Quantization Without Postulates: Deriving ℏ from Phase Winding

Planck’s constant $\hbar$ is usually introduced as a fundamental postulate of quantum theory. In this work, we derive $\hbar$ analytically from a topological action principle, showing that it emerges as the minimal quantized action required to stabilize a coherent spinor phase configuration. We model the field as $\Psi(x) = \rho(x) e^{i\Theta(x)}$, where $\Theta(x)$ is a compact scalar valued on $S^1$. Within this framework, we define the class of minimal winding configurations $\mathcal{C}_{1/2}$, characterized by half-integer topological charge $\oint_\gamma \partial_\mu \Theta\, dx^\mu = \pi$. We demonstrate that the least non-vanishing action over this class is finite, topologically invariant, and equal to $\hbar$. This implies that $\hbar$ is not a postulate, but a phase-ontological consequence of topological fixation. We further analyze connections with Aharonov–Bohm phenomena, persistent phase currents, and quantized interference effects as physical manifestations of discrete winding. Our results open a new perspective on quantization grounded in global phase topology.