SBCM Field Theory: The General Equations of Regional Flux and the Control of Divergence ― From Meso-Economics to "Administrative Hydraulics": The Continuity Equation of Wealth ― Abstract In the previous studies (Part 1-3), we defined the "Standard Block" as a discrete unit and analyzed the "Distortion" and "Leakage" of administrative measures. However, real-world economy behaves not as rigid blocks, but as a continuous fluid field where wealth flows, accumulates, and dissipates. This study introduces the "SBCM Field Theory," which applies the Continuity Equation of physics to regional economics. By defining the Economic Density (ρ) and Economic Flux (J), we derive the "Governing Equation of Regional Survival." The mathematical analysis reveals that the "Straw Effect" is equivalent to the positive divergence (∇・J > 0) of the economic vector field. We prove that without algorithmic flow control (G-Cart Protocol) to enforce Mesh Refinement of budget injection, any large-scale fiscal stimulus thermodynamically results in vacuum decay (economic collapse) of the local region. Key Concepts: Administrative Hydraulics Continuity Equation of Wealth Leakage Rate Theorem G-Cart Protocol (Flux Controller)