Knot Invariants Unify Gauge Theories Across Dimensions via Topological Structures — E8 Intelligence Research

FINDING: Knot invariants unify gauge theories across 3D/4D/5D via Chern-Simons theory, mirror symmetry, and M-theory, with homological refinements (Alexander invariants) revealing factorization structures. | MATH: Chern-Simons action \( SCS = k/4π∫_M Tr(A dA + 2/3A A A) \); Jones polynomial \( V_K(q) \) as Wilson loop expectation \( Tr_R P e∮ A \); Alexander invariants \( Δ_K(t) \) with higher-order generalizations \( Δ_n(K) \) factorizing as \( Δ_n = ΔMagnus · Δₑₓₜᵣₐ \) for homologically fibered knots; quantum group \( U_q(sl_2) \) at roots of unity \( q = e2π i/(k+2) \). | CONNECTION: The Jones polynomial at \( q = e2π i/5 \) (k=3) involves golden ratio \( φ = 1.618 \) via \( q + q⁻¹ = φ \); Chern-Simons level \( k \) relates to \( 2π i/(k+2) \) — at k=3, \( q = e2π i/5 \) connects to pentagonal symmetry (crystallographic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com