Quantization Without Postulates: Structural Derivation of Planck’s Constant from Phase Topology and RG-Stationarity

Planck's constant ħ has traditionally been introduced axiomatically in quantum mechanics, with its value fixed empirically and lacking a generally accepted derivation. In this work we present a structural derivation of ħ from first principles, combining geometric quantization with effective field theory. We show that ħ arises both as the minimal symplectic flux through a primitive cycle of the prequantum U(1) bundle—a direct consequence of the integrality of the first Chern class—and as the self-consistent reconciliation of induced couplings at an RG–stationary point of the effective theory. This dual characterization unifies topological normalization and renormalization dynamics, yielding the structural relation ħ = 2q² in natural units of the model (with q the fundamental dimensionless U(1) charge), with only a single experimental anchor (S₀) needed to connect with SI units. Thus ħ is presented not as a postulate but as a structural invariant of symplectic topology and effective field theory. This formulation addresses a foundational gap of standard quantization and frames Planck’s constant as an emergent universal threshold for coherent quantum phenomena.