Geometric Origin of Dark Matter and Dark Energy and Its Observational Verification

This paper proposes a geometric framework based on three-dimensional spatial curvature evolution (GDUT) and independently derives the cosmic expansion rate. Calculations show that, after considering the volume correction of the visible universe and the equivalent mass conversion of expansion energy, the local prediction of the Hubble constant is approximately 77.9 km/s/Mpc, while the SH0ES local measurement is 73.0 ± 1.0, and the CMB-derived global value is 67.4 km/s/Mpc. In the Milky Way, for r > 10 kpc, the rotation velocity converges to ∼ 212 km/s; the angular separation between the mass center (gravitational lensing) and the X-ray gas center in the Bullet Cluster collision is approximately 38 arcseconds. The predictions for galaxy rotation curves and Bullet Cluster separation are in significant agreement with observations; the deviation of the Hubble constant prediction from the local measurement (SH0ES) is about 6.7%, attributed to the systematic underestimation of visible volume and total mass by the standard model; the dynamical evolution features of dark energy are consistent with DESI observational trends within specific model frameworks, though the exact numerical values depend on modeling details of the curvature release flux. Overall, the GDUT framework provides a self-consistent geometric interpretation for dark matter and dark energy, though the verification degree varies across different phenomena. Starting from fundamental axioms of three-dimensional spatial evolution, this framework derives a modi fied Ricci flow equation through rigorous mechanisms, thereby reproducing the Hubble tension, independently predicting galaxy rotation curves and dark energy fractions without invoking dark matter particles, and nat urally producing dynamical dark energy evolution features consistent with observations. This paper aims to demonstrate that dark matter and dark energy can be uniformly understood as inevitable consequences of spatial curvature evolution.