Orthogonal completion of mixed neutral lepton kinetic terms ($n_L=c_{\alpha }{\nu }_L+s_{\alpha }{N}_L,n_L^{\perp }=-s_{\alpha }{\nu }_L+c_{\alpha }{N}_L$)

If a chiral fermion triplet uses one normalized linear combination of two neutral leptons, adding the perpendicular combination as a gauge singlet completes their canonical kinetic terms. The two combinations are related to the original fields by a real orthogonal matrix. Hence their summed kinetic quadratic form is exactly that of the two original fields, with no mixed terms. The singlet carries the same chirality; no right-handed component is created for a purely left-handed massless neutrino.