As Large Language Models (LLMs) increasingly saturate the internet with synthetic content, the risk of future modelsbeing trained on generated data grows exponentially. This paper introduces the “Ainex Law,” a mathematical principle definingthe upper bound of semantic integrity in recursive self-learning systems. Through rigorous experimentation using a GPT-2 architec-ture within a closed feedback loop, we empirically demonstrate that without external human-grounded data, the model’s semanticspace—measured via the Convex Hull Volume (Vhull) of latent embeddings—suffers a deterministic decay. We observe a 66%reduction in semantic diversity within 20 generations, accompanied by a sharp increase in Centroid Drift (μAI ) away from thehuman baseline. Our findings suggest that “Model Collapse” is not merely a quality degradation but a geometric inevitability akinto thermodynamic entropy. We propose the Ainex Score (A) as a standardized metric to quantify this decay.