Hopf Fibration Unifies Quantum Spin, Rigid-Body Holonomy, and Polytope Geometry — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Hopf fibration emerges as the geometric backbone linking quantum angular momentum, rigid-body holonomy, and polytope combinatorics — with a new result decomposing rotation angles via fiber-bundle holonomy. | MATH: Hopf fibration \(S^3 \to S^2\) with fiber \(S^1\); total space \(S^3 = \{|z_1|^2+|z_2|^2=1\}\); projection \((z_1,z_2)\mapsto (2z_1\bar{z}_2,\,|z_1|^2-|z_2|^2)\); holonomy angle \(\theta = \oint A\) where \(A\) is the Berry connection \(A = \mathrm{Im}(\bar{z}_1 dz_1 + \bar{z}_2 dz_2)\); rotation-angle decomposition: \(\theta_{\text{total}} = \theta_{\text{dynamic}} + \theta_{\text{geometric}}\) (arXiv:2512.04481). Newton polytope of Morse discriminant: vertices correspond to monomials of the discriminant — combinatorial data encoding critical-point degeneracies. | CONNECTION: The Hopf fibration's base \(S^2\) carries the natural \(SO(3)\) action whose holonomy yields rotation angles — the ratio of fiber twist to base area is exactly \(1/2\) (the Hopf invariant \(H=1 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7219697109
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