Quantization Across Scales and Levels. A Hierarchical Extension of Planck's Constant in Light of the Underlying Properties Hypothesis

Planck's constant $\hbar$ governs the quantization of action at the microscopic scale, setting the fundamental limit expressed in Heisenberg's uncertainty relations. The Underlying Properties Hypothesis (UPH) posits that organizational principles do not vanish as complexity increases, but are modulated and re-expressed across levels of reality. This paper proposes that $\hbar$ is not an isolated constant, but the first member of a hierarchy of quanta---each governing its own level of complexity, from quantum mechanics to biology, psychology, and social systems. Crucially, we introduce the coupling factor $\mathcal{F}$, a topological property of each system that modulates how strongly the quantization constraint applies. This refinement connects the hierarchy of quanta to the Kuramoto model of coupled oscillators, providing a bridge between structure and dynamics. We present candidate quanta for thermodynamics ($k_B$), biology (characteristic frequencies), psychology (attention limits), and sociology (Dunbar's number), and propose experimental strategies to identify them. This work is not a claim of final truth, but an invitation to explore quantization as a universal structural principle---with some levels fully formalized, others offering structured conjectures for future empirical work.