Burnside-Type Derivation of the Four CP-Violating Phases of the Standard Model on a Joyce G2-Orbifold

The four CP-violating phases of the Standard Model — the Cabibbo-Kobayashi-Maskawa Dirac phase δ_CKM, the Pontecorvo-Maki-Nakagawa-Sakata Dirac phase δ_PMNS, and the two Majorana phases α_21/2 and α_31/2 — are derived from a Burnside-type orbit analysis of the cyclic subgroup Z_5 ⊂ I* embedded in the binary icosahedral group I* = SL(2,5) acting on a Joyce G_2-orbifold X_7 = T^7/(Z_3 ⋊ I*) at Betti numbers (b_2, b_3) = (27, 451). The 25 commuting pairs of Z_5 × Z_5 split, under the diagonal Z_5-action, into exactly 5 orbits of size 5, indexed by the integer n ∈ {0, 1, 2, 3, 4}. The orbit with n = 0 corresponds to the CP-conserving sector; the remaining four orbits with n ∈ {1, 2, 3, 4} are identified with the four CP-violating phases of the Standard Model through cycle-topology analysis of M2-brane instantons on X_7. The leading-order predicted values {72°, 144°, 216°, 288°} agree with the Particle Data Group 2024 value of δ_CKM at 0.06σ (with subleading C-field correction included) and remain compatible with the T2K+NOvA 2025 combined fit of δ_PMNS at the edge of the 1σ allowed band. A structural identity δ_PMNS + α_21/2 ≡ 0 (mod 2π) is derived from the seesaw-inversion mechanism and provides a falsification test of the framework. The effective Majorana mass is predicted to be |m_ββ| = 5.57 ± 0.10 meV, within reach of the nEXO Phase II experiment. The framework reduces 4! = 24 a priori possible assignments to a unique configuration without empirical input, through a chain of group-theoretic theorems and the constraint |Out(I*)| = 2 ≠ 3 that fixes the Z_3 ⋊ I* structure.