Abstract
Artificial intelligence (AI) continues to face fundamental mathematical challenges such as optimization in high-dimensional nonconvex landscapes, generalization under uncertainty, lack of interpretability, and sharp phase transitions in learning dynamics. Similar unresolved problems appear in physics and engineering---for example in turbulence, nuclear fusion, neural information processing, and extreme events \cite{riemann_turb_chaos, riemann_ml_zeros}. We propose that the universal approximation property of the Riemann zeta function offers a unified mathematical framework for these phenomena \cite{voronin1975universality, Bagchi1981}. In particular, we introduce the zeta-derived potential \[ S(\Re s, \Im s) = \bigl|\zeta(s)\bigr| - \ln\bigl|\zeta(s)\bigr| - 1, \] where $s = \Re s + i \Im s$, which generates a family of self-consistent measures reproducing canonical physical distributions such as Boltzmann, Planck, and Kolmogorov spectra \cite{riemann_zeta_f_turb, riemann_hyperlog_turb}. By incorporating the zeros of the zeta function, we develop a zero-aware reparameterization framework that improves optimization, accelerates convergence, and provides a principled turbulence closure mechanism \cite{riemann_ce_opt, riemann_mhd_turb}. This approach creates a bridge between data, dynamics, and statistical measures while preserving analytical properties of $\zeta(s)$ and basic conservation laws. As a result, it offers a single coherent structure for understanding AI optimization, turbulence modeling, and critical transitions in complex systems.