Starting from only three ingredients: (i) variational formulation with cumulative action, (ii) interferential dependence on $S$, and (iii) PFu's episodic compatibility theorem, this paper assumes a single additional hypothesis of the universality of the action constant ($h$) and a minimal hypothesis of macroscopic stability, and derives mathematical consequences in an axiomatic and constructive manner, without introducing new fields, potentials, or \textit{ad hoc} phenomenological terms. Three main results are obtained. First, it is demonstrated that the existence of a universal action constant $h$ is a structural requirement for interferential consistency among multiple systems: the phase $\phi$ must be treated as a global structure, defined modulo $h$, common to all admissible processes. Second, it is shown that dynamic compatibility between systems can only occur at discrete events of phase coincidence, characterized by $\delta\phi = 0$; the observable dynamics are, therefore, reconstructible as sampling over a discrete sequence of compatibility events, whose density is proportional to the rate of variation of $S$ (abstract relativistic sampling theorem). Third, under hypotheses of invariance, extensivity, and coercivity, a global functional $\mathcal{I}$ is constructed that measures the compatibility stability of a configuration of systems, and it is proven that, in the infrared regime, it is equivalent to a quadratic spectral functional $Q = \langle \psi, \mathcal{A} \psi \rangle$, where $\mathcal{A}$ is a positive self-adjoint operator that encodes the compatibility structure. In the continuous limit, when $\mathcal{A}$ admits a realization as an effective elliptic operator and its spectrum is described by a spectral density $\rho(\lambda)$, the abstract functional $\mathcal{I}$ is rewritten as a geometric functional of the PESG type, but now interpreted as a consequence of universal action and episodic compatibility, rather than as an independent geometric principle.