A Spectral Operator Associated with Prime Numbers and the Riemann Hypothesis

This document presents an honest account of an AI-assisted exploration of the Riemann Hypothesis. It is the fourth iteration of this work, following critical feedback from the mathematical community (primarily on the MersenneForum). What this is: - A case study in using AI language models (DeepSeek, ChatGPT, Gemini, Grok) to investigate a deep mathematical problem. - A documentation of a learning process, including mistakes and the lessons learned from them. - Numerical experiments with a spectral operator on prime numbers (see the comparison table inside). What this is NOT: - A claim of proving the Riemann Hypothesis. Earlier versions (1.0-3.0) made such claims, but they were based on AI-generated arguments that I did not fully understand. - A rigorous mathematical proof. The feedback from experts has made it clear that several key steps lack proper justification. Contents: - A description of the operator construction. - A summary of the critical feedback received. - Numerical data comparing computed eigenvalues with Odlyzko's zeros. - A reflection on the limitations of AI in mathematical research. This work is published to document my journey and to thank the mathematicians who took the time to provide honest criticism. I am now focusing on learning the necessary mathematics properly.