The Entropy of Autonomy: The Mathematics of Agentic AI and the Scaling Law of Systemic Risk

As organizations transition from monolithic Large Language Models (LLMs) to autonomous 'Agentic' AI systems, they enter a new regime where risk is no longer a linear function of model size, but a geometric function of agent interaction. This report reveals the critical '45% Threshold'—a mathematical inflection point where adding more agents to a workflow can actually decrease performance and exponentially increase the attack surface. Research from 2025 indicates that independent agent swarms amplify errors by a factor of 17.2x, creating a 'Telephone Game' effect that traditional observability tools are ill-equipped to detect.To mitigate these systemic risks, organizations must move beyond prompt engineering and adopt a discipline of 'Agentic Engineering.' This includes implementing formal verification protocols, such as the 4/δ convergence bound for verifiers, and adopting architectural 'circuit breakers' recommended by NIST and Gartner. By shifting from a trust-based model to a zero-trust, verified-transition framework, enterprises can harness the power of autonomous agents without succumbing to the mathematical certainty of cascading failure.