What question did this study set out to answer?

To derive a parameter-free prediction of the PMNS CP-violating phase using the G₂ root system and the Fano plane.

March 30, 2026Open Access

CP-Violating Phase δCP = 7× (π/6) = 210° from the Fano Plane and G₂ Root System within the OTIS Framework

Key Points

To derive a parameter-free prediction of the PMNS CP-violating phase using the G₂ root system and the Fano plane.
Utilized the G₂ root system and Fano plane PG(2,2) for analysis.
Calculated the CP-violating phase δ_CP as 7 times the minimum root angle (π/6).
Referenced experimental values from PDG 2024 for accuracy.
Derived δ_CP = 210°, which is within 0.33σ of the experimental value of 197°±40°.
Confirmed linkage of sin(210°) = −1/2 to baryon asymmetry of the Universe.
Prediction will be tested by the Hyper-Kamiokande experiment with a precision of approximately 10°.

Abstract

A parameter-free prediction of the PMNS CP-violating phase is derived from the G₂ root system and the Fano plane PG (2, 2). The minimum root angle of G₂ is π/6 = 30°. The Fano plane contains 7 points. The prediction δCP = 7×30° = 210° lies within 0. 33σ of the experimental value 197°±40° (PDG 2024). At δCP = 210°, sin (210°) = −1/2 exactly, directly linking the CP phase to the baryon asymmetry of the Universe. The prediction will be decisively tested by Hyper-Kamiokande (2027–2030) with precision ~10°. Part of the OTIS series (DOI: 10. 5281/zenodo. 19160535).

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