Causal horizons—encompassing kinematic, gravitational, and cosmological event boundaries—are classically modeled in General Relativity as continuous, zero-volume mathematical abstractions permitting unbounded proper acceleration. This coordinate-dependent description induces severe non-local information loss, infinite mathematical divergences, and unphysical firewall paradoxes. This Letter provides a rigorous, non-circular operational proof demonstrating that causal horizons are discrete physical entities with an impassable minimum structural thickness equal to exactly one Compton wavelength. By deriving the horizon's properties from the closure of the local phase algebra under maximum metric strain, the Universal Law of Horizon Oscillation is systematically deduced. Crucially, we invoke the Strong Equivalence Principle to generalize this boundary condition as a covariant geometric invariant across all reference frames. This structural quantization resolves the 120-order-of-magnitude cosmological vacuum energy catastrophe as an applied boundary example, yielding a non-tuned density that precisely matches the order of magnitude of empirical observations, and provides a dynamic dark energy scaling framework that naturally reconciles the contemporary Hubble expansion tension.