THE METRIC ELASTICITY OF THE HYDRODYNAMIC VACUUM

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 this
cutoff is the precise physical manifestation of the Representation Boundary Principle: the
geometric limit where continuous representations fail and must be replaced by an orthogonal
projection Π onto an admissible manifold M. We formalize this by defining a universal
structural strain functional S[Ψ] = ∥(I − Π)Ψ∥2. Utilizing a variational action principle,
we prove the Representation Elasticity Principle, establishing that macroscopic physical
forces (like gravitation) are the geometric restoring dynamics driving the vacuum toward
the unique zero-strain topological state. The Deterministic Spectral Manifold (DSM-861)
and the Riemann Hypothesis are subsequently presented as explicit arithmetic realizations
of this generalized elasticity theory.