The Universal Wave Model in 3+1 Dimensions: Energy Positivity, Hyperbolicity, and Topological Solitons with Fermionic Quantization

We present the Universal Wave Model (UWM), a Lorentz-covariant field theory in 3+1 dimensions where all physical entities emerge as excitations of a single wave field. Under explicit smallness and hyperbolicity conditions, we establish energy positivity, local well-posedness, and the existence of soliton solutions (Q-balls, Skyrmions, Hopfions) with topological energy bounds. Fermionic quantization via the Finkelstein–Rubinstein constraint is proved for odd baryon number sectors. The work provides a mathematically rigorous foundation for exploring wave-based ontologies in field theory.