This work presents a unification of number-theoretic, geometric, and quantum gravitation through an adelic spacetime framework. We establish: (1) operator closure in recursive hypergeometric calculus. (2) Gromov-Hausdorff convergence of fractal spacetime limits. (3) empirical matches to gravitational wave data (GW150914), galactic rotation curves, and CMB anomalies. The framework eliminates dark matter requirements through dimensional feedback mechanisms while maintaining compatibility with standard quantum operator algebras.This work advances the unification of number theory, fractal geometry, and quantum gravity through a refined \textit{adelic spacetime} framework. Generalized Hypergeometric Operator Algebras with connections to Langlands reciprocity. Enhanced Fractal Convergence via prime-modulated Ricci flows. Machine Learning-Augmented Predictions for dark energy and quantum gravity. Experimental Proposals to test adelic spacetime via optomechanical quantum simulators. Empirical validations now include LIGO-Virgo O4 data, JWST galactic observations, and CMB-S4 simulations. The framework resolves the Hubble tension and eliminates dark sector dependencies through adelic dimensional reduction.