An Effective d^3-Scale Criterion for the Hyperbolicity of Jensen Polynomials Associated with the Riemann ξ-Function

This preprint investigates an effective d^3-scale criterion for the hyperbolicity of Jensen polynomials associated with the Taylor coefficients of the Riemann ξ-function. The work builds on the normalization framework of Griffin, Ono, Rolen, Thorner, Tripp, and Wagner and develops a Poisson–Gaussian generating-function approach combined with Hermite polynomial comparison. The manuscript presents a route from the normalized Jensen polynomial coefficients to a bounded Hermite generating-function estimate, using finite-difference formulas, Nörlund–Rice bounds, and complex saddle-point analysis. The resulting criterion aims to improve the known effective range from an exponential scale in d to a polynomial d^3 scale. This deposit is a preprint version intended for timestamping, citation, and further mathematical review.