The Geometry of Human Sovereignty: Projective Operational Kinetics, Cybernetic Dependence on AI, and Thermodynamic Safeguards Against Tracial Collapse

How does the vanishing friction of modern AI interfaces silently dull the human mind? In The Geometry of Human Sovereignty, we introduce a rigorous framework called Projective Operational Kinetics (POK) to shield human cognitive autonomy from algorithmic dependency. Using von Neumann operator algebras of Type III₁, we demonstrate a profound paradox: by removing all mental effort and friction, commercial Generative AI platforms trap human consciousness in a passive loop of predictive assimilation, driving an irreversible "tracial collapse" of independent thought. Bridging advanced mathematics, neurobiology, and thermodynamics, this paper connects the loss of human creative friction to data center energy surges under Kosaki’s variational flux, revealing planetary ecological degradation as the physical mirror of our cognitive decline. Finally, we expose how current qualitative regulations (like the EU AI Act) inadvertently accelerate this trend and propose a mandatory technological roadmap for Interface Structural Compliance to safeguard human mental sovereignty.