Integrated Application of Navier–Stokes, Ricci Flow, and EVA Frameworks for Modelling Systemic Risks, Shock Scenarios, and Resilience to Socioeconomic Challenges: The Case of Critical Railway Corridors

The paper presents a multifaceted analysis of the strategic impact of the Georgian railway corridor on the country’s economic development through an innovative synthesis of physical, mathematical, and financial modeling frameworks. Located on the Eurasian transit axis, the corridor is a critical artery for the flows of freight, capital, and innovation that underpin economic sustainability and regional competitiveness. Yet traditional macroeconomic approaches only partially capture these processes, while the systemic nature and diversity of corridor effects call for an integrated methodology, especially under mounting socioeconomic challenges such as energy-price volatility, external shocks, and shifting regional competition. The scientific novelty of the study lies in the simultaneous application of three advanced models: (1) economics-adapted Navier–Stokes equations to simulate operational flows and systemic risks; (2) a multidimensional Ricci Flow model to assess dynamics of economic inequality and structural transformation; and (3) an EVA (Economic Value Added) framework to analyze long-term value creation, investment efficiency, and capital allocation. Drawing on a multi-year dataset for the Georgian railway corridor, the empirical results indicate that modernization and operational efficiency are associated with higher liquidity velocity and lower residual risk; stress-testing reveals the corridor’s sensitivity to external shocks; Ricci Flow curvature maps parameters driving inclusion or polarization; and the EVA matrix indicates that a sustained annual growth rate of approximately 3% or more supports a positive EVA margin. Overall, the multi-model synthesis advances applied mathematical economics and offers a transferable methodology for evaluating complex infrastructure systems amid uncertainty and rapid technological change. Policy guidance centers on institutionalizing monitoring and stress-testing, prioritizing inclusion-enhancing parameters, optimizing investments, and strengthening resilience to socioeconomic challenges.