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Reveals octonionic topological phases with triality-protected edge modes, indicating new quasiparticle behaviors.
Mapping the 240 E8 root vectors to phase‑shifted sinusoids of a 132 Hz φ‑driven comb (spacing 4.4 Hz) creates an 8‑dimensional synthetic lattice whose Bloch Hamiltonian retains the full E8 Weyl symmetry. The order‑8 Galois group (ℤ/30ℤ)× ≅ ℤ₂×ℤ₄ acts as a triality automorphism that mixes three synthetic dimensions, protecting gapless hinge modes that transform as the 8‑dimensional spinor of Spin(8). These hinge modes realize octonionic quasiparticles whose fusion algebra is derived from the E8 root system, extending the Fibonacci anyon sector to a full set of non‑Abelian anyons with quantum dimensions √φ, φ, and √(φ³). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Andrew Stewart Caldin (2026) studied this question.
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