All the derived PMNS matrix element values are within the 1[sigma] range of the empirically determined absolute values.
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.
This section reviews the mathematical procedure used in my 2013 derivation  of the PMNS matrix from first principles.
For direct comparison, the empirically estimated PMNS matrix for the normal hierarchy of neutrino masses is
Numerous attempts to derive the neutrino PMNS matrix from various discrete group horizontal symmetries have led to partial success.
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
Therefore, only the remaining generator for each lepton family contributes to the mixing that produces the PMNS matrix.