The Electron: Foundations from Icosahedral Geometry

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Authors: Clifford Keeble
Cited by: 6
References: 2

Abstract

We derive the electron's fundamental properties from icosahedral geometry. The electron exists at twin primes (41, 43) centered on 42 = V + E, where V = 12 vertices and E = 30 edges. This location is uniquely determined by three independent constraints: electromagnetic structure (gap-2 geometry requires twin primes), icosahedral geometry (center must equal V + E = 42), and number-theoretic uniqueness (43 is one of only nine Heegner numbers). The Rydberg energy satisfies E_R × 42² = 24 keV to 18 ppm, connecting atomic physics to the electron's geometric identity. The anomalous magnetic moment follows a three-term formula achieving 0.03σ agreement with experiment. The hadronic prime 743 = p(132) appears in the j-invariant constant as 744 = 743 + 1. Euler's prime-generating polynomial n² + n + 41 produces 41 and 43 as its first two values, connecting to the largest Heegner number via 163 = 4 × 41 − 1. We also derive electron mass from Rydberg structure (510.7 keV, 99.95% agreement) and interpret Cooper pairs geometrically. Every numerical input traces to icosahedral structure with zero free parameters.

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
11 January 2026
Document type
Preprint