Emergence of Fundamental Physical Constants from Vacuum Coercivity and Topological Admissibility.

We investigate the structural origin of the fundamental physical constants $c$, $\hbar$, and $G$ within the TUO–NS framework, where physical laws emerge from admissibility, localization, and stability constraints imposed by a coercive vacuum operator. We show that these constants are neither free parameters nor symmetry postulates, but threshold values delimiting the domain of physically admissible vacuum excitations. A universal limiting velocity, a minimal quantum of action, and a maximal gravitational coupling arise respectively as necessary stability bounds associated with hyperbolic propagation, temporal localization, and vacuum–matter interaction in a coercive medium. In particular, the limiting speed $c$ is identified *a posteriori* as the measured ratio $c=\sqrt{K_v/\varrho_v}$ of vacuum rigidity to vacuum inertial density. The quantum of action $\hbar$ emerges as a strictly positive lower bound on the time–energy product required for a nontrivial localized excitation to remain within the admissible Sobolev sector. The gravitational constant $G$ appears as the maximal attractive coupling compatible with boundedness from below of the total energy. Configurations attempting to violate these bounds are shown to exit the admissible functional space through loss of localization, divergence of the coercive energy, or dynamical instability. The analysis is supported by a minimal coercive elastic model isolating the mechanism, in which the emergence of $c$, $\hbar$, and $G$ follows deductively from the structure of the vacuum functional, without invoking canonical quantization, symmetry axioms, or phenomenological inputs. In this perspective, the fundamental constants encode the intrinsic rigidity and stability limits of the vacuum itself, rather than independent microscopic postulates.