Unifying Knot Invariants with Helicity, Quantum Computing, and Mirror Symmetry — E8 Intelligence Research

FINDING: Knot polynomial invariants (Jones, Alexander, higher-order) are being unified with physical helicity, quantum computing, and mirror symmetry—revealing a deep algebraic-topological core underlying fluid dynamics and gauge theory. MATH: - Jones polynomial \( V_L(t) \) satisfies \( t⁻¹VL_+ - tVL_- = (t1/2 - t-1/2)VL_0 \) (skein relation). - Alexander polynomial \( Δ_K(t) \) — classical invariant; higher-order Alexander invariants factorize via Magnus matrix \( M \) for homologically fibered knots: \( Δ⁽ⁿ⁾_K = (M) · (torsion part) \). - Helicity \( H = ∫ A · B \, d^3x \) — topological measure of linkage in fluid/plasma; knot polynomials expressed via helicity integrals (Liu). - Chern–Simons action \( SCS = k/4π ∫ Tr(A dA + 2/3 A A A) \) — knot invariants arise as Wilson loop expectation values. - Mirror symmetry: homological invariants (Khovanov Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com