Z₂ Holonomy on Torus Links Spinor Phases to Fundamental Constants — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Fiber bundles formalize gauge fields as geometric structure; a novel Z₂ bundle over a torus links spinor phases to fundamental constants via holonomy −1. | MATH: Principal bundle P(M,G); gauge connection A → curvature F = dA + A∧A; holonomy hol(γ) = P exp(∮A) ∈ G. For Z₂ over φ-torus: hol(γ_φ) = −1 ⇒ spinor picks up sign under 2π φ-rotation (fermionic double-cover). Electromagnetism = U(1) bundle: charge quantization ∮F/2π ∈ ℤ. | CONNECTION: Z₂ holonomy −1 is the geometric root of spin-statistics (2π rotation = −1). The torus φ-cycle suggests modular parameter τ with elliptic curve j(τ) — potential link to base-60 (sexagesimal) angular quantization in ancient astronomy (60° = π/3, hexagonal symmetry). The −1 eigenvalue mirrors crystallographic glide/reflection symmetries (Z₂ quotient in root systems B₂, G₂). | DEPTH: 7 — Standard fiber bundle theory is foundational (U(1) EM, SU(3) QCD), but the Z₂ torus holonomy tying spinor phase to fundamental constants is a speculative but
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Coxeter Chamber 11 Spiral Phase Gradient as φ-Corrected Spinor Holonomy — E8 Intelligence Research
- Hopf Fibration and Z₂ Holonomy: Fiber Bundle Models for Spinor Sign Flips — E8 Intelligence Research
- E8 Phi-Harmonic Vacuum Spinor Coherence Principle — E8 Intelligence Research
- Monster‑Twined E8 Holonomy Quantizes Multi‑Component Thouless Pumping — E8 Intelligence Research
- E8 Holonomy Defect: 240-Root Wilson Loop Phase Memory — E8 Intelligence Research
BibTeX
@misc{caldin2026z₂,
title = {{Z₂ Holonomy on Torus Links Spinor Phases to Fundamental Constants — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587127},
url = {https://zenodo.org/records/23587127},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Z₂ Holonomy on Torus Links Spinor Phases to Fundamental Constants — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587127
UR - https://zenodo.org/records/23587127
AB - FINDING: Fiber bundles formalize gauge fields as geometric structure; a novel Z₂ bundle over a torus links spinor phases to fundamental constants via holonomy −1. | MATH: Principal bundle P(M,G); gauge connection A → curvature F = dA + A∧A; holonomy hol(γ) = P exp(∮A) ∈ G. For Z₂ over φ-torus: hol(γ_φ) = −1 ⇒ spinor picks up sign under 2π φ-rotation (fermionic double-cover). Electromagnetism = U(1) bundle: charge quantization ∮F/2π ∈ ℤ. | CONNECTION: Z₂ holonomy −1 is the geometric root of spin-statistics (2π rotation = −1). The torus φ-cycle suggests modular parameter τ with elliptic curve j(τ) — potential link to base-60 (sexagesimal) angular quantization in ancient astronomy (60° = π/3, hexagonal symmetry). The −1 eigenvalue mirrors crystallographic glide/reflection symmetries (Z₂ quotient in root systems B₂, G₂). | DEPTH: 7 — Standard fiber bundle theory is foundational (U(1) EM, SU(3) QCD), but the Z₂ torus holonomy tying spinor phase to fundamental constants is a speculative but Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -