The Infinite Choice Barrier: A Triangulated Mathematical Proof of the Impossibility of AGI

This paper is a mathematical consolidation of my papers on the impossibility of AGI. It presents a triangulated impossibility proof for Artificial General Intelligence (AGI), defined as an algorithmic system capable of solving a sufficiently broad class of human problems at human-level competence. Three formally independent but converging mathemati- cal arguments-based in computability theory, information theory, and algorithmic complexity- jointly demonstrate that AGI, as such, cannot exist. This boundary, named the Infinite Choice Barrier (ICB), is neither technical nor architectural. It is structural by its nature. It marks a categorical limitation on algorithmic cognition. Philosophical groundwork and contextual development of the formal proof are explored in: Part I: AGI is Impossible - Here is The Proof Part II: AGI is Mathematically Impossible 2: When Entropy Returns (Both papers available on Philpapers) A third part is still to be finalized and will be uploaded, the formal part is already in this paper.