The Gödel–Heisenberg Horizon: Axiomatic Saturation and the Informational Inaccessibility of Counterexamples to the Riemann Hypothesis

This paper develops an information-theoretic framework for analyzing the epistemic status of the Riemann Hypothesis (RH) within formal systems such as Zermelo–Fraenkel set theory with the axiom of choice (ZFC). It introduces the notion of Axiomatic Saturation (SSA), a conceptual threshold beyond which the informational complexity required to certify a counterexample may exceed the capacity of the formal system. The work combines arithmetic reduction, computability theory, and Kolmogorov complexity, and proposes a Gödel–Heisenberg horizon characterizing limits of resolution in formal mathematics. This article constitutes a substantially revised and extended version of a previous work published in French (Hayoun, 2026, Zenodo), in which earlier claims have been reformulated within a rigorous complexity-theoretic framework. This version is submitted as a preprint.