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

In his 1920 Leiden address, Albert Einstein argued that space-time cannot be physically defined in the absence of an underlying medium. Motivated by this perspective, this work explores the possibility that galactic rotation anomalies may be interpreted as an effective response of the vacuum rather than as evidence for unseen matter components.We introduce the REV framework (Response of Energy of the Vacuum), in which the vacuum is treated phenomenologically as a medium capable of exhibiting a collective, hydrodynamic-like response under baryonic constraints. Using a high-quality sample of 64 galaxies from the SPARC catalog, we investigate the empirical relationship between the observed velocity discrepancy and the baryonic surface density.The analysis reveals a strong monotonic correlation between these quantities, suggesting the existence of two distinct dynamical regimes within a single phenomenological description: a saturation regime in dense galactic cores, where the effective response is suppressed, and a lift regime in diffuse outer regions, where the velocity discrepancy is enhanced. These regimes recover, at an effective level, several well-known galactic scaling relations, including the baryonic Tully–Fisher relation.The dataset includes the statistical analysis, the associated phenomenological formalism, and the complete CSV tables used in this study. While no fundamental mechanism is claimed, the results indicate that part of the so-called “missing mass” phenomenology can be consistently described as an emergent, thermodynamic-like response of the vacuum to baryonic structure.