Spatial-Material Continuum Theory: Complete Formulation

The complete formulation of the Spatial-Material Contin-uum (SMC) theory is presented, incorporating the attrac-tor mechanism through the parameter Ξ. The system ofequations with fixed parameters ω0 = 40000, α = 1/π,ℓc = α/H0 yields numerical solutions: H0 = 73.2 ± 0.5km/s/Mpc, w0 = −0.77 ± 0.02, S8 = 0.781 ± 0.015,a0 = 1.18 × 10−10 m/s2. The theory predicts a mod-ified Hubble parameter evolution: H2(a) = H20 [1 +β1−ΩmΩma−3Ωma−3+(1−Ωm) ] where β emerges from the attractordynamics. All predictions are derived without parameterfitting. Keywords: cosmology: theory – cosmology: parameters– gravitation – dark energy – dark matter – modified grav-ity