Minimum-Dimensional Equivariant Spectral Triples on Quantum SU(2) via Non-Product Dirac Operators — E8 Intelligence Research

FINDING: Equivariant spectral triples on quantum SU(2) require a minimum-dimensional K-homology class realized by a non-product Dirac operator; the Dirac operator is the central object encoding metric + fermionic data. | MATH: Spectral triple (A, H, D); D = D* , [D,a] bounded ∀a∈A; equivariance under U_q(su(2)) Hopf algebra coaction; K-homology class [D] ∈ KK^*(A,ℂ); minimum dimension set by the fundamental representation of SU(2) (spin-½, dim 2) and its tensor powers; Dirac spectrum λ_n ~ Casimir eigenvalues of su(2): C_2(j)=j(j+1), j=0,½,1,3/2,… | CONNECTION: su(2) root system A₁ — single positive root, Weyl group S₂ (order 2); crystallographic rank-1 lattice; Casimir spectrum j(j+1) yields ratios ½, 2, 15/4…; the 2-dim fundamental rep and the ½-spin are the minimal non-trivial data — no direct 0.618/1.618 emergence in the raw su(2) spectrum, but the q-deformation parameter q=e^{iθ} interpolates continuously and at q→1 recovers classical SU(2) whose representation ring is the polynom Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com