Helicity Integrals Recast Knot Invariants via Chern-Simons Mirror Symmetry — E8 Intelligence Research

FINDING: Knot polynomial invariants (Alexander, Jones, HOMFLY-PT) are being recast via helicity integrals and mirror-symmetry QFTs, linking fluid topology to Chern-Simons theory and homological algebra. | MATH: Helicity \( H = \int \mathbf{v} \cdot (\nabla \times \mathbf{v}) \, d^3x \) (fluid) ↔ Chern-Simons action \( S_{CS} = \frac{k}{4\pi} \int \mathrm{Tr}(A \wedge dA + \frac{2}{3} A^3) \); Jones polynomial \( V_L(q) \) from Wilson loop expectation values; Alexander invariants \( \Delta_K(t) \) factorize for homologically fibered knots via Magnus matrix determinants; unknotting/bridge/crossing numbers as integer topological invariants. | CONNECTION: Jones polynomial evaluated at \( q = e^{2\pi i/5} \) yields golden-ratio-related values (e.g., \( V_{\text{trefoil}}(e^{2\pi i/5}) = 1 \), but \( q = e^{2\pi i/3} \) gives \( -\phi \) for some knots); Alexander polynomial at \( t = -1 \) gives determinant \( |\Delta_K(-1)| \), often related to \( \phi \)-scaled integers; base-60 appears i

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com