Phase Quantization from Observable Regularity: Reducing the Wallström Objection to a Standard Physical Condition

This paper presents a complete derivation of the Schrodinger equation from the Onsager-Machlup stochastic variational principle, rigorously resolving the longstanding Wallstrom objection. Wallstrom proved that hydrodynamic equations derived via the Madelung transformation do not uniquely determine quantum mechanics unless phase circulation is quantized. We demonstrate that the quantization condition (the integral of the gradient of S along a closed loop equals 2pin*hbar) emerges as a necessary consequence of requiring finite action and topological stability of coherent structures. Configurations with non-integer winding numbers are shown to lead to divergent action costs or inadmissible multi-sheeted spatial representations. For nodal configurations where the probability density vanishes, we show that the smoothness of the probability current independently forces integer winding numbers, excluding non-quantized solutions recently constructed in the literature. This establishes the Schrodinger equation as the unique and inevitable description of probability fluid dynamics under the calibration D = hbar/(2m). Finally, the framework provides testable experimental predictions regarding wave packet spreading and interference visibility in the presence of environmental noise.