Golden-Ratio Lattice in Stereographic Projection of Decision Qubits — E8 Intelligence Research

FINDING: Bloch sphere equatorial projection reveals a stereographic lattice structure where decision-theoretic qubit states map to a golden-ratio-modulated plane. | MATH: Qubit state \(|\psi\rangle = \cos(\theta/2)|0\rangle + e^{i\phi}\sin(\theta/2)|1\rangle\); stereographic projection from south pole to equatorial plane: \(z = \tan(\theta/2)e^{i\phi}\). Equatorial circle (\(\theta=\pi/2\)) projects to unit circle \(|z|=1\). Golden ratio appears in the *lattice* of projected decision points: successive \(\phi\)-increments of \(2\pi/\tau\) (where \(\tau = (1+\sqrt{5})/2 \approx 1.618\)) generate a quasi-crystalline 5-fold symmetric pattern on the plane — the same symmetry forbidden in periodic crystals but allowed in Penrose tilings. | CONNECTION: The ratio \(\tan(\theta/2)\) for \(\theta = 2\arctan(0.618) \approx 63.43^\circ\) yields radial coordinate \(0.618\) (inverse golden ratio) — a natural "decision boundary" on the Bloch sphere. The stereographic map itself is conformal, preserv Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com