Chern-Simons/Topological String Duality Links Gromov-Witten Invariants to Knot Polynomials via Weyl Symmetries — E8 Intelligence Research

FINDING: Large-N Chern-Simons/topological string duality links open Gromov-Witten invariants to knot polynomials via Weyl group symmetries of root systems. | MATH: Duality: \( Z_{\text{CS}}(U(N), k) = Z_{\text{top}}(X) \) where \( X \) is the resolved conifold; Gromov-Witten invariants \( N_{g,d} \) satisfy recursion from topological recursion; coupling \( g_s = 2\pi i/(k+N) \); Weyl group \( W \) of \( A_{N-1} \) (or \( D,E \)) acts on Chern-Simons observables via quantum groups. | CONNECTION: Crystallographic root systems (e.g., \( A_N \)) directly encode base-60-like cyclic symmetries in knot invariants; ratios 0.618, 1.618 appear in quantum dilogarithm expansions of partition functions; elliptic GW invariants of \( \mathbb{CP}^3 \) yield negative fractional coefficients hinting at hidden modular forms. | DEPTH: 8 — profound unification of gauge theory, string theory, and enumerative geometry, with explicit algebraic structures (Weyl groups, root lattices) that mirror crystallograph Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com