Geometric Origin of CP Violation — Three No-Go Theorems, Effective Berry Holonomy, and Gyroscopic Unification

Structural preprint on the geometric origin of CP violation. We investigate whether the CP-violating phase delta_CP of the CKM matrix can arise from the geometry of null screens on Kerr-Newman spacetime. The Phase 4 research program (40 notes) produces a structural preprint rather than a first-principles completion, with confidence labels [A] (rigorous), [C] (conjectural), and [E] (effective/axiomatic) separated transparently. Main structural results: Three no-go theorems [A] delimit the solution space: (i) Universal Phase Theorem for single-rho-tilde real-weight integrals [A/C weak form], (ii) commutativity barrier for linear Weyl coupling [A], (iii) parallel transport limitation from real Sturm-Liouville structure [A]. Berry holonomy as effective theory [E]: Phi_B = -2pi(s_f + lambda_f beta(theta)) cos(theta) is formally positioned as an axiomatic effective action, not an exact derivation. Numerical computation yields J approx 10⁻⁴, order-consistent with PDG. Two-layer (gravity/EM) log-modulation structure [A/C] derives the product form from heat kernel coupling term. Gyroscopic Unification Hypothesis [A/C]: MPD (Mathisson-Papapetrou-Dixon) gyroscope on the null plane suggests that Howlett's mass formula m_f = v_EW sqrt(n_f/27) and the present CP phase are dual projections of a single gyroscopic equation. Remaining [C] gaps (6 points): log-modulation first principles, twistor contour, null projection rigor, light-quark lattice assignment, SU(3)_gyro concrete values, Theorem 14.1 strong form. Related work: Companion Riemann Hypothesis proof (concept DOI 10.5281/zenodo.19035966). The relationship with Howlett (2026, zenodo:19278346) is complementary: the present work focuses on CP phase, Howlett addresses the mass spectrum.