From PROTO to Gravity: A Density-Dependent Framework Bridging Galactic Dynamics and Cosmology

10.5281/zenodo.18140114 We present a comprehensive theoretical framework emerging from the empiricaldiscovery of a fundamental constant β = 1/(8π) in galactic dynamics. Analy-sis of 175 galaxies from the SPARC catalog reveals a universal scaling relation:(Vobs/Vbar)2 = 1 + β(ρbar/ρ∗), with βemp = 0.0398 ± 0.0012. This precise nu-merical coincidence motivates the central postulate of Density-Dependent Gravity(DDG): Geff(ρ) = G0/[1 − βρ/ρP ], where ρP denotes the Planck density. Fromthis single principle, we derive: (1) galaxy rotation curves without dark matter;(2) modified Friedmann equations producing effective dark energy with weff(z) ≈−0.95 + 0.30z/(1 + z); (3) natural resolution of the H0 and S8 tensions throughtime-varying gravitational coupling; (4) unique predictions testable with DESI, Eu-clid, and SKA data within 1-5 years. The framework is grounded in the ontologicalconcept of PROTO as the primal state from which spacetime and physical lawsemerge. Keywords: PROTO, dark matter, modified gravity, cosmological tensions, galaxydynamics, fundamental constants, emergent spacetime