Spectral Log-Stiffness of the Gravitational Vacuum: A Constitutive Framework for Emergent Acceleration

This work proposes a constitutive interpretation of the gravitational vacuum in which spacetime is treated as a carrier medium characterized by bulk and deviatoric response modes. Within this framework the emergence of a characteristic acceleration scale is shown to follow from a stability condition of the carrier rather than from additional matter components. A simple spherically symmetric toy model demonstrates how a critical scale can arise from the constitutive properties of the vacuum response. The goal of the paper is not to provide a microscopic theory of the vacuum, but to isolate the macroscopic mechanism through which such an emergent scale may appear.