The Electron from Icosahedral Geometry

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Authors: Clifford Keeble
Cited by: 7
References: 2

Abstract

We show that the electron's fundamental properties emerge from the geometry of the icosahedron. The electron and proton share 132 = V(V−1) irreducible tension channels, balanced through the hyperfactorial bridge H(3) = 108: the proton arrives via 12 divisor channels × 11, the electron via 36 coprime channels × 11/3 — a D × (1/D) = 1 balance that spacetime preserves regardless of mass. The electron mass is the quark mass difference projected through the five-fold vertex geometry: mₑ = mᵤ × ((19/11)^(7/5) − 1)/5 = 0.506 MeV (1.0% from the measured 0.511 MeV). The anomalous magnetic moment base term is 1/(F × 43) = 1/860, where F = 20 is the icosahedral face count and 43 is the upper twin prime bracketing V + E = 42. We derive two corrections from the projection of irreducible 3D tension onto a single measurement axis: cross-axis vertex leakage adds +(V+2)/(2D) = +7/3, and the self-pair fraction in the reducible pair space subtracts −1/V² = −1/144. The resulting formula aₑ = 1/(F × 43 + (V+2)/(2D) − 1/V²) matches experiment to 1.3 parts per million, with every term derived from icosahedral constants. The electron's field extends across 741 × 113 = 83,733 lattice units, matching μα⁻¹/3 to 0.17% and connecting the anomalous moment to the spacetime lattice. A companion paper extends this to a four-term harmonic series achieving 0.094σ agreement with Fan et al. (2023).

Fields of Study & Subjects

Advanced Mathematical Theories and Applications Advanced Mathematical Theories Analytic Number Theory Research

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
8 February 2026
Document type
Preprint