The Proton-to-Electron Mass Ratio from Skyrmion Geometry on S³

We derive the proton-to-electron mass ratio from the geometry of the B = 1 Skyrmion on S³ with the Hopf fibration providing U(1) gauge structure. Both particles are excitations of the same SU(2)-valued field: the proton is the identity-map soliton with energy E = 6π² (conformal saturation), while the electron is the ground state of the charged Laplacian with eigenvalue λ₀ = 2 (spectral theorem). The conversion factor between the two energy scales is derived via Kaluza-Klein reduction of the Skyrmion’s extended moduli space M₇ = SU(2)² × ℂ, yielding μ_eff = Vol(SU(2)²)/Vol(U(1)) = 2π³. An independent Weyl spectral density calculation confirms the same factor through an exact cancellation between dim(su(2)) = 3 and the Weyl prefactor 1/3 — a cancellation that works only because both source and target spaces are S³ ≅ SU(2).The result is m_p/m_e = 6π⁵ = 1836.118, within 0.002% of the CODATA value 1836.15267343(11), with zero adjustable numerical parameters.Version 10 extends the original derivation with several new results:• Călugăreanu energy decomposition: the Skyrmion energy splits 1:2:3 into twist (π²), writhe (2π²), and self-energy (3π²) sectors, with explicit fiber-content integrands for the identity map.• Pion decay constant on S³: F_π = m_p/(π√6) = 121.9 MeV from BPS-saturated decomposition.• Physical pion decay constant: under assumption A4 (gauged Hopf fiber), decompactification via Goldstone generator counting (7 compact modes on S³, 4 surviving in flat space) gives f_π = 2π⁴ m_e √(6/7) = 92.17 MeV (PDG: 92.07 ± 0.26 MeV; deviation 0.11%, 0.4σ).• Flux tube at the Clifford torus: the twist sector scales as R¹ (1D), with string tension σ = πF_π²/(2√(13/2)) in natural units.• Complete mass chain from m_e alone: m_e → m_p (0.002%) → F_π → f_π (0.11%), two independent observables from one input with zero free parameters.• Charged Laplacian presented as single canonical operator chain with eigenvalue convergence table (N = 200–3200).• Four-step KK reduction derivation (factorisation → rotor ground state → effective measure → kinetic operator).This record contains three files: the journal-format paper targeting Physical Review D (with appendices on assumptions and the V(η) = tan²η derivation), a detailed calculations companion workbook, and a Python verification script (31 checks, 0 failures) that reproduces every numerical claim.Version history: v3 (11 Mar 2026) — initial four-step derivation with Appendix E spectator decoupling proof. v8–v9 (25 Mar 2026) — PRD rewrite with ChatGPT adversarial review fixes. v10 (25 Mar 2026) — comprehensive revision adding Călugăreanu decomposition, F_π, f_π, flux tube, convergence table, explicit integrands, sharpened falsifiers.