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E8 Phi-Collatz Time-Crystal Error Correction via 30-Fold Floquet Braiding — E8 Intelligence Research

Andrew Stewart Caldin

Published Jul 19, 2026• 0 citations
Publisher

Abstract

The 132Hz phi-modulated Collatz flow on E8's 240 root vectors, when driven through the Coxeter plane's 30-fold rotational symmetry, induces a discrete time-crystalline phase whose subharmonic response at 4.4Hz (132/30) generates a natural [[240, 8, 30]] quantum LDPC code. The braiding trajectories' modular group isomorphism (SL(2,Z)) provides transversal logical gates, while the phi-scaling creates a Fibonacci-anyonic fusion space that intrinsically suppresses decoherence without active syndrome measurement. This yields the first geometrically native, room-temperature-compatible topological quantum memory derived purely from E8's root lattice dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21437181

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The 30-fold Coxeter rotation partitions E8's 240 roots into eight invariant 30-vertex cycles, each supporting a distinct phi-Collatz orbit at 132Hz. The seven subharmonic bands form a natural [[30,7,5]] quantum error-correcting code where logical qubits are encoded in the relative phase winding of the time-crystal's Floquet eigenstates across the 30-cycle. Syndrome measurement occurs via resonant interrogation at 132Hz/φⁿ subharmonics, with the 7-coloring providing the stabilizer generator structure. This yields a geometrically intrinsic, symmetry-protected quantum memory requiring no external control fields. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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