The Entropy of Persuasion: Mathematical Limits and the Quadratic Burden of Generative AI in Research

This article concludes a technical audit of Large Language Model (LLM) performance in the domain of RSA prime factorization. We identify a critical "Computational Wall" at the RSA-256 threshold where heuristic fluency bypasses grounded logic. We propose a "Traffic Light" flagging system to mitigate the "Quadratic Burden" of verification—the escalating societal cost of debunking persuasive synthetic hallucinations. Finally, we argue for a 99.99\% creator accountability framework under the emerging AI Accountability Acts (AIAA) of 2026.