Wu, Yining: Minimal Nonzero CP/T Orientation and Full Weak-Sector Consistency CKM-PMNS Orientation Capacity, Texture Independence, and the Three-Family Threshold in Finite Distinction Systems
The hard theorem in FDS-X2 is the Dirac orientation-capacity theorem: for an N × N chargedcurrent mixing matrix, the number of independent rephasing-invariant Dirac CP/T orientation
phases is
Corient(N) = (N − 1)(N − 2)
2.
Therefore N = 3 is the unique minimal dimension carrying exactly one primitive Dirac orientation.
The theorem applies canonically to the CKM sector and treats the PMNS sector as a full weak-sector
consistency extension: if the Dirac-type PMNS charged-current interface also dem
