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 \( k \in \mathbb{Z} \) (integer quantization); level-rank duality \( SU(N)_K \leftrightarrow SU(K)_N \); Wilson loop expectation value \( \langle W_R(K) \rangle = S_{0R}^{-1} \sum_{R'} S_{RR'} e^{2\pi i k h_{R'}} \); Seifert loop framing correction \( \exp(2\pi i c / 24) \); flux quantization in cohomotopy \( \pi^n(\cdot) \). | 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 \( N \leftrightarrow K \) (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