Chern-Simons Level Shift Quantized by Dual Coxeter Number — E8 Intelligence Research

FINDING: Chern-Simons theory moduli space symplectic structure is quantized by level k, with root system Coxeter number determining shift k → k + h^∨. | MATH: Symplectic form ω on moduli space M(G,C) satisfies [ω/2π] = k · c₁(L) ∈ H²(M,ℤ); level shift k → k + h^∨ where h^∨ is dual Coxeter number of Lie algebra 𝔤; Chern-Simons action S_CS = (k/4π) ∫_M Tr(A ∧ dA + (2/3)A ∧ A ∧ A). | CONNECTION: Root system Coxeter numbers: A_n → h^∨ = n+1, D_n → h^∨ = 2n-2, E₆ → h^∨ = 12, E₇ → h^∨ = 18, E₈ → h^∨ = 30. These integers relate to golden ratio via E₈: 30 = 2·3·5, and 30/φ² ≈ 11.46, 30/φ ≈ 18.54, showing E₈ Coxeter number near 2.618·φ². Base-60 connection: 60 = 2·30, linking E₈ Coxeter number to sexagesimal system. | DEPTH: 8 — Core geometric quantization of gauge theory, tying symplectic geometry to Lie algebra combinatorics and modular tensor categories. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com