The Electron: Foundations from Icosahedral Geometry
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