Relational Wave Cosmology: An Exact Self-Interacting Vacuum Solution for the Rotation Curves and Virial Masses of Disk Galaxies

Abstract (English) We derive the equilibrium rotation curve of disk galaxies from the Relational Wave Cosmology (COR), a field theory in which space-time geometry and gravitational phenomena emerge from the dynamics of a complex scalar field with intrinsic memory. Under the assumptions of static spherical symmetry, the field equation reduces to the Lane--Emden equation of index n=5, whose analytic solution is the Schuster--Emden profile. Through the core hypothesis of relational densification (rho_r proportional to |Phi|^2), this amplitude profile produces a circular velocity that rises linearly in the inner region and asymptotically approaches a constant value — a flat rotation curve. We show that the resulting velocity function is virtually identical to the phenomenological CVR-K model, fitting 115 SPARC disk galaxies with a decisive AIC/BIC preference over the standard NFW halo. Furthermore, by imposing a virial boundary condition tied to the cosmic critical density, the COR predicts halo virial masses M_200 and an internal Tully--Fisher scaling. The COR thus provides a first-principles explanation of galactic dynamics without invoking particulate dark matter. Bundle Contents (Reproducibility):- LaTeX manuscript (main.tex)- SPARC dataset files and MRT/TXT tables- Python analysis pipelines (benchmark_cor_native.py, calculate_virial_cor.py, plot_virial_scaling.py)- Diagnostic plots and README instructions