Entropy–Concentration Diagnostics for Indian State Finances Using Arithmetic Power Geometry: A Reproducible Study Based on CAG State Finances Data (2013–14 to 2022–23)

Indian state finances are commonly evaluated using revenue, expenditure, deficit, debt, and guarantee indicators. While these measures provide essential information for fiscal assessment, they primarily examine individual fiscal components and do not directly quantify the structural concentration of an entire state-year fiscal profile. This study introduces a reproducible entropy–concentration diagnostic based on the empirically applicable weight construction of Arithmetic Power Geometry (APG). Using a machine-readable dataset derived from the Comptroller and Auditor General (CAG) of India covering 28 Indian states from 2013–14 to 2022–23, each state-year fiscal profile is represented as a positive six-component vector consisting of revenue receipts, revenue expenditure, capital expenditure, committed expenditure, public debt plus public account liability, and outstanding guarantees. APG squared normalization transforms these vectors into probability weights from which Shannon entropy, normalized entropy, maximum concentration, dominant fiscal component, and the composite APG Fiscal Concentration Index (AFCI) are computed. The master dataset contains 280 state-year records, of which 279 complete positive profiles are used for APG computation. The analysis reports a mean normalized entropy of 0.647, mean APG concentration of 0.529, and mean AFCI of 0.441. The all-state mean AFCI increased from 0.409 in 2013–14 to 0.468 in 2022–23, reaching its highest value during 2020–21. High-concentration profiles are predominantly associated with liability-related fiscal components. Validation against established concentration measures, including the Herfindahl–Hirschman Index, Simpson diversity, and the Gini coefficient, demonstrates strong agreement, while robustness analyses show that state rankings remain stable under alternative fiscal-vector specifications. The proposed APG framework is intended as a transparent, interpretable, and reproducible structural diagnostic that complements, rather than replaces, conventional fiscal indicators. The accompanying dataset, source code, and analysis workflow support fully reproducible computational public finance research.