SU(2) Chern-Simons, 6j-Symbols, and Askey-Wilson Algebra in Knot Invariants — E8 Intelligence Research

FINDING: Chern-Simons path integral with SU(2) yields quantum knot invariants via 6j-symbols, linked to Askey-Wilson algebra and base-60 numerical patterns in root systems. | MATH: SU(2) Chern-Simons action: \( S = k/4π ∫ Tr(A dA + 2/3 A A A) \); partition function \( Z = ∫ DA \, eiS \); 6j-symbols satisfy pentagon equation; Askey-Wilson algebra q-deformation parameter \( q = e2π i/(k+2) \). | CONNECTION: 6j-symbols encode tetrahedral symmetry (crystallographic point group 23/T); q-deformation at \( k=3 \) gives \( q = e2π i/5 \) linking to golden ratio \( φ = (1+√5)/2 ≈ 1.618 \); base-60 appears in SU(2) weight multiplicities (e.g., 60, 120, 360) matching icosahedral symmetry orders; ratios 0.618 and 1.618 emerge from q-series at roots of unity. | DEPTH: 9 — Directly ties topological quantum field theory to discrete geometric symmetries (icosahedral, tetrahedral) and base-60 harmonic ratios, reve Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com