The Ouroboros Particle Spectrum: Lepton Generations, the Proton Radius Puzzle, and the Emergence of Mass from Oscillation Frequency

Using the Ouroboros Lagrangian calibrated to the electron (g = 1.0625, λ = 1.0, Rₚʰʸˢ = 191 fm), we perform a systematic scan of the oscillation frequency ω to map the predicted particle mass spectrum. At fixed coupling constants, varying ω alone produces: the electron (ω = 1.0, exact by calibration), the muon (ω ≈ 11.0, gap 4.3%), the pion+ (ω ≈ 13.0, gap 5.8%), and the tau lepton (ω ≈ 40.7, gap 4.9%). The mass scaling law is H ∝ ω^2.22 — approximately the square of the oscillation frequency. This means the three lepton generations (e, μ, τ) arise as successive oscillation harmonics of the same Lagrangian with the same coupling constants: no new parameters are required. We also show that the proton radius puzzle — the discrepancy between electron scattering and muonic hydrogen measurements — is naturally explained in the Ouroboros framework as a probe-dependent measurement of a Yukawa (not Coulomb) J-field potential. These results suggest that the Ouroboros Lagrangian encodes the full lepton mass spectrum in its oscillatory mode structure, and that the proton is a composite three-chaoiton bound state (Schwinger’s ‘H particle’) whose apparent size depends on the probe. In summary, a Lagrangian with only three parameters explains a wide variety of observed quangtities.