The Agency Horizon: An Information-Theoretic Bound on Action at a Distance

I introduce the Agency Horizon, a finite delay beyond which an agent’s action becomes statistically indistinguishable from background variation in a noisy observation channel. Within the Observed Agency Through Simulation (OATS) framework, I define agency operationally as the mutual information between an action and a delayed observation, and define the agency horizon as the earliest delay at which this coupling falls below a fixed threshold. Using the included OATS simulation suite, I validate the predicted scaling of the agency horizon under linearly growing noise (E1), quantify estimator convergence (E2), and demonstrate robustness under non-Gaussian conditions including bounded actions and heavy-tailed noise (E4). I further show that saturating noise can yield an unbounded horizon by producing a nonzero information floor, referred to as Eternal Agency (E3). Finally, I distinguish statistical coupling from functional survivability using a delayed-feedback control task, demonstrating a sharp control cliff at delays where mutual information remains nontrivial (E5), and map an Agency Capacity Surface showing how latency, quantization, and packet loss constrain effective influence (E6). To ensure physical consistency, I include quantum no-signaling checks (E7).