Meta-One Field Equation: Definition, Symmetries and Plane Wave Explicit Form

This preprint serves as the foundational first work of the three-part Meta-One Field Theory series. It systematically upgrades the empirical unified formula $E=mc^2e^{i\theta}$ into a rigorous 10-dimensional complex scalar field theory. We construct the complete renormalizable action functional including Higgs self-interaction and non-minimal curvature coupling, derive the full set of field equations via variational calculus, and analyze global U(1) symmetry, corresponding Noether conserved currents and energy-momentum tensor. The existence of topological vortex excitations on the compact internal manifold is verified, and the explicit plane wave solution for free Meta-One field is strictly deduced under flat spacetime approximation. This foundational framework provides the complete underlying mathematical basis for the two companion preprints in the series: 1. Deriving the Three-Generation Neutrino Mass Ratio from High-Dimensional Vortex Solutions 2. Variational Derivation of Neutrino Mass Formula from Vortex Wavefunctions and Higgs Overlap Integral The author works as an unaffiliated independent researcher with no institutional affiliation. The whole theoretical system adopts consistent Kaluza-Klein 6D compactification and topological excitation mechanism to explain the geometric origin of fermion generations and tiny neutrino mass, with only a small number of experimental calibrated parameters. The high-dimensional relativistic correction predicts measurable neutrino velocity deviation, which can be tested by long-baseline neutrino experiments such as JUNO and DUNE.