EntropyRuntime: A Discrete-Time Autonomous Control System with Hierarchical Gear State Abstraction and Utility-Gated Execution

We present EntropyRuntime, a discrete-time event-driven autonomous control system for deploying general intelligence agents in long-running, minimally supervised environments. Unlike conventional AI agent frameworks that treat autonomy as a binary property, EntropyRuntime introduces a hierarchical discrete control variable -- the Gear state -- that interpolates agent autonomy across five ordered levels. Actions are executed through a utility-gated policy that thresholds system curiosity scores against Gear-dependent bounds. We provide five formal theorems establishing Gear monotonic stability, execution safety bounds, eventual stabilization, fallback completeness, and a representation theorem for Lipschitz-bounded-risk policies. An ablation-validated production implementation demonstrates sustained multi-month operation with zero critical failures. This is PRE-GHR Series IX, companion to the unified PRE-GHR axiomatic framework (10.5281/zenodo.20933342).