Andrei Sakharov (1967) proposed that gravitation is not fundamental, but an emergent“metric elasticity” of the vacuum reacting to spacetime deformation. His theory, however,relied on an unexplained ultraviolet momentum cutoff (k0). We demonstrate that thiscutoff is the precise physical manifestation of the Representation Boundary Principle: thegeometric limit where continuous representations fail and must be replaced by an orthogonalprojection Π onto an admissible manifold M. We formalize this by defining a universalstructural strain functional S[Ψ] = ∥(I − Π)Ψ∥2. Utilizing a variational action principle,we prove the Representation Elasticity Principle, establishing that macroscopic physicalforces (like gravitation) are the geometric restoring dynamics driving the vacuum towardthe unique zero-strain topological state. The Deterministic Spectral Manifold (DSM-861)and the Riemann Hypothesis are subsequently presented as explicit arithmetic realizationsof this generalized elasticity theory.