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 \( t^{-1}V_{K_+} - tV_{K_-} = (t^{1/2} - t^{-1/2})V_{K_0} \); Chern-Simons action \( S_{CS} = \frac{k}{4\pi} \int_M \text{Tr}(A \wedge dA + \frac{2}{3}A \wedge A \wedge A) \); 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., \( t = e^{2\pi i / r} \)) 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