Structural Rigidity in Public Budget Systems: A Graph-Theoretic Early Warning Framework for Governance Stability

This working paper introduces a quantitative governance-analytic framework for detecting structural rigidity in public budget systems. The study models fiscal governance as a multilayer directed network integrating decision authority, budget allocation, and information flow. Structural rigidity—conceptualized as progressive variance compression and centralization within administrative systems—is operationalized through a composite metric combining a Budgetary Centralization Index (λB), Structural Resonance Indicators (SRI), and a cryptographically enforced Early Warning Distributed Audit Chain (EWDAC). The framework distinguishes between resource scarcity and pathological singularization by measuring dispersion, approval-depth distribution, justification entropy, and override traceability. Empirical validation combines Monte Carlo simulation (N = 10,000 synthetic school-year environments) with a 24-month pilot dataset (N = 150 public schools across three administrative districts). Results demonstrate statistically significant early-warning lead-time advantages relative to conventional variance-based and latency-only audit heuristics. Classification performance for singularization detection achieves F1 ≥ 0.85, while cryptographic audit chaining eliminates untraceable override events (δ = 0). The methodological contribution lies in treating fiscal governance as a measurable network system rather than a purely procedural or performance-driven structure. The model integrates graph centralization metrics, distributed lag regression, interrupted time-series evaluation, and adversarial robustness testing. While the legal implementation of discretionary reform mechanisms remains jurisdiction-specific, the graph-theoretic diagnostic logic generalizes to other public-sector domains including healthcare administration, municipal finance, and procurement governance. All simulation seeds, pseudocode structures, and metric definitions are documented to ensure reproducibility. Version: Working Paper v1.0. Governance Analytics Public Financial Management Network Centralization Metrics Structural Rigidity Early Warning Systems Graph-Theoretic Modeling Fiscal Resilience Distributed Audit Chains Organizational Variance Compression Administrative Decision Networks