Global Riemann-Zeta FPAS+ζ Inflation Forecasting: Layered Validation of a Hybrid Structural-Spectral Model for World Macroeconomic Pressure

This study develops and empirically audits a Global Riemann-Zeta FPAS+ζ inflation-forecasting framework for world aggregate inflation. The model augments a structural FPAS baseline with a normalized Riemann-zeta critical-line cyclical signal transformed into a signed and alpha-calibrated forecast correction. The Riemann-zeta function is used only as an analogical and computational cyclical signal, not as a proof, test, or verification of the Riemann Hypothesis. The empirical architecture is layered: the principal annual validation layer covers 1970-2024 (N = 55), the annual robustness layer covers 1980-2024 (N = 45), the compact crisis-era annual comparison layer covers 2005-2024 (N = 20), the quarterly dynamic-validation layer covers 2000Q1-2024Q4 (N = 100), and the monthly spectral-diagnostics layer covers 2005M1-2024M12 (N = 240). The methodology constructs a composite global inflation-pressure index, a nonlinear macro-financial tau argument, a normalized zeta-cycle, a zeta deviation from neutrality, and an alpha-weighted FPAS+ζ forecast. Forecast performance is evaluated against FPAS and ARIMA through RMSE, MAE, sMAPE, rolling no-look-ahead validation, Mincer-Zarnowitz calibration, forecast-encompassing tests, Diebold-Mariano and Clark-West comparisons, residual diagnostics, HMM/Markov-switching regimes, Fourier/wavelet coherence, and spectral-entropy screens. The corrected results show that FPAS+ζ improves the reported forecast hierarchy: in the N = 55 annual layer, RMSE is 0.421 compared with 0.612 for FPAS and 1.081 for ARIMA; in the N = 45 robustness layer, RMSE is 0.398 compared with 0.578 and 0.983; and in the N = 20 crisis-era layer, RMSE is 0.233 compared with 0.443 and 1.913. Zeta deviations, composite pressure, F_zeta, W_zeta, and regime diagnostics concentrate around the 2008 global financial crisis, the 2020 pandemic shock, and the 2022 energy-food-monetary tightening shock. The contribution is a bounded mathematical-econometric forecast-diagnostic architecture for global inflation modelling; it does not claim theorem proof, unrestricted causality, residual-problem elimination, or universal forecast dominance across all economies, samples, and horizons.