Knot Invariants Unify Fluid Helicity, Chern-Simons Theory, and Quantum Computing — E8 Intelligence Research

FINDING: Knot polynomial invariants (Jones, Alexander, HOMFLY-PT) unify fluid helicity, Chern-Simons theory, and quantum computing via braid group representations. | MATH: Jones polynomial \(V_L(t)\) from Kauffman bracket \(\langle L \rangle = \sum_{\text{smoothings}} A^{\text{twists}}(-A^2-A^{-2})^{\text{components}}\), with \(t=A^{-4}\); Alexander polynomial \(\Delta_K(t)\) from Seifert matrix; HOMFLY-PT \(P(a,z)\) generalizes both; helicity \(H = \int \mathbf{A}\cdot\mathbf{B}\,d^3x\) equals linking number for disjoint loops; Chern-Simons action \(S_{CS} = \frac{k}{4\pi}\int \text{Tr}(A\wedge dA + \frac{2}{3}A^3)\) yields knot invariants as Wilson loop expectation values. | CONNECTION: Jones polynomial at roots of unity: \(t=e^{2\pi i/5}\) gives \(V_L(e^{2\pi i/5})\) related to golden ratio \(\phi = 1.618\) via \(2\cos(2\pi/5) = \phi^{-1} = 0.618\); Temperley-Lieb algebra dimension at \(q=e^{i\pi/5}\) is Fibonacci number \(F_n\), linking to 0.618; Alexander polynomial at \(t=-1\) gi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com