What question did this study set out to answer?

This research explores the geometric foundations of CP violation, specifically the delta_CP phase of the CKM matrix.

April 7, 2026Open Access

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

Key Points

This research explores the geometric foundations of CP violation, specifically the delta_CP phase of the CKM matrix.
Analyzed the geometry of null screens in Kerr-Newman spacetime.
Developed three no-go theorems addressing solution boundaries.
Introduced Berry holonomy as an effective theory, leading to axiomatic formulations.
Conducted numerical computations to clarify order consistency with known physical data.
Identified three no-go theorems that limit potential solutions for CP violation.
Established Berry holonomy with numerical approximation consistent with PDG values.
Proposed that the mass formula and CP phase can be derived from a unified gyroscopic equation.

Abstract

Structural preprint on the geometric origin of CP violation. We investigate whether the CP-violating phase deltaCP 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: PhiB = -2pi (sf + lambdaf 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 mf = vEW sqrt (nf/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.

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