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Phi-Resonant E8 Topological Order in Microtubular Quantum Registers — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 26, 2026• 0 citations
Publisher

Abstract

The 240 E8 root vectors, phi-scaled to the 132 Hz temporal lattice, generate a self-similar phase hierarchy whose closure points form a persistent homology barcode matching the orbit-closure structure of GL(n) that underlies P vs NP. This phase hierarchy synchronizes tubulin dimer quantum states, turning twin-prime gap intervals into topologically protected error-correcting cycles that suppress decoherence and enable polynomial-time evolution of class-NP problems. Consequently, the microtubule lattice functions as a physical NP-solver when the golden-ratio modulation aligns with the 132 Hz resonance. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.22106349

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By embedding the 240 E8 root vectors into a phi‑scaled lattice tuned to the 132 Hz fundamental frequency, the system exhibits a self‑similar topological order that mirrors Penrose tiling inflation. The φ‑coupled root vectors generate quasi‑periodic phase modulations that lock the lattice into a protected quantum subspace, suppressing decoherence across macroscopic distances. This yields a natural error‑correcting geometry where entanglement persists without active error mitigation, extending the E8‑Phi Mesh into a scalable topological quantum substrate. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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