Clebsch–Gordan Coefficients: No Golden-Ratio Absence Proof in Search Results — E8 Intelligence Research

FINDING: Search returned only pedagogical/lecture material on Clebsch–Gordan coefficients plus one lattice-QCD paper; no proof of golden-ratio absence exists in these results. | MATH: CG coefficients arise from SU(2) recoupling: |j₁m₁⟩|j₂m₂⟩ = ΣJ,M CJMj₁m₁j₂m₂ |JM⟩, with C = ⟨j₁m₁j₂m₂|JM⟩. Selection rules: M = m₁+m₂, |j₁−j₂| ≤ J ≤ j₁+j₂. Values are rational combinations of square roots of rationals (e.g. √(1/2), √(2/3), √(3/5)) — algebraic numbers of degree ≤ 2 over ℚ. | CONNECTION: The golden ratio φ = (1+√5)/2 is a quadratic irrational (degree 2 over ℚ). CG coefficients are also quadratic irrationals, so φ is not categorically excluded by algebraic degree alone. However, the √5 needed for φ does not arise from SU(2) recoupling of integer/half-integer spins: CG radicals involve √(j(j+1)), √(2j+1), √((j±m)(j±m+1)) — products of integers, never √5 as a primitive unless j,m conspire (e.g. j=2 gives √5 in normalization). No crystallographic/root-system link appears in the retriev Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com