A fundamental fact of physics is that the physical reality we can observe must be a result of statistical coarse-graining. This work seeks the ultimate origin of this empirical necessity within the fabric of spacetime itself. We postulate that the underlying structure of the macroscopic physical world is an infinite and continuous spacetime manifold (M, g). Its dynamics are governed by two geometrized first principles: the conservation of energy, guaranteed by the existence of a timelike Killing vector field (Axiom I, Noether's Theorem), and the asymptotic stability of equilibrium states against perturbations (Axiom II, Lyapunov Stability).From these axioms, we prove that the linear response function Φ(t) of spacetime must be completely monotone (Bernstein's theorem), implying that its relaxation is a superposition of myriad exponential decay modes. In the simplest model describing the coupling of two local spacetime degrees of freedom, this mathematical necessity manifests concretely in only four fundamental response modes: (I) pure exponential relaxation, (II) damped oscillation, (III) strictly conserved behavior, and (IV) critical power-law dynamics.It is a profound insight that these four modes, originating from the intrinsic stability of spacetime geometry, correspond precisely to the characteristic behaviors of the four fundamental interactions in nature. Electromagnetism, the weak and strong forces, and gravity can all be understood as different macroscopic phases exhibited by the same spacetime geometric entity—different responses emerging from a "change" in the perturbation paths under varying conditions of symmetry and energy scale. This paper argues that the four fundamental forces we observe may not be independent physical entities, but rather different macroscopic patterns emerging from the statistical coarse-graining of spacetime's microscopic perturbation paths.This study derives, for the first time from a purely Riemannian geometric framework and its inherent axioms, the prototypes of all known interactions, providing a new cornerstone for the construction of a fully geometrized unified theory.