Canonical Ambient su(2) Structure on C[Q5]

This theorem extends Theorem 23 spin-1 structure on the T22 middle sector H₁₂ ≅ V₄ ⊗ T₃ to a canonical ambient representation of su(2) on all of ℂ[Q₅] ⊗ℝ ℂ, via explicit residual-axis substitution operators. Three operators are defined on ℂ[Q₅] ⊗ℝ ℂ: Ĵ_z(e_x) = (x₄ − x₂)e_x — diagonal, canonical, grading-preserving Ĵ_x = (1/√2)(T2→3 + T3→2 + T3→4 + T4→3) Ĵ_y = (−i/√2)(T2→3 − T3→2 + T3→4 − T4→3) Four results are established: (1) All three su(2) commutation relations hold: [Ĵ_x, Ĵ_y] = iĴ_z, [Ĵ_y, Ĵ_z] = iĴ_x, [Ĵ_z, Ĵ_x] = iĴ_y: verified by direct operator computation using eigenvalue shifts and the substitution operator algebra. (2) Grading compatibility: Ĵ_z preserves the complementary grading; Ĵ_x and Ĵ_y act by residual-axis substitution preserving total residual Hamming weight. (3) Restriction: Ĵ_α|{H₁₂} = I{V₄} ⊗ J_α for each α ∈ {x, y, z}. (4) T23 compatibility: Under the T23 Lie algebra isomorphism Ψ, the induced action on the T21 carrier C_X is compatible with the adjoint so(3)-structure of Theorem 21. No free parameters enter. No uniqueness of the ambient extension is claimed. No dynamical or physical interpretation is asserted beyond the algebraic structure. Status: Solid. All commutation relations established by direct operator computation. No conditionality beyond T22 and T23 structures.