Unifying Galactic Dynamics and Cluster Collisions via a Phase-Transitioning Vacuum Fluid

This work presents an effective hydrodynamic framework modeling the galactic dark sector as a barotropic fluid in hydrostatic equilibrium within standard General Relativity. The model yields a pseudo-isothermal density profile characterized by two free parameters per galaxy (Vᵢnf, rₛ), with all baryonic inputs held fixed across competing models. Validated against 165 galaxies from the SPARC database under a fixed mass-to-light ratio protocol, the framework achieves a median R² = 0. 961, compared to 0. 924 for NFW and 0. 791 for MOND under identical fitting conditions. The model naturally produces cored density profiles (inner slope γ = −0. 020), recovers the Baryonic Tully-Fisher Relation (r = 0. 80, p = 1. 70 × 10⁻³³), and achieves per-galaxy Radial Acceleration Relation scatter of 0. 092 dex, approaching the observed inter-galaxy floor of ~0. 13 dex. Solar System deviations remain below 10⁻¹³ km/s without any screening mechanism. Cosmological consistency requires a phase transition at zc ≈ 1240, from which three independent microphysical calculations converge: a scalar boson mass m ≈ 0. 875 eV/c², a primordial Jeans mass of ~10⁷ M⊙ matching the observed dwarf galaxy scale, and a falsifiable scale-radius power law rₛ ∝ (1 + zform) ⁻³/² testable with JWST. The framework spans eight orders of magnitude in mass, from dark-matter-deficient galaxies to the Coma Cluster, and passes 20 independent validation tests.