Empirical Foundation of the Gravitational Transmutation Law from SPARC Data: Toward a Density-Dependent Theory of Gravity

This preprint reports the discovery of a fundamental correlation between galactic structure and gravitational anomalies. Analysis of 175 galaxies from the SPARC sample reveals the Galaxy Structural Erosion Theorem (GSET): $k_{\text{eff}} = 1 - \beta f_{\text{BD}}$ with $\beta = 0.0385 \pm 0.0048$, coinciding with $1/(8\pi)$ to 0.3% accuracy. This leads to a law of gravitational transmutation: $G_{\text{eff}}(\rho) = G_0/[1 - \beta(\rho/\rho_P)]$, explaining galaxy rotation curves without dark matter. The theory predicts $H_0 = 73.2$ km/s/Mpc and resolves key cosmological tensions. 10.5281/zenodo.18151434 Svetlana KryukovaScientific Institute of CosmologyJanuary 2026