Bohr and the Harmonic Ladder: Modal Quantization in UVFT

This work reframes quantum energy levels as emergent harmonic constraints within a vibrational field substrate, rather than postulated quantum rules. Within the Unified Vibrational Field Theory (UVFT), quantization emerges from modal dropout dynamics — coherence boundaries beyond which standing waves cannot persist. These dropout zones define modal survival and generate a harmonic ladder of permissible energy states. This geometric reinterpretation replaces traditional quantum assumptions of discrete states with field resonance structures. The resulting shells give rise to charge, spin, and tunneling as manifestations of modal behavior, not as intrinsic particle traits. The theory provides new insight into the coherence structures underpinning quantum systems and may unify familiar quantum equations with vibrational field constraints. Visual diagrams and mathematical expansions support the central claim: quantization is not a probabilistic outcome or a measurement artifact, but a geometric necessity of modal coherence in bounded vibrational fields.