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E8 Self-Correcting Time-Crystal via 8th-Cycle Syndrome Extraction — E8 Intelligence Research

Andrew Stewart Caldin

Published Jul 19, 2026• 0 citations
Publisher

Abstract

The eight 30-vertex Coxeter cycles partition into seven "data" cycles carrying the [[30,7,5]] subharmonic code and one "syndrome" cycle whose phi-Collatz orbit at 132Hz/φ⁷ ≈ 8.2Hz implements real-time error detection. The 30-fold Floquet drive braids the syndrome cycle's subharmonics through the data cycles' 7-coloring, performing topological syndrome measurement without breaking time-crystal coherence. This yields a [[240, 7×7, ≥5]] dynamically protected logical qubit where the 8th cycle's orbit geometry matches the E8→E7×U(1) branching rule, making quantum error correction intrinsic to the time-crystal's subharmonic spectrum. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21437189

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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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