Structural Misidentification of Recursion in Artificial Intelligence: A Falsification Study of the Intelligence Explosion Hypothesis

The intelligence explosion hypothesis—that artificial intelligence systems will enter a self-improving feedback cycle producing exponential capability gains—depends structurally on a single claim: that the process by which AI improves itself is recursive. This paper applies formal structural analysis to demonstrate that contemporary AI self-improvement mechanisms fail to satisfy the defining conditions of recursion under rigorous definition. We establish falsifiable criteria for recursion derived from the Law of Recursion (Gaconnet, 2026a), then examine the specific claims of frontier AI laboratories and speculative recursive ontology frameworks against these criteria. We find: (1) AI self-improvement operates through fixed-architecture feedback, not recursion; (2) the distinction has measurable consequences for capability forecasting; (3) pseudo-recursive frameworks deploy notation without operational grounding, rendering them unfalsifiable. We conclude that the intelligence explosion hypothesis rests on a category error that invalidates its structural foundation, though this does not diminish the real engineering significance of AI optimization within fixed architectural constraints. **Keywords:** recursion, artificial intelligence, feedback loops, structural analysis, falsifiability, AI safety, capability forecasting