Space-Matter Continuum (SMaC) Paradigm: A Unified Theory with Formal Proof Protocol

10.5281/zenodo.183929The Space-Matter Continuum (SMaC) paradigm offers a unified description of gravity as a property of a single field ϕ. From the fundamental equation Geff(ρ) = G0/[1 −β(ρ/ρP )] with β = 1/(8π), it derives: (1) A cosmological model resolving H0, S8 tensionsand predicting w0 = −0.949 (fundamental regime) or w0 = −0.771 (comparison regime,matching DESI); (2) A fundamental scaling law for galaxies ℓ ∝ ρ−0.5eff , confirmed by SPARC data (β = 0.501±0.011, R2 = 0.973). The work includes a Formal Proof Protocol(FPP) with clear falsification criteria. Keywords: space-matter continuum, modified gravity, H0 tension, DESI, formalproof protocol