Finite-Capacity Completion of the Einstein Field Equations A Causal, Stable, and Lorentz-Covariant Constitutive Closure

We present a completion of the Einstein field equations in which the geometrical structure of General Relativity is left entirely unchanged, while the dynamical closure between spacetime curvature and physical content is specified by a finite-capacity, finite-memory vacuum response. The vacuum is treated as a physical response medium characterized by a microscopic relaxation time tau and a saturation capacity time tau_cap, both fixed independently in the electroweak and leptonic sectors. The completion is formulated as a local constitutive relation defining an effective energy-momentum source, governed by a universal demand variable X (accumulated causal step time along a response channel). The resulting formulation is local, causal, linearly stable, Lorentz covariant, and recovers classical General Relativity in the linear-response limit. No new fields, particles, or adjustable parameters are introduced, and operator-level, sign-definite falsifiability conditions are obtained.