From Universal Galaxy Scaling to the Kryukova-Friedmann Equation: Space-Matter Continuum Theory (SMC) as a Solution to Cosmological Tensions

Modern cosmology faces systemic tensions, including the Hubble constantH0 discrepancy and anomalously low S8 parameter. We present the Space-Matter Continuum (SMC) theory, based on the principle of gravitationaltransmutation: Geff(ρ) = G0/[1 − (ρ/ρβ )], where ρβ = ρP /β is the crit-ical density and β = 1/(8π) is a fundamental dimensionless constant.This principle, derived from a triad of empirical discoveries in SPARCdata (bimodality at Planck density, universal scaling law Rd ∝ Σ−1/2b ,and β ≈ 1/(8π)), leads to a new cosmological equation—the Kryukova-Friedmann equation. It predicts H0 = 73.2 ± 1.4 km/s/Mpc (consistentwith SH0ES), dynamic dark energy (w0 ≈ −0.95, wa ≈ −0.30, consistentwith DESI), and reduced S8, while simultaneously explaining galaxy rota-tion curves without dark matter. The theory makes a series of stringent,quantitatively testable predictions for DESI, Euclid, lunar laser ranging,and binary pulsar observations, forming a falsifiable alternative to theΛCDM model. 10.5281/zenodo.18234476 Keywords: cosmology, modified gravity, galaxy scaling, Kryukova-Friedmann equation,space-matter continuum (SMC), H0 tension, dark energy, Planck density.