Level-Rank Duality Links Chern-Simons Knot Invariants to Cohomotopy Quantum Computing — E8 Intelligence Research

FINDING: Wilson loop knot invariants in Chern-Simons theory are governed by level-rank duality and flux quantization, linking topological quantum computing to cohomotopy theory. | MATH: Chern-Simons level \( k ∈ Z \) (integer quantization); level-rank duality \( SU(N)_K ↔ SU(K)_N \); Wilson loop expectation value \( W_R(K) = S0R⁻¹ ∑R' SRR' e^{2π i k hR'} \); Seifert loop framing correction \( exp(2π i c / 24) \); flux quantization in cohomotopy \( π^n(·) \). | CONNECTION: Seifert loops and knot invariants relate to modular \( S \)-matrix symmetries (root system \( A_n \), \( D_n \), \( E_6, E_7, E_8 \)); level \( k \) and rank \( N \) exchange mirrors golden ratio-like duality \( N ↔ K \) (analogous to 1/φ scaling in dual Coxeter numbers); base-60 not explicit but modular forms (e.g., Dedekind eta) underpin quantization. | DEPTH: 9 — Directly ties topological invariants (knot polynomials, Jones polynomi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com