Pressure-Mediated Gravity v9 (PMG v9) A Unified Superfluid Vacuum Framework for Galactic, Cluster, and Cosmological Dynamics

Abstract Pressure-Mediated Gravity v9 extends the superfluid vacuum framework of PMG v7 with three improvements derived from the v8 theoretical review. The complex scalar field Phi(x) = sqrt(rho_s) exp(i theta) is retained as the fundamental degree of freedom, with the laminar-turbulent transition now governed by a dimensionless Vacuum Reynolds Number R_v = |nabla Phi_b|/a0, replacing the phenomenological transition function f(k). In the turbulent regime (R_v > 1), the equation of state w = 1/2 for the vortex medium is derived from first principles via the transverse tension of quantized filaments in an isotropic vortex glass, solidifying the 5/2 gravitational lensing boost factor on a rigorous physical basis. The baryon-superfluid interaction is reformulated as a covariant derivative coupling L_int = -(beta/a0 rho_c) J^mu_b partial_mu theta, with manifest dimensional consistency. These amendments strengthen the Bullet Cluster and CMB predictions of PMG v7 without altering their quantitative values. Three falsifiable predictions are refined: a growing CMB amplitude excess (+0.7% to +5.8% from ell_1 to ell_5, detectable at ~8sigma with CMB-S4), a B-mode polarisation phase shift of pi/4, and environmental variation a0 proportional to H_local. A proposed resolution of the H0 tension via bulk vacuum viscosity is noted as a direction for Paper VIII but is not developed here pending a proper derivation.