The AI Trilemma: Socio-Economic Deadlocks and the Erosion of Sovereignty in the Post-Labor Era

This paper introduces the Algorithmic Leviathan Framework (ALF) by identifying a fundamental "AI Trilemma" between productivity, equity, and sovereignty. We demonstrate through a formal macroeconomic model that when AI-driven automation exceeds a specific threshold ($\alpha^*$), the traditional "production-consumption" loop enters a terminal deflationary spiral. The study concludes that private concentration of computational power necessitates a transition to Public AI Infrastructure to prevent a collapse into digital neo-feudalism.