Stereographic Qubit Lattice Reveals Golden-Ratio Harmonic Structure on the Bloch Sphere — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Bloch sphere equatorial projection reveals qubit decision space as a stereographic lattice with golden-ratio harmonic structure | MATH: Qubit state \(|\psi\rangle = \cos(\theta/2)|0\rangle + e^{i\phi}\sin(\theta/2)|1\rangle\); stereographic projection from south pole maps to complex plane \(z = \tan(\theta/2)e^{i\phi}\); equatorial circle \(\theta=\pi/2\) gives \(z = e^{i\phi}\) (unit circle); lattice points on equator at \(\phi = 2\pi k/n\) for \(n\)-fold symmetry; golden angle \(\phi_g = 2\pi(1-1/\varphi) \approx 2.39996\) rad \(\approx 137.5^\circ\) | CONNECTION: Equatorial projection yields unit circle — the natural domain for roots of unity \(e^{2\pi i k/n}\), linking to crystallographic point groups (C\(_n\), D\(_n\)); golden angle partitions circle in irrational ratio \(1/\varphi \approx 0.618\), maximizing lattice aperiodicity — same ratio appears in quasicrystal diffraction patterns (Penrose tilings, 5-fold symmetry forbidden in periodic crystals but allowed in quasic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212268279
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