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

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: delta_PMNS,U131 = -pi/2 - atan(phi^-2) and delta_CKM,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 J_CKM,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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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-19
DOI
https://doi.org/10.5281/zenodo.20279569
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

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

Ken Takada, Enumiaze
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

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

Ken Takada, Enumiaze
preprint en

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: delta_PMNS,U131 = -pi/2 - atan(phi^-2) and delta_CKM,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 J_CKM,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.

Zenodo (CERN European Organization for Nuclear Research)
Gender equality
Particle physics theoretical and experimental studies
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