Invariant vacuum crossover and emergent gravity: Scalar-tensor EFT with non-linear kinetics, disformal metric and no-slip lensing

We propose an effective field theory (EFT) in the gravitational sector where the galactic acceleration discrepancy arises as an invariant environmental crossover of the vacuum, described by a scalar field with non-linear kinetic structure and disformal coupling to matter. The crossover is not implemented through ad-hoc "environment filters", but through fundamental Lorentz scalars built from the matter sector. In particular, the trace T≡ gμνTμν⁽ᵐ⁾ controls (i) a density-dependent effective mass meff(T) that freezes the field in dense media and (ii) the activation/suppression of the MOND-like kinetic term through a T-dependent coupling. In the galactic regime, the non-linear kinetic term yields Φ^∝1/r under spherical symmetry, generating flat rotation curves and the baryonic Tully-Fisher relation. To ensure lensing consistency without fine tuning, we impose an algebraic no-slip condition linking disformal and conformal parts and guaranteeing Ψeff=Φeff at post-Newtonian order. The model is stable (no ghosts/gradient instabilities in the k-essence sector) and suggests as an observational signature a scaling estimate for environmental truncation of effective halos, Rc∝√Mbσₑₙᵥ⁻¹.