Comparative Study of the 1–2 Exchange Symmetries in Neutrino Frameworks with Global and Local Validities

A new picture ``one-resonance - one-symmetry'' has been proposed recently to reveal nature of the reparametrization symmetry in neutrino oscillation matter and where it resides: Symmetry $i \leftrightarrow j$ state-exchange type exists at around a resonance with $i$ $j$ being states which participate level crossing. Consistently, 1-2 1-3 state exchange symmetries are identified solar atmospheric resonances, respectively, locally-valid frameworks. On other hand, Denton {\it et al.} (DMP) perturbation theory, globally-valid framework, is akin one aforementioned solar-resonance (SRP) theory. In our picture, must be associated resonance, not if so these two identical each other. We conduct comparative study possessed by SRP DMP confirm their identity. An almost identity verified, but highly nontrivial way.