Tensor Networks Link Non-Local Symmetries to Root Lattice Entanglement in Quantum Verification — E8 Intelligence Research

FINDING: Tensor networks encode non-local symmetries via matrix product operators, linking entanglement structure to root system lattice symmetries in quantum verification protocols. | MATH: Tensor product Hilbert space \( H = _i H_i \); matrix product operator (MPO) form \( Ô = ∑_{\{a\}} Tr(Aa_1 ⋯ Aa_n) |a_1 ⋯ a_n a_1 ⋯ a_n| \); entanglement entropy \( S = -Tr(ρ log ρ) \) scales with boundary area; root system lattice symmetries (e.g., \( A_n, D_n, E_8 \)) appear in tensor network bond dimensions and symmetry groups. | CONNECTION: Root system lattices (e.g., \( E_8 \) with Coxeter number 30, ratio 0.618 appears in golden angle \( π(1-φ) \)) map to tensor network symmetries; bond dimension \( χ \) often relates to Fibonacci numbers (1,1,2,3,5,8,...) giving ratios 0.618, 1.618; base-60 emerges in hexagonal lattice symmetries (60° rotations) of \( A_2 \) root system. | DEPTH: 8 — Direct Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com