Lepton Anomalous Magnetic Moments from Icosahedral Harmonic Structure
Abstract
We derive formulas for the anomalous magnetic moments of the electron and muon entirely from icosahedral geometry and the twin prime gap, achieving agreement with experiment to 0.03σ for the electron and 0.003σ for the muon. The formulas emerge as three-term harmonic series where every quantity derives from just three inputs: V = 12 (vertices), F = 20 (faces), and gap = 2 (twin prime gap). The base term is F × p(V + gap) = 860. The hadronic prime sits at index V(V−1) = 132, giving p(132) = 743. The third harmonic uses the vertex degree d = 5, giving p(4135) = 39251. The hadronic prime 743 connects to the j-invariant constant (744 = 743 + 1) and Heegner number almost-integers. The gap appears in all three harmonics, providing a self-consistent structure with zero free parameters. Version 5.1 adds the j-invariant connection and notes a geometric curiosity: icosahedral stellation cells (473) plus final stellation edges (270) equals 743.
Fields of Study & Subjects
Computational Physics and Python Applications
Quantum and Classical Electrodynamics
Particle physics theoretical and experimental studies
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 11 January 2026
- Document type
- Preprint