Structural Vacuum Deformation and Emergent Classical–Quantum Limits

We propose a “structural vacuum” in which gravitation and effective spacetime geometry arise from deformation of a real physical medium described by a density field
ρ(x) and a rigidity λ(x, t). Matter corresponds to confined deformation; gravity to extended relaxation of ρ around defects; and radiation to internal gauge-field excitations
propagating on a stable background. A compact covariant action yields (i) a Poissonlike Newtonian limit for static weak deformations, (ii) an emergent Einstein sector at
elastic equilibrium, and (iii) a clean linearized regime reproducing Klein–Gordon and Schrödinger kinematics. A multiscale rigidity profile λ(r)
yields Newtonian gravity at short distances, MOND-like galactic dynamics at intermediate scales, and an effective late-time acceleration without inserting a fundamental cosmological constant. We highlight falsifiable signatures: mild drifts in G eff and c and possible birefringence from constitutive vacuum response.