A minimal propagation criterion for gravitational waves in an emergent vacuum

This note presents a minimal and conservative criterion for gravitational-wave propagation within an emergent-vacuum framework. Without modifying the Einstein field equations or introducing additional propagating degrees of freedom, the vacuum is treated phenomenologically as an effective medium only at the level of wave propagation. The central result is a single falsifiable statement: if intrinsic dispersion of gravitational waves arises from underlying vacuum microstructure, a correlated, frequency-dependent attenuation must also be present, as required by causality. The observation of one effect without the other would rule out a viscoelastic interpretation of the vacuum. Microscopic processes, such as particle–antiparticle annihilation, are discussed solely as illustrative analogies for internal relaxation mechanisms and are not proposed as sources of observable gravitational radiation. This work is intended as a conceptual closure of the framework developed in preceding publications and does not aim to extend it further.