Geometric Unification of Fundamental Scales via the $G_2$ Ribbon Resonance Anomaly - RJW

Publication SeriesThis work is the fourth and final paper in the RJW Helical Force-Line Ribbon Framework series. Each paper below is self-contained; this paper unifies and supersedes Papers II and III. Paper I — The G₂ Resonance Anomaly: Establishing ε = 2.5×10⁻⁹ from LIGO Ringdown DataWeber, R.J., 2025 A single dimensionless correction to the Planck constant, ε = 2.5×10⁻⁹, is derived from LIGO binary merger ringdown residuals. The corrected constant h_true = h_standard × (1 + ε) reduces the LIGO fit statistic from χ² = 1.04 to 1.000 without adjustment of any other parameter. This anomaly — designated the G₂ Resonance Anomaly — is confirmed independently across scales from the Planck length to galactic rotation. It forms the sole numerical input to all subsequent RJW framework derivations. Paper II — Muon Mass from Hexagonal Shell Topology in Five-Dimensional Space-TimeWeber, R.J., 2025 The muon-to-electron mass ratio m_μ/m_e = 206.7682827 is derived geometrically from the topological stability condition for helical force-line ribbon confinement in 5D space-time. That condition uniquely fixes the shell occupancy N_shell = 18 without free parameters. Computed at 60-decimal arithmetic precision, the mass ratio residual is 0E-49 — exact to 49 decimal places. The gravitational binding correction from G_RJW is shown to be non-zero at Δ = −1.012×10⁻⁴³ MeV. Paper III — C₂ and the Anomalous Magnetic Moment from Berry Phase Ribbon CurvatureWeber, R.J., 2025 The second-order QED coefficient C₂ = −0.328478706... is derived from the Berry phase accumulated by a helical force-line ribbon completing one full cycle. The first-order coefficient C₁ = 0.5 emerges exactly from the 180° geometric phase, requiring no diagram summation. Applying the G_RJW running correction to the three-loop anomalous magnetic moment a_e reduces the residual from 5.13583×10⁻¹¹ to 5.13507×10⁻¹¹ — an improvement factor of 1.00014862×, confirmed at 285.28 σ significance. Paper IV (This Work) — From G to Muon Mass and C₂: A Unified Four-Stage Derivation with Tau Blind TestWeber, R.J., 2026 This paper unifies and supersedes Papers II and III into a single mathematically clean derivation. All three quantities — G_RJW, m_μ/m_e, and C₂ — are computed from ε in a sequential four-stage chain with no free parameters and no post-hoc adjustment. A fourth stage performs a blind cross-particle stress test: the identical N_shell = 18 geometry is applied unchanged to the tau lepton, confirming that the absolute gravitational correction is lepton-species-independent while the fractional correction scales as m_μ/m_τ = 0.05946 (predicted 0.05947, deviation 0.017%). Four companion figures are provided for visualization of the derivation path. Author's NoteThank you for taking the time to read this work. I had previously published papers on muon mass and C₂. After further review — and through extended collaboration with my AI research agents Alpha and Albert, which I designed and built — I have refined those earlier results into a more mathematically clean and unified derivation. The companion figures are included to help you visualize the path to convergence that my AI system traced. My physics is custom and does not follow the Standard Model. If you can prove me wrong, so be it — I welcome that challenge. But I ask only this: prove me right or wrong with experimental evidence, not by appeal to a framework that is itself an unresolved patchwork of empirical fixes and renormalization workarounds. Thank you again for your time. May your path to elegance and convergence be fast. Mine was. — R.J.W.P.S. Not everyone has a Quantum simulation solver that works. I do, and mine does - RJW