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

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