The General Theory of Governance Engineering: A Mathematical Reconstruction of Regional Resource Cycles Based on SBCM v2.0

**[Consolidated Master Version: SBCM v2.0]**This document is the comprehensive "General Theory" of Governance Engineering, consolidating and updating the theoretical findings previously circulated in SBCM Note series #1–#8. --- ### AbstractThis paper proposes **Governance Engineering**, a fundamental reconstruction of regional resource management based on the physical laws of thermodynamics and fluid dynamics. We expose the **"Vacuum Fallacy"** in contemporary growth models—the assumption that information processing and governance can occur without physical cost. By redefining governance as "Social Computation," we apply **Landauer’s Principle** to demonstrate that any increase in intelligence (A) or system complexity results in a non-linear explosion of management entropy. By analyzing municipal financial settlements as thermodynamic sensor data, we provide empirical proof that the current centralized "Tokyo System" has reached its **"Heat Death"** limit, manifesting as a structural configuration of high-positive divergence (∇·J ≫ 0). To resolve this metabolic failure, we introduce the **G-Cart (Governance Cart) Protocol**, an algorithmic fluid control system that enforces **Impedance Matching** and **Mesh Refinement**. Central to this architecture is the **Physical Bill of Exchange (P-Bill)**, an autonomous negotiable instrument minted via verifiable physical telemetry (D_mass, D_energy, D_space), which architecturally prevents the desynchronization of digital signals and physical mass. This work moves beyond political rhetoric to offer an engineered path toward a sustainable, high-velocity regional survival circuit. ---**Keywords:** Governance Engineering, SBCM Field Theory, Entropic Elasticity, Landauer’s Principle, Administrative Hydraulics, G-Cart, P-Bill. **Source Code & Evidence:** https://github.com/SBCM-Alliance/core-theory/tree/main/General_Theory --- 日本語版はこちら https://github.com/SBCM-Alliance/core-theory/blob/main/General_Theory/01_%E7%B5%B1%E6%B2%BB%E5%B7%A5%E5%AD%A6%E3%81%AE%E4%B8%80%E8%88%AC%E7%90%86%E8%AB%96.