A Covariant Viscoelastic Spacetime Origin of the Galactic Acceleration Relation (Spacetime Elastic Hysteresis Theory Part 1:)

Note: This is an earlier draft. For the latest finalized manuscript, please visit: https://zenodo.org/records/18680896 We propose the Spacetime Elastic Hysteresis Theory, a novel scalar-tensor framework that models spacetime as a physical viscoelastic medium possessing intrinsic stiffnessand memory. Central to this framework is a constitutive relation we term ’Kim’s Law’(V (ψ) = 12κψ2), which posits that the vacuum energy density is proportional to the squareof the macroscopic entanglement strain. Here, ’Kim’s Constant (κ)’ represents the BulkModulus of spacetime. By deriving the Kim Tensor (Kµν), we demonstrate that the gravitational effects typically attributed to Dark Matter arise instead from the elastic stress ofthe spacetime lattice. Our MCMC numerical analysis, based on Planck 2018 and SH0ESdata, yields an effective elastic density fraction of κeff ≈ 0.182 and implies a recalibratedcosmic age of approximately 16.54 Gyr. This framework provides a unified, non-particulateexplanation for flat galactic rotation curves and the baryonic Tully-Fisher relation.