Yuanji Field Theory: Phase Synchronization† Origin of Gravity and Derivation of Gravitational Constant G

Based on the four core axioms of Yuanji Field Theory — the Transverse Wave Divergence-free Axiom, Phase Single-valuedness Axiom, Principle of Minimum Energy, and the standard deformation energy functional — this paper investigates the microscopic origin of gravity. This study demonstrates that gravity can be interpreted as the statistical emergence of the phase synchronization effect of the Yuanji Field, rather than an intrinsic geometric curvature property of spacetime, providing a novel explanatory paradigm for gravitational phenomena rooted in continuous field dynamics. This paper derives the analytical form of the dimensionless gravitational coupling constant αG, whose pre-factor is the fine-structure constant α (a universal feature of orthogonal topologies in the Yuanji Field framework), and whose statistical attenuation term is constrained by three independent mechanisms: three-dimensional geometric properties, discrete-continuum transition correction, and multi-path coherent transmission. The derivation of the gravitational constant relies exclusively on the intrinsic geometric parameters and statistical rules of the Yuanji Field, with no adjustable parameters fitted to experimental measurements. The theoretical value of the universal gravitational constant G derived in this work has a relative error of less than 0. 1% compared with the 2018 CODATA recommended value, showing excellent quantitative agreement. This work achieves full logical consistency between microscopic particle topologies and macroscopic gravitational effects, completing the final link for the unified explanation of the four fundamental interactions within the Yuanji Field theoretical framework.