Leptonic CP Conservation and the Quark CP Phase from Octonionic Flavor Structure
Abstract
One generation of standard-model fermions can be realized on the complexified octonions through the Clifford algebra ; the octonionic unification programme extends this to three generations, with generation transport implemented by automorphisms or by rotors built from the ladder operators. We prove a localization theorem for the CP-violating phases of this structure, using only the construction and the stated three-generation representatives, independently of the wider programme. For quarks, the first-to-second generation step is the occupation flip of one ladder mode, with the up and down species coupling to conjugate ladder directions; a conjugation theorem forces for every real transport, and the most general rung-generated rotor yields the exact one-parameter law : the transport phase is twice one Yukawa orientation angle. The programme's geometric rotor sits exactly at the quadrature-balanced point ; the companion analysis reproduces the Cabibbo \emph{magnitude} with a single real tilt, leaving the rung near quadrature, but it does not extract a CKM CP phase, so the quark Dirac phase is fixed only once the underlying Yukawa orientation is computed. For leptons we prove a reality theorem: every charged-lepton and every neutrino transport amplitude is exactly real for every automorphism and every rotor that does not mix the identity line with the lepton--flavor plane a class that contains the entire quark-rung family--and identity--flavor mixing across that plane is the unique possible source of a leptonic phase. [Truncated]
Keywords
Cite
@article{arxiv.2606.27836,
title = {Leptonic CP Conservation and the Quark CP Phase from Octonionic Flavor Structure},
author = {Bishnu Gupta Teli and Tejinder P. Singh},
journal= {arXiv preprint arXiv:2606.27836},
year = {2026}
}
Comments
7 pages, 1 figure