Phase-5 Global Closure: Time-Gradient Curvature and the Geometric Origin of Newton's Constant

Phase-5 Global Closure develops the global stage of the protected constrained-null geometry program. The paper extends the Phase-4 protected scalar response sector to a global realization field and derives gravity as a time-gradient effect of the local realization lapse. The construction proceeds from protected scalar response to global response field, local time measure, static source law, metric completion, connection, curvature, and first-loss exterior geometry. In the weak-field limit the theory recovers the Newtonian acceleration law, gravitational redshift, light bending, Shapiro delay, and perihelion shift. The strong-field exterior is obtained as the finite first-loss completion of the protected global time-response field and gives the Schwarzschild exterior. The main result is a closed geometric expression for Newton’s gravitational constant. The derivation reduces the gravitational coupling to a protected boundary action density. The boundary patch is obtained from the spinor-admissible radial projection of one electron closure volume onto the global first-loss boundary. The protected channel count gives the geometric matter-response share 6/19, the spinor first-loss guard gives 27/26, and the global transfer operator gives the geometric closure rate H0. The final closed formulas contain no fitted value of G, no external H0, and no adjustable numerical coefficient. The numerical certificate gives H0_geom = 67.342436809647 km s^-1 Mpc^-1 G_geom = 6.674295559935318 x 10^-11 m^3 kg^-1 s^-2 G_geom / G_obs = 0.999999334752 relative error = -6.65248 x 10^-7 difference from CODATA G = -0.02960 sigma_G The supplementary archive contains the notebook and CSV files used to reproduce the numerical certificate. The notebook evaluates only the closed formulas stated in the paper. It does not fit G, does not fit H0, and does not introduce a free numerical coefficient. Included supplementary files: phase5_final_closure_audit_certificate_v1.ipynb phase5_final_closure_results.csv phase5_final_proof_audit.csv phase5_final_formulas.csv phase5_final_closure_inputs.csv phase5_alternative_patch_scalings.csv