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    The remarkable coincidence of the empirical Pythagorean equation for SM flavor hierarchy angles with the outer euclidean symmetry 3-space metric equation for constant vector direction angles is the data evidence of basic connection between flavor phenomena and geometry of outer euclidean 3-space. It relates three SM particle generations to the three dimensions of euclidean space. There is no more important problem in the phenomenology of the Standard Model than the problem of elementary particle mass and mixing flavor hierarchies. We observe a universal SM hierarchy feature that the lepton and quark mass and mixing flavor patterns at leading approximation are represented by ‘hierarchy angle’ cosine triads (0, 0, 1) as particular solutions without free parameters of the Pythagorean equation. Outstanding in the SM Tau-lepton, Top-quark and Down-quark masses and neutrino Reactor mixing angle visualize this regularity. Neutrino mass spectrum is still the unknown one. The present phenomenology points to ‘normal mass ordering’ with zero smallest mass if neutrinos are of Dirac type. It points to Majorana neutrinos if the mass spectrum is of ‘inverted ordering’ or quasi-degenerate or normal ordering with near degenerate not zero two smallest masses.   

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