REV Theory: The Minimal Law of Vacuum Response: Unifying Galactic Rotation via Hydrodynamic Constraint from LAF

• Abstract In his 1920 Leiden address, Albert Einstein argued that space-time cannot be physically defined in the absence of an underlying medium. Building upon this foundational insight, this paper introduces the REV model (Response of Energy of the Vacuum). Unlike passive particle-based models (Dark Matter) or purely geometric modifications (MOND), the REV framework treats the vacuum as a superfluid-like medium capable of local thermodynamic response under the Projected Baryonic Constraint (Cb). By analyzing a high-fidelity sample of 64 galaxies from the SPARC catalog, we identify and validate a Minimal Law of Vacuum Response. This universal empirical relation, supported by a strong Spearman correlation (ρ ≈ −0.85), directly links the observed velocity anomaly to the baryonic surface density. This effective hydrodynamic description unifies two dynamical regimes within a single relation with no galaxy-dependent tuning parameters: Saturation (K 1): In diffuse outer disks, the vacuum releases energy, sustaining flat rotation curves and naturally recovering the Baryonic Tully–Fisher relation. The dataset includes the theoretical Lagrangian formalism, the statistical validation, and the complete CSV data tables used to generate the results, suggesting that the so-called “missing mass” may instead represent the thermodynamic signature of a reactive vacuum.