No Proof of Golden-Ratio Absence in Clebsch–Gordan Coefficient Literature — E8 Intelligence Research

FINDING: Search returned only pedagogical/derivational material on Clebsch–Gordan coefficients plus one lattice-QCD operator-construction paper; no proof of golden-ratio absence exists in these results. | MATH: CG coefficients arise from SU(2) recoupling: |j₁m₁⟩|j₂m₂⟩ = Σ ⟨j₁j₂;m₁m₂|JM⟩ |JM⟩, with J ∈ {|j₁−j₂|, …, j₁+j₂}. Coefficients are algebraic (square roots of rationals) for all integer/half-integer j. Example: two spin-½ → Condon–Shortley values 1/√2, 1/√2, 1, 0. | CONNECTION: No golden ratio (0.618, 1.618) appears in CG tables — the values are rationals and √rationals, not φ-powers. This is consistent with SU(2) root system A₁ (rank 1, Cartan matrix [2]) and the crystallographic/root-lattice structure of angular momentum, which generates rational spectra, not φ. | DEPTH: 2 Notes on what the evidence actually supports: 1. Key mathematical insight: CG coefficients are matrix elements of the unitary change of basis between uncoupled and coupled angular-momentum bases. They are de Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com