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May 21, 20260 citationsOpen Access

Quark-Lepton CP Phase Complementarity in the U131 Framework A Golden-Ratio Corner-Phase Audit of PMNS and CKM CP Violation and the Jarlskog Invariant

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KTKen TakadaEEnumiaze

Key Points

  • This research aims to analyze the CP-phase complementarity between PMNS and CKM matrices using a specific mathematical framework.
  • Utilized bounded U131 CP-phase complementarity audit combining cpphasev1-v6 and jarlskogv1-v6.
  • Derived CP phases delta_PMNS and delta_CKM based on golden-ratio corner shifts.
  • Calculated J_CKM using embedded CKM magnitudes and the standard Jarlskog formula.
  • Established J_CKM,U131 = 3.179865e-5 using the derived values.
  • Identified CP phases sharing a golden-ratio upper-corner shift atan(phi^-2).
  • Clarified that exact CP-phase derivation claims are not made in this analysis.

Abstract

This record contains Paper 054 of the Enumiaze Research Program. The manuscript presents a bounded U131 CP-phase complementarity audit combining cpphasev1-v6 and jarlskogv1-v6. The central candidate relation is that PMNS and CKM CP phases share the same golden-ratio upper-corner shift atan (phi^-2) while carrying complementary quarter-turn orientations: deltaPMNS, U131 = -pi/2 - atan (phi^-2) and deltaCKM, U131 = +pi/2 - atan (phi^-2). The PMNS candidate lies in the same negative lower-half sector as the embedded PMNS row, while the CKM candidate yields JCKM, U131 = 3. 179865e-5 using embedded CKM magnitudes and the standard Jarlskog formula. The paper explicitly blocks stronger claims: it does not claim exact CP-phase derivation, exact Jarlskog derivation, baryogenesis, or full derivation of the Standard Model. Mathematical definitions, algorithmic steps, exact-check summaries, and claim boundaries are provided for reproducibility; source code is not reproduced in the paper.

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Cite This Study

Takada et al. (2026) studied this question.

synapsesocial.com/papers/6a0ea127be05d6e3efb5f8c8https://doi.org/10.5281/zenodo.20279569
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