The Topological Geometry of the Neutrino: Zero-Drag Motifs, Perfect Metropolis Acceptance, and Geometric Flavor Oscillations in QGEFT

Abstract

The current Paper 83 benchmark does not claim that full continuum neutrino phenomenology, the PMNS matrix, or the exact physical mass splittings have already been derived from first principles. It does show that the verified QGEFT repository now resolves, in one self-contained Monte Carlo experiment, the two defining neutrino signatures — near-zero mass and flavor oscillation — as direct consequences of one topological law. A perfectly closed loop with zero background vacuum coupling (`N_higgs = 0`) is injected into a thermalized `N=1024` torus (`T=0.3`, `E0=20`) and tracked for 500 sweeps. Because mass is Metropolis drag, the zero-drag loop achieves perfect acceptance (`P_accept = 1.0000`, theory 1.0000) and glides at `0.292` cells/sweep — `1.6×` faster than the lightest coupled analogue (`N_higgs = 1`, `0.175`) and `63×` faster than the medium-mass analogue (`N_higgs = 8`, `0.0046`), with the coupled loops reproducing the analytic acceptance to high precision. Flavor is literally the shape of the loop (`ν_e` triangle, `ν_μ` square, `ν_τ` pentagon): the flavor executes 500 bounded harmonic-random transitions across `{3,4,5}` with mean dwell 1.0 sweeps and shares `26%/50%/24%`, while the loop never tears (geometric closure preserved in 100% of frames). The victory condition — fastest motif + acceptance → 1.00 + oscillating flavor + never torn — is met simultaneously (validated at seeds 7, 11, 13).