Structural Selection in Magnetic Quantization: From Landau Levels to the Quantum Hall Regime

Landau quantization and the quantum Hall effect are traditionally derived from dynamical equations describing charged particles in magnetic fields. In this work, we present a complementary, structure-first interpretation in which magnetic fields function as constraining geometries that select admissible phase-space manifolds rather than generating states dynamically. We show that Landau levels arise naturally as a consequence of degeneracy resolution under magnetic confinement, while the quantum Hall regime represents a further topological stabilization of these selected manifolds under disorder and dissipation. This framing preserves all standard results while re-ordering interpretation: quantization reflects structural admissibility prior to dynamics. The approach provides a unified language for magnetic quantization without introducing new forces, mechanisms, or modifications to established theory.