Accessible Predictive Information and the Limits of Observation

This paper introduces accessible predictive information — the mutual information between a fragment-limited observer’s observations and a target system variable at a future time — as a single quantity governing observer viability, classical objectivity, and prediction capability in fragmented physical environments.Five principal results are derived. The Minimum Classicality Threshold (Theorem 1) establishes the minimum environmental information supply required for fragment-limited observers to infer pointer variables with bounded error, and is generalized to arbitrary CPTP interactions (Proposition 1). The Viability–Objectivity Separation Theorem (Theorem 2) proves that global environmental encoding of classical information does not guarantee the existence of viable observers when fragment-scale information ceilings fall below inference thresholds. The Viability Pressure Principle (Theorem 3), derived from the repeated-interaction framework, explains why macroscopic environments dynamically evolve toward observer-supporting regimes. The Informational Prediction Horizon (Theorem 4 and Corollary 4.1) shows that chaotic dynamics degrade accessible predictive information at a rate set by the Kolmogorov–Sinai entropy, producing finite prediction horizons. The Information-Limited Observation Theorem (Theorem 5) unifies these results and derives a Viability–Prediction Tradeoff demonstrating that the prediction horizon is proportional to the environment’s viability margin.