Data and Replication Package for "Global Perelman-Ricci-Poincare-Inspired Inequality Diagnostics: Curvature, Entropy and Graph-Topological Modelling of Macro-Regional Pressure and Smoothing Capacity"

This dataset provides the complete data, methodological registry, results tables and replication-support materials for the study “Global Perelman-Ricci-Poincare-Inspired Inequality Diagnostics: Curvature, Entropy and Graph-Topological Modelling of Macro-Regional Pressure and Smoothing Capacity.” The package supports a mathematical-econometric and graph-topological diagnostic framework that interprets global inequality as a macro-regional pressure-smoothing system rather than as a single isolated inequality indicator. The framework is an economic analogue inspired by Perelman, Ricci-flow and Poincaré terminology. It does not claim to prove, test or replicate Perelman’s proof, the classical Ricci-flow theorem or the Poincaré conjecture. Instead, it translates their structural modelling logic into bounded economic diagnostics of inequality pressure, smoothing capacity, curvature-like deformation, entropy-like complexity, graph connectedness and macro-regional heterogeneity. The empirical architecture is based on ten macro-regional blocks observed over the 2010–2024 annual period, producing a balanced diagnostic panel of N = 150 region-year observations. The dataset includes sixteen stress-coordinate variables: income inequality, productivity, unemployment, investment rate, inflation, migration pressure, education, social mobility, trade infrastructure, capital-flow pressure, innovation activity, healthcare access, fiscal deficit, trade openness, social protection and technology access. These variables are transformed onto a common 0–100 pressure-oriented diagnostic stress scale, where higher values indicate greater pressure or weaker smoothing capacity. The package includes the Excel replication workbook and supporting machine-readable files covering the methodology and results architecture of the study. It documents the construction of the global inequality-pressure index, standardised stress coordinates, correlation-based economic metric tensor, Ricci-style component curvature, normalised Ricci-flow summaries, scalar-curvature path, Perelman-type F-functional and W-functional, graph Laplacian connectedness diagnostics, Betti numbers, Euler characteristic, cycle density, Ollivier-Ricci and Forman-Ricci network-curvature proxies, Ricci-surgery candidate rankings, counterfactual sensitivity tests, econometric validation layers, rolling forecast discipline, AR(1) benchmark comparison, Monte Carlo/bootstrap uncertainty bands, regional pressure and curvature change decompositions, crisis-year deformation rankings and final evidence-synthesis matrices. The package is designed to make the manuscript’s results transparent, reproducible and auditable. It includes non-empty structured worksheets and CSV files for methodology equations, algorithmic steps, variable definitions, table indices, figures metadata, results tables, QA checks, data dictionary, file manifest, citation metadata and Zenodo-ready documentation. The data should be interpreted as model-implied diagnostic evidence rather than as literal geometric invariants, unrestricted causal estimates or universal forecasting claims. This archive is intended for researchers working on inequality diagnostics, mathematical economics, macro-regional modelling, graph-topological economic systems, Ricci-flow-inspired economic analogues, econometric validation, constructed-index methodology and uncertainty-based stress diagnostics.