The Hypermorphic Gearbox and RH Pressure A Jensen Sturm Certificate Architecture for Riemann-Hypothesis Forcing, Obstruction, and Cumulant-Chamber Reduction

This paper presents the Hypermorphic Gearbox as a conditional proof architecture for studying the Riemann Hypothesis through Jensen polynomials, Sturm certificates, Hermite stability, and cumulant-chamber reduction. The work does not claim to prove the Riemann Hypothesis. Instead, it develops a structured framework for organizing several RH-equivalent and RH-adjacent routes. The local “RH pressure” approach is formalized using band-limited test functions, Taylor-jet prime annihilation, and conditional local-bin exclusion theorems, while also identifying genuine leakage, derivative, and bounded-complexity obstructions. The main global route reformulates the problem through corrected Riemann-kernel moment sequences, normalized Jensen polynomials, Gearbox curvature states, and Hermite/Sturm hyperbolicity chambers. Exact symbolic chamber reductions are derived for degrees 2, 3, and 4, where the first gates correspond to variance, skewness, and kurtosis-type constraints for tilted Riemann-kernel measures. The paper also proposes an all-order saddle-cumulant domination mechanism as a sufficient closure principle. The remaining open object is a Riemann-specific uniform all-degree analytic inequality controlling the non-Gaussian cumulant remainder by a Hermite stability radius outside a finite Sturm-certified region. This draft is intended as a rigorous independent research record, obstruction audit, and certificate architecture for future work on the Jensen–Pólya route to RH.