SDRIS: The Unity of Fields - Deriving the Optical Metric from the Hydrodynamic Limit of the Recursive Vacuum

The Static-Dynamic Recursive Information Space (SDRIS) framework has successfully modeled galactic rotation curves via vacuum hydrodynamics (Paper 57) and gravitational lensing via an optical metric (Paper 105). However, these two descriptions—one dynamic and viscous, the other static and refractive—appear formally distinct. In this paper, we provide a rigorous consistency proof unifying these approaches. We demonstrate that the Optical Refractive Index $n(\mathbf{x})$ derived in General Relativity is physically isomorphic to the Effective Viscosity $\eta(\mathbf{x})$ of the recursive vacuum in the stationary, low-Reynolds limit. Key Results: Viscosity-Refraction Duality: We derive the linear response relation $n(\mathbf{x}) \approx 1 + C \cdot \eta(\mathbf{x})$, proving that "spacetime curvature" and "fluid viscosity" are dual descriptions of the same underlying information density. The Laminar Limit: The paper interprets the Schwarzschild metric as the "frozen" laminar limit of a dynamic vacuum flow ($Re \to 0$). Numerical Verification: Includes a Python simulation demonstrating how a turbulent "Dark Matter" viscosity field converges exactly to the static $1/r$ optical metric when fluctuations are suppressed. Implication: This result reduces the free parameters of the theory, establishing that Gravity (Statics) and Dark Matter (Dynamics) are not separate entities, but different hydrodynamic modes of the same recursive substrate. Includes: Mathematical Proof of the Equivalence Theorem. Python Simulation Code (107_18130770_Maier_Lutz_SDRIS_Consistency_Simulation.ipynb) visualizing the convergence of turbulence to geometry.