The Leptonic CP Phase Is 0 or π Because the C60 Adjacency Is Real

The adjacency matrix of the C60 cage is real. A real matrix equals its own transpose, so the mixing operator built from it satisfies T-dagger = T-transpose, and a mixing operator that equals its own transpose cannot carry a complex phase. The leptonic CP phase is therefore pinned to 0 or π. This is a theorem, not a fit. A small leakage from the family lag widens the prediction from the two exact points to a narrow band, π ± 6.3 degrees at the present flow position. The current global best fit for the phase sits on π, within one sigma. The framework takes the opposite side from maximal CP violation: a phase resolved away from 0 and π, beyond the leakage band, ends the result. The experiments that decide it are the long-baseline neutrino programs.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-31
DOI
https://doi.org/10.5281/zenodo.23841767
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

The Leptonic CP Phase Is 0 or π Because the C60 Adjacency Is Real

Jason Almasy
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

The Leptonic CP Phase Is 0 or π Because the C60 Adjacency Is Real

Jason Almasy
preprint en

Abstract

The adjacency matrix of the C60 cage is real. A real matrix equals its own transpose, so the mixing operator built from it satisfies T-dagger = T-transpose, and a mixing operator that equals its own transpose cannot carry a complex phase. The leptonic CP phase is therefore pinned to 0 or π. This is a theorem, not a fit. A small leakage from the family lag widens the prediction from the two exact points to a narrow band, π ± 6.3 degrees at the present flow position. The current global best fit for the phase sits on π, within one sigma. The framework takes the opposite side from maximal CP violation: a phase resolved away from 0 and π, beyond the leakage band, ends the result. The experiments that decide it are the long-baseline neutrino programs.

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