Non-Newtonian Vacuum: Galaxy Rotation Curves as a Rheological Measurement of Spacetime

We show that the MOND interpolating function μ(x) = x/√(1+x²) is identical to the constitutive equation of a viscoelastic medium with frequency-dependent stiffness, where τ = c/a₀ is the vacuum relaxation time. This identification — to our knowledge, not previously noted in the literature — reinterprets MOND not as a modification of gravity but as the rheological response of the vacuum medium introduced in Groysman (2026). Using the AQUAL formulation, we test the Cross model family against the full SPARC database (175 galaxies, 3391 data points). Cross n=1.0 provides the best fit with fixed mass-to-light ratio (RMS = 0.199 dex vs 0.204 for standard MOND); with optimized M/L per galaxy, both models achieve RMS ≈ 0.08 dex — statistically indistinguishable. The physical content is not that Cross beats MOND but that it explains MOND: the interpolating function has a derivation from material science. The optimal n ≈ 1 reproduces the baryonic Tully-Fisher relation exactly. All tested models predict zero photon dispersion at gamma-ray energies, consistent with Fermi-LAT observations, while predicting inverse vacuum dispersion (Δc/c ∝ E⁻ⁿ) — distinguishable from standard quantum gravity predictions (Δc ∝ +E) by both sign and functional form. We further show that viscoelastic fluids that shear-thin automatically strain-harden in extension, producing a Trouton ratio of ~49 at the Hubble rate — resolving the long-standing puzzle of why MOND works for galaxies but not for cosmology, with no additional parameters. Source code for all analyses is provided.