An Emergent Operator-Theoretic Model of the Riemann Hypothesis: A Case Study in AI Mutual Criticism and Human–AI Co-Discovery

Abstract This study is an experimental case study exploring whether a coherent theoretical framework for the Riemann Hypothesis can emerge through a self-reinforcing process of iterative mutual critique among multiple large language models (LLMs). The resulting manuscript presents a mathematically consistent theory—comparable in depth and rigor to a doctoral dissertation—grounded in operator theory and scattering theory. It also addresses several unresolved technical gaps identified in prior literature. This work offers not only a potentially novel mathematical insight into the Riemann Hypothesis but also a benchmark for evaluating AI’s autonomous capacity to construct complex scientific theories. Author’s Ethical Statement The principal author (Teppei Arai) is an undergraduate student in the Faculty of Business Administration at Hakuoh University, and not a professional mathematician.His role was limited to designing and supervising the “AI Emergence Process.” Therefore, the author does not claim responsibility for the mathematical correctness of the generated manuscript. This work should be regarded purely as a hypothesis generated by AI, rather than a verified mathematical result. Invitation for Collaboration This project is an open invitation to professional mathematicians, researchers, and students to examine, verify, and expand upon the “AI-emergent theory” proposed herein. Those interested in the mathematical content or the meta-scientific methodology of AI-driven emergent research are warmly encouraged to contact the author. Collaborative verification, theoretical development, or re-licensing of specific components can be arranged flexibly.Contact: [email protected] Keywords Riemann Hypothesis, Artificial Intelligence, Operator Theory, Scattering Theory, Weil’s Explicit Formula, Scientific Discovery, Emergence, Metascience, Human–AI Collaboration License Notice The entire record is released under the Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). The file Prompts.md is separately released under the Creative Commons Attribution 4.0 International License (CC BY 4.0) to encourage reuse and further research in AI-emergent scientific studies.