CKM and PMNS
mixing matrices from discrete subgroups of SU(2).
Therefore, following up the success I had deriving the neutrino PMNS matrix, the CKM mixing matrix should be derivable by using the same geometrical method, i.
If this geometrical derivation of both the PMNS and CKM mixing matrices is based upon the correct reason for the mixing of flavor states to make the mass states, then one must reconcile the empirical data with the prediction of a fourth quark family.
This section reviews the mathematical procedure used in my 2013 derivation  of the PMNS matrix from first principles.
From experiments , the PMNS angles have been estimated to be
Consequently, for the normal hierarchy of neutrino masses, one has the empirically determined PMNS matrix
which can be compared to my resultant derived PMNS matrix in the standard parametrization
Several key features differentiate PMNS from delayed cerebellar ataxia (DCA).
We also consider possibilities that ADEM following Plasmodium infection explains the pathogenesis of some cases of PMNS.
One can define a 3 x 3 unitary matrix  and substitute angle difference values for the lepton mixing matrix PMNS
and a 3 x 3 quark mixing matrix CKM3, producing
PMNS occurs up to nine weeks after complete recovery from P.
The etiology of PMNS remains unclear and a wide range of neurological manifestations have been reported.