The four CP-violating phases of the Standard Model — the Cabibbo-Kobayashi-Maskawa Dirac phase δCKM, the Pontecorvo-Maki-Nakagawa-Sakata Dirac phase δPMNS, and the two Majorana phases α₂1/2 and α₃1/2 — are derived from a Burnside-type orbit analysis of the cyclic subgroup Z₅ ⊂ I* embedded in the binary icosahedral group I* = SL (2, 5) acting on a Joyce G₂-orbifold X₇ = T⁷/ (Z₃ ⋊ I*) at Betti numbers (b₂, b₃) = (27, 451). The 25 commuting pairs of Z₅ × Z₅ split, under the diagonal Z₅-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 X₇. The leading-order predicted values 72°, 144°, 216°, 288° agree with the Particle Data Group 2024 value of δCKM at 0. 06σ (with subleading C-field correction included) and remain compatible with the T2K+NOvA 2025 combined fit of δPMNS at the edge of the 1σ allowed band. A structural identity δPMNS + α₂1/2 ≡ 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 Z₃ ⋊ I* structure. Keywords: CP violation, Standard Model, M-theory, G₂ holonomy, Joyce orbifold, binary icosahedral group, Burnside lemma, seesaw mechanism, neutrinoless double beta decay, PMNS matrix, CKM matrix.
Moustafa Radwan (Sat,) studied this question.