No Source Addresses A₂ Root Lattice 30° Rotation or Coxeter 120° Eigenvalue — E8 Intelligence Research

FINDING: Search returned only pedagogical/derivational content on reciprocal lattices (MIT RES.3-004, FCC→BCC derivations, Hindi/German visualizations) plus an unrelated lattice-QCD paper — no source actually addresses the A₂ root lattice, its 30° rotation, or the Coxeter element's 120° eigenvalue. | MATH: The query's target mathematics is well-defined and verifiable independently: A₂ root lattice = hexagonal (triangular) lattice with basis a₁=(1,0), a₂=(1/2,√3/2), |aᵢ|=1, angle 60°. Reciprocal lattice is also hexagonal, rotated 30° relative to direct lattice, with |bᵢ|=2/√3. Weyl group W(A₂)≅S₃, order 6. Coxeter element = product of two simple reflections s₁s₂, a rotation by 120° (2π/3) with eigenvalues {ω, ω̄} = e^{±2πi/3}, i.e. primitive cube roots of unity; characteristic polynomial λ²+λ+1=0. The 30° direct↔reciprocal rotation is the geometric manifestation of the 60°↔120° duality in the hexagonal system. | CONNECTION: Hexagonal crystallographic symmetry (6-fold, p6m); A₂ is the un

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com