Geometric Origin of Lepton Anomalous Magnetic Moments: A Dimensionless Framework from Primitive Triangle Families

TL;DR

This paper introduces a geometric framework that derives lepton magnetic anomalies from a single constant linked to primitive triangle families, achieving high-precision predictions without relying on quantum field theory.

Contribution

It presents a novel geometric approach connecting classical mathematics to lepton anomalies, identifying a unique constant from primitive triangle families supported by Diophantine constraints.

Findings

Accurately predicts electron, muon, and tau anomalies within experimental precision.

Identifies a unique geometric constant V0 from primitive triangle families.

Establishes links between the constant V0, the Koide formula, and cyclotomic fields.

Abstract

We present a phenomenological geometric framework deriving the anomalous magnetic moments of leptons from a single dimensionless constant V0 = 0.658944. This value emerges as a geometric attractor identified from exactly 18 primitive triangle families, whose completeness is supported by Diophantine constraints and extensive computational searches. The methodology connects three classical mathematical frameworks: De Moivre s theorem (1707), Chebyshev polynomials (1854), and results on the finiteness of integral points. Extended searches expanding the parameter space by a factor of 15 yield no new families, confirming saturation. The constant V0 connects to the Koide formula through Delta = 2/3 - V0 and approximates cos(13*pi/48) to 0.06 percent, suggesting links to cyclotomic fields. Using only dimensionless quantities, we obtain the electron anomaly ae with precision 0.15 ppb, the muon anomaly a_mu with 17 ppb, and the tau anomaly a_tau with 3.4 ppm. The framework is phenomenological and does not claim a derivation from quantum field theory, but its mathematical constraints yield testable predictions for future precision measurements.