge ratio L/Q lies in the range 0.79–2.6, in the same order of magnitude as the electron's g-factor. No fine-tuning is required; stability persists over broad parameter ranges. These results constitute the first evidence of stable, oscillatory, nontopological localized solutions in a relativistic two-vector-field theory, and suggest a new avenue for modeling elementary particles as oscillating field configurations — a possibility of direct relevance to the Zitterbewegung program and to the theory of nuclear detection signatures.

Keywords: chaoiton, soliton, Ouroboros Lagrangian, vector field theory, Derrick's theorem, superrenormalizable, Zitterbewegung, nuclear detection