Global Hodge-Econometric Modeling of the World Economy: A Regional Benchmark Prototype for Topological Flow Decomposition, Systemic Circulation, Shock Transmission, and Macroeconomic Resilience

This study develops a regional benchmark and proof-of-concept Hodge-econometric framework for measuring the world economy as a connected topological macro-flow system rather than as a set of isolated output aggregates. Using official public macroeconomic anchors--regional GDP, world-output share, projected growth, transition GDP, and income depth--the study constructs a weighted regional network of ten global macro-regions, with the World used as a normalization anchor and the Caucasus retained as an explicit corridor-sensitive subregional node. The methodology is quantitative, non-experimental, computational, and validation-oriented: it combines gravity-style network construction, directed macro-flow pressure, discrete Hodge decomposition, spectral and higher-order Hodge-Laplacian diagnostics, robust econometric testing, machine-learning forecast validation, and persistent-homology confirmation. The central novelty is the transformation of standard macroeconomic indicators into a decomposable edge cochain, allowing regional hierarchy, local-cycle imbalance, harmonic systemic circulation, shock-transmission exposure, resilience, and tail risk to be measured within one coherent empirical architecture. The regional benchmark shows that the constructed graph is connected and cycle-rich, with 10 nodes, 27 edges, a density of 0.600, and a transitivity of 0.740. The Hodge energy decomposition separates macro-flow pressure into gradient hierarchy (49.69%), curl/local-cycle imbalance (36.22%), and harmonic/systemic circulation (14.09%), indicating that global-regional structure is not reducible to GDP size alone. Econometric, predictive, and topological tests are used as internal benchmark-validation diagnostics, not as final causal estimates for all countries or observed dyadic flows. The study therefore contributes a reproducible measurement architecture for international macroeconomic analysis and is best understood as a mathematically grounded prototype for future all-country, dyadic, multilayer, and longitudinal replication.