Topological Dynamics of Gravitational and Electromagnetic Interactions via Spatial Superfluid Tensors: Covariant Field Equations and Geometric Resolution of the Large Number Hierarchy (Version 3.0)

Update in V3. 0 Update in V2. 1: This version introduces the Manifest Control Theory matrix (C_) and mathematically resolves four major Standard Model anomalies (including Muon g-2 and Casimir deviations) strictly through spacetime fluid hydrodynamics. For a long time, the precise measurement of the gravitational constant G has been plagued by systematic discrepancies between different experimental methods. This paper investigates a hydrodynamic approximation model for describing gravitational and electromagnetic interactions via covariant fluid tensors, termed Spiral Space Dynamics (SSD). By introducing the hypothesis of a continuous and compressible spatial medium and treating matter particles as topologically correlated structures within this medium, this paper attempts to establish an analytical framework based strictly on classical mechanical parameters. Without introducing additional phenomenological parameters, this model utilizes background fluid density (ₛ), bulk modulus (K), and topological coupling parameters to theoretically derive the physical origins of the gravitational constant (G), vacuum permittivity (₀), and vacuum permeability (₀). This dynamical approach not only offers a potential systematic explanation for the 45 ppm discrepancy observed in dynamic gravitational measurements, but also provides an algebraic perspective based on topological geometric scaling for the 10^42 hierarchy problem. Furthermore, this paper discusses the equivalent form of the Schwarzschild metric in the acoustic fluid limit, derives the hydrodynamic dynamic pressure superposition effect for the gravitational lensing deflection angle, and preliminarily analyzes the topological correspondences of fermion spin and quantum entanglement phenomena. This study aims to provide a new theoretical reference for exploring the dynamical connection between macroscopic physical interactions and the underlying vacuum medium.