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

Percy Quispe Hancco, Artemio N. Condori Mamani, Ceferino Quispe Hancco, Aldo H. Zanabria Galvez, Hugo Quispe Hancco

TL;DR

The paper introduces a phenomenological geometric framework in which the lepton anomalous magnetic moments are determined by a single dimensionless constant $V_0$, arising from 18 primitive triangle families. By integrating De Moivre’s theorem, Chebyshev polynomials, and finiteness of integral points (via Siegel-type reasoning), the authors identify a saturated set of primitive solutions linked to $V_0$. The resulting base $g$-factor and lepton anomalies for the electron, muon, and tau match known values with ppb–ppm precision and yield four concrete, testable predictions for future experiments. A Koide-mass-inspired connection through $ extDelta = rac{2}{3}-V_0$ and hints of cyclotomic-root origins underpin the framework, though it remains phenomenological rather than a QFT derivation.

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.

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

TL;DR

The paper introduces a phenomenological geometric framework in which the lepton anomalous magnetic moments are determined by a single dimensionless constant , arising from 18 primitive triangle families. By integrating De Moivre’s theorem, Chebyshev polynomials, and finiteness of integral points (via Siegel-type reasoning), the authors identify a saturated set of primitive solutions linked to . The resulting base -factor and lepton anomalies for the electron, muon, and tau match known values with ppb–ppm precision and yield four concrete, testable predictions for future experiments. A Koide-mass-inspired connection through and hints of cyclotomic-root origins underpin the framework, though it remains phenomenological rather than a QFT derivation.

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.

Paper Structure

This paper contains 45 sections, 3 theorems, 37 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Mathematical Foundation
  3. The Convergence Problem
  4. Theorem 1: De Moivre (1707)
  5. Theorem 2: Chebyshev Polynomials (1854)
  6. Finiteness of Primitive Solutions
  7. Supporting Theorems
  8. The Role of $\sqrt{5}$
  9. Convergence of Three Frameworks
  10. The 18 Primitive Triangle Families
  11. Selection Criteria
  12. Complete Classification
  13. Multiplier Structure and the Factor 22
  14. Geometric Visualization: The Two Fundamental Roots
  15. Emergence of $V_0$
  16. ...and 30 more sections

Key Result

Theorem 1

For any angle $\theta$ and integer $n$:

Figures (1)

  • Figure 1: Angular geometry showing the division of $360^\circ$ by the muon angular factor $F_{\text{ang}} \approx 16.23$, yielding approximately 16 sectors of $22.2^\circ$ each. This geometric construction motivates the factor 22 appearing in the phenomenological corrections.

Theorems & Definitions (4)

  • Theorem 1: De Moivre
  • Theorem 2: Chebyshev
  • Definition 1
  • Theorem 3: Siegel, 1929