Unified Harmonic Field Theory: A Geometric and Predictive Framework for Mass Quantization and Gauge Symmetry

The Standard Model accurately describes known particles and interactions but leaves several foundational questions unanswered, including the origin of particle masses, the structure of gauge symmetries, and the value of fundamental constants. We propose a unified harmonic field theory (UHFT) in which all fields and forces emerge from quantized eigenmodes of a curvature-modulated carrier wave field defined over four-dimensional spacetime. In this framework, particle rest masses correspond to standing wave solutions subject to boundary conditions, and gauge symmetries arise as constraints required to preserve local phase coherence across coupled modal structures. The model analytically reproduces the lepton and gauge boson mass spectrum with high precision and derives the fine-structure constant \( \alpha \approx 1/137 \) as a geometric modal overlap integral, matching experiment to within \( 0.001\% \) without fitting parameters. Photons and gluons emerge as unconfined or collectively confined modal structures, respectively, and gravity appears as the geometric backreaction of the carrier wave energy-momentum distribution. UHFT also predicts subtle deviations in neutrino oscillation lengths, Higgs decay widths, and gravitational wave polarizations. These results position UHFT as a mathematically structured and testable framework for unifying quantum field behavior, interaction geometry, and curvature-based dynamics under a single harmonic principle.