Agentic Compute Criticality: A Proof-of-Concept Framework for Measuring Branching-Process Amplification in Recursive LLM Inference

Modern AI scaling laws describe stable relationships between model parameters, dataset size, and compute efficiency. However, agentic AI systems—systems that perform multiple recursive inference calls rather than a single forward pass—can require substantially more compute than static inference predicts. This paper presents a proof-of-concept (PoC) measurement framework for studying compute amplification in simulated agentic inference. We simulate agentic recursion by interpreting reasoning patterns in model responses and programmatically triggering structured follow-up inference calls, without relying on native tool-calling infrastructure. Across 36 clean trials, the median compute amplification factor reached 13.40× for the moderate-autonomy variant. The maximum observed trial achieved 55.68× amplification at a branching factor of 0.975. A fitted branching amplification model suggests amplification approaching 100× at approximately 60 recursive calls. These results indicate that compute amplification in agentic systems may grow non-linearly with recursion depth and motivate formal measurement frameworks for this emerging regime. Code and experimental artifacts are publicly available:https://github.com/Siva2015143/llm-agentic-behavior-experimenthttps://github.com/Siva2015143/AI-Agentic-Compute-Criticality