The Spatial-Material Continuum (SMaC) Paradigm: A Unified Framework from Fundamental Principle to Cosmological and Galactic Predictions

10.5281/zenodo.18391878 The Spatial-Material Continuum (SMaC) paradigm presents a unified frameworkwhere gravity emerges as a property of a unified spatial-material field ϕ. From theempirical law β = 1/(8π) derived from 175 SPARC galaxies (βexp = 0.501 ± 0.011,R2 = 0.973), we derive the state equation Geff(ρ) = G0/[1 − β(ρ/ρP )]. The theorypredicts without free parameters: H0 = 73.2 ± 0.5 km/s/Mpc (0.2σ from SH0ES),w0 = −0.949 ± 0.02 (fundamental prediction) or w0 = −0.771 ± 0.02 (in ΛCDMparametrization, matching DESI), and S8 = 0.781 ± 0.015 (0.8σ from KiDS). AFormal Proof Protocol with binary falsification criteria is provided. All code anddata are publicly available. Keywords: cosmology, modified gravity, Hubble tension, S8 tension, galactic dynam-ics, scaling laws, SPARC, falsifiability License: Creative Commons Attribution 4.0 International (CC BY 4.0)DOI: 10.5281/zenodo.14671512Status: Preprint