Mathematical Global Domain Proof of Equivalence Between FQ Graviton Fluid Pressure Difference Field and General Relativity Metric System

Abstract General relativity describes gravity through the metric tensor g_{\mu\nu} and geodesic equations within the Riemannian geometric framework, achieving high-precision consistency with observational results such as Mercury’s perihelion precession, gravitational light deflection, gravitational redshift, and satellite time dilation. However, this framework generates divergent infinite curvature singularities in the central region of black holes and the dense initial state of the universe, resulting in the failure of physical validity. Based on the established axiomatic system of FQ unified field theory without introducing new assumptions, this paper conducts weak-field steady-state expansion on the background pressure P_0, background number density \rho_0, and mass shielding cross-section S(M) of the FQ graviton fluid. It is proven that the spacetime metric of general relativity is mathematically equivalent to the pressure gradient and density gradient distribution of graviton fluid, and geodesic motion is equivalent to the momentum transport trajectory of objects along the path of least resistance in the fluid pressure difference field. Under weak-field spherically symmetric conditions, the FQ algebraic model can directly reproduce the observational values of three classical tests of general relativity. In the strong-field dense limit, the FQ fluid automatically converges to a finite saturation density \rho_{\text{sat}} via the compression stiffness saturation mechanism, with globally smooth field equations and no infinite singularities. This paper does not negate general relativity, but realizes the underlying takeover of its mathematical formalism: geometry is appearance, and fluid pressure difference is ontology.