Non-Linear Mass Coupling in Galactic Rotation Curves: A Statistical Validation of Dissipative Vacuum Dynamics against the SPARC Catalog

This work presents Dissipative Information Topology (DIT) as a novel theoretical framework for explaining galactic rotational dynamics without invoking galaxy-specific dark matter halos in the investigated regime. Instead of compensating for kinematic anomalies through invisible mass halos, DIT models the vacuum as a dissipative, information-processing medium. Based on a formal  inversion in the ultraviolet limit and the application of relativistic Israel-Stewart hydrodynamics, an anisotropic vacuum stress tensor is derived, whose retarded dynamics induce an emergent radial binding tension. This macroscopic vacuum hysteresis leads to a non-linear mass coupling, which determines the fundamental acceleration scale of galactic systems.

The theoretical predictions are statistically validated against the SPARC (Spitzer Photometry and Accurate Rotation Curves) catalog. In the isolated topological core regime, the model achieves a logarithmic scatter of dex without galaxy-specific tuning parameters. Within this Core Sample, DIT achieves an accuracy comparable to the algebraic MOND benchmark and outperforms the fixed NFW proxy in the employed residual metrics. The results suggest that the Baryonic Tully-Fisher Relation (BTFR) does not necessarily indicate the existence of non-baryonic matter, but rather represents the direct macroscopic signature of a universal topological vacuum saturation.