Casimir Decomposition of the Ambient T24 Action

This theorem computes the Casimir decomposition of the ambient su(2) action established in Theorem 24. The Casimir operator Ĵ² = Ĵ_x² + Ĵ_y² + Ĵ_z² decomposes ℂ[Q₅] ⊗ℝ ℂ into 8 copies of the spin-0 module V₀ and 8 copies of the spin-1 module V₁. The decomposition is grading-stratified: m = ±2: 2V₀ m = ±1: 2V₀ ⊕ 2V₁ m = 0: 4V₁ The middle sector H₁₂ (dimension 12, grading m = 0) decomposes as 4V₁, consistent with the T22 identification H₁₂ ≅ V₄ ⊗ T₃. All phase dynamics live in the middle sector. No free parameters enter. The middle-sector consistency is a verification, not an assumption: failure would be a contradiction. Status: Solid. All results by direct computation within the T24 operator framework. Dependencies: T22, T23, T24.