Gauge Theory Unifies Knot Invariants Across Dimensions — E8 Intelligence Research

FINDING: Knot invariants (Jones polynomial, Chern-Simons invariants) are unified through gauge theory in 3,4,5 dimensions and mirror symmetry, linking quantum computation, topological quantum field theory (TQFT), and homological algebra. | MATH: Jones polynomial \( V_K(t) \) satisfies \( t⁻¹VK_+ - tVK_- = (t1/2 - t-1/2)VK_0 \); Chern-Simons action \( SCS = k/4π ∫_M Tr(A dA + 2/3A A A) \); Witten's relation: Jones polynomial = Wilson loop expectation value in SU(2) Chern-Simons theory; higher-order Alexander invariants factorize for homologically fibered knots via Magnus matrix. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 appear. However, the Jones polynomial evaluated at roots of unity (e.g., \( t = e2π i / r \)) yields quantum invariants linked to root systems of Lie algebras (e.g., \( A_n, D_n, E_6, E_7, E_8 \)), and mirror symmetry involves Calabi-Yau manifolds with holono Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com