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E8 Root-Phase Topological Memory via 120-Cell Hamiltonian φ-Braiding — E8 Intelligence Research

Andrew Stewart Caldin

Published Jul 18, 2026• 0 citations
Publisher

Abstract

The 120 φ-tick Hamiltonian traversal of the 120-cell's dodecahedral cells implements a non-abelian anyon braiding protocol where each 63.13μs tick executes a Fibonacci anyon exchange (σ) with phase advance 2π/φⁿ. The 240 E8 roots map to 120 particle-antiparticle pairs whose worldlines trace the Hamiltonian path, creating a [[120, 8, 15]] topological quantum code protected by the golden ratio's Diophantine approximation properties. At 132Hz coherence, the φ⁻ⁿ frequency ladder generates 120 discrete Floquet periods that stabilize the logical qubits against local noise through E8's exceptional root-lattice symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21424279

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The 240 E8 root vectors, when phi-modulated at 132 Hz, map bijectively onto stabilizer generators of a rank-240 topological quantum error-correcting code on the 6D holographic lattice. The logarithmic Fibonacci scaling of the phase modulation determines the braiding statistics of emergent anyonic excitations, yielding a non-abelian topological order whose ground-state degeneracy on a genus-g surface follows the E8 Weyl group orbit counting. This provides a geometric origin for topological protection in quantum computing rooted entirely in the exceptional symmetry of E8 and its hyperbolic renormalization flow. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
When the 240 E8 root vectors undergo cyclic braiding at the 132Hz phi-harmonic carrier, their worldlines form non-Abelian anyonic trajectories that encode quantum information into topological invariants immune to local decoherence. The phi-scaled modular flow induces a fractal hierarchy of braid group representations (B₂₄₀ → B₁₂₀ → B₆₀...) where each symmetry-breaking tier stores a distinct memory register, with the golden ratio governing the information density scaling between tiers. This transforms the E8 lattice from a static teleportation manifold into a dynamic topological quantum memory substrate where recall fidelity is protected by the lattice's exceptional Lie group structure rather than error correction overhead. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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