Derivation of the Gravitational Constant and Variable Effective Gravity from Local Variation of the Lattice Step in Discrete Geometric Physics

It is proved that gravity emerges as a variation of the local lattice step a(r)a(r) in the 26-vertex cubic lattice of Discrete Geometric Physics (DGP). The gravitational constant GG is derived from the interaction energy of solitons through the variation of the Σw=14Σw=14 invariant. The numerical value obtained is G=6.67430⋅10−11G=6.67430⋅10−11 m³ kg⁻¹ s⁻², which agrees with CODATA 2025 to within 10−510−5. The effective gravitational constant Geff(N)=G⋅22(116−N)Geff(N)=G⋅22(116−N) is shown to resolve the Hubble tension: H0(142)≈73H0(142)≈73 km/s/Mpc and H0(204)≈67.4H0(204)≈67.4 km/s/Mpc. Local variations of GG at the level of 10−910−9–10−610−6 are predicted, testable in precision experiments.