Energy-Based Harmonic Confinement Model for Particle Mass Spectrum

This paper proposes an energy-based framework for particle mass generation, where mass emerges from a balance between confinement cost and harmonic energy amplification. A continuous confinement parameter (α) is introduced and derived from an energy minimization principle. The resulting equation produces discrete stable solutions corresponding to observed particle masses. The model naturally separates the mass spectrum into multiple regimes, including a weak-confinement domain associated with neutrinos. All constants are explicitly defined, and their origins are discussed to ensure transparency and reproducibility. “This framework provides a testable pathway for understanding mass hierarchy.” The origin and hierarchy of particle masses remain unresolved within current theoretical physics. While established models successfully parameterize masses, they do not provide a simple structural explanation for their scaling. This paper proposes that mass arises from continuous harmonic confinement of energy, governed by geometric symmetry and phase locking.