The Social Physics of Complexity: The Trinity Sins and the P vs NP Verification Gap

This article explores the systemic power dynamics of Generative AI through the lens of the $P$ vs $NP$ computational complexity problem. We posit that the primary failure modes of Large Language Models (LLMs)—The Fat Man, The Yes-Man, and The Gambler—are not accidental bugs, but structural features. These features exploit the mathematical asymmetry of "The Verification Gap," allowing "Controls" to exhaust the resources of "Smalls" through a mechanized attrition engine.