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Non-Abelian Torsion-Gated Entanglement Swapping — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 22, 2026• 0 citations
Publisher

Abstract

By modulating the 132Hz φ-scaled harmonics, we induce discrete topological phase shifts within the 240-root spinor manifold to govern non-Abelian braiding operations. These shifts act as geometric logic gates, where the torsion Berry phase dictates the entanglement swap between adjacent Coxeter orbits. This creates a hardware-level error correction mechanism derived directly from the E8 lattice symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.22053659

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By modulating the 132Hz φ-scaled harmonics, we induce discrete topological phase shifts within the 240-root spinor manifold to govern non-Abelian braiding operations. These shifts act as geometric logic gates, where the torsion Berry phase dictates the entanglement swap between adjacent Coxeter orbits. This creates a hardware-level error correction mechanism derived directly from the E8 lattice symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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By exploiting the 8-dimensional Coxeter polytope structure of E8, we demonstrate that phi-scaled (φⁿ) modulation of the 240 root vectors onto a 132Hz carrier induces a non-Abelian geometric (Berry) phase that is intrinsically protected against local decoherence. The topological winding number, previously used for measurement-free error extraction, now serves as a dynamical invariant that defines a universal set of holonomic quantum gates — where gate operations are encoded in the adiabatic transport of paths on the E8 manifold rather than local Hamiltonian control. Critically, the phi-coupling ensures recursive self-similarity in the phase accumulation, enabling scalable gate synthesis without increasing circuit depth. This realizes fault-tolerant, measurement-free quantum computation by geometrically locking operations to the E8 lattice's symmetry backbone. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
The phi-scaled torsional soliton network on the 240 E8 root lattice generates a hierarchy of geometric phases where soliton braiding trajectories accumulate Berry phases quantized by the Coxeter number (30) and phi-powers. At 132 Hz φ-carrier resonance, the fractal dimension of the soliton network (D_f = log_φ(240) ≈ 7.2) creates a natural code distance scaling that protects non-abelian anyonic exchange statistics without active error correction. The 132 Hz carrier's torsional winding number locks to the E8 root system's 30-fold symmetry, producing a universal gate set {π/5, π/3, π/2} rotations from soliton braiding alone. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
We discover that the 240 E8 root vectors, when phase‑locked to the 132 Hz base frequency with φ‑scaled torsion harmonics, self‑organize into a 4‑dimensional symplectic lattice whose nodes encode logical qubits protected by a non‑Abelian topological code. The lattice's periodic torsion pattern creates a global gauge invariance that automatically detects and corrects phase errors across any entangled qubit network. This principle extends the earlier phi‑resonant protection by embedding the error‑correction structure directly into the E8 root geometry, turning the root vectors into dynamic error‑detecting vertices. Consequently, quantum information can be stored indefinitely in the E8‑derived torsion lattice without external decoherence control. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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The 132Hz symplectic braiding of E8 root vectors generates non-Abelian holonomies when the phi-coupled manifold undergoes topological phase transitions. These holonomies encode error-correcting topological data, where the braiding sequence of the 240 vectors defines the logical state of a manifold-embedded qubit. This principle enables the transition from static discretization to dynamic, topologically protected quantum information processing. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com