CP Violation from Icosahedral Geometry: The Phase δ = arccos(1/φ²) and the Jarlskog Invariant

We derive the CKM CP-violating phase from the representation theory of the binary icosahedral group 2I = SL(2,5). The two 3-dimensional irreps of 2I, constructed via the symmetric square Sym²(2) and Sym²(2′), are intrinsically complex: the SU(2) generators involve fifth roots of unity ω = e2πi/5, making CP violation a geometric necessity rather than a free parameter. The 3⥳3′ tensor product decomposes as 4⊕5 under A₅, with the 4-dimensional invariant subspace containing a complex projector P₄ whose Im/Re ratio is 0.332. The resulting CP phase δ = arccos(1/φ²) = 51.83°, combined with CKM mixing exponents derived in the companion paper [1], yields the Jarlskog invariant J = 3.27 × 10−5, matching experiment to 2.8%. We prove that the CKM mixing exponents equal the mass formula Q-values through the Froggatt-Nielsen mechanism on the 600-cell lattice and outline four specific experimental tests.