The Dependency Theorem: Structural Environmental Dependency in Sustained Predictive Learning Systems

Applying the Law of Predictive Non-Closure (Paper 1 of this series), we prove that any finite physical system sustaining predictive learning is permanently, measurably, and increasingly dependent on its environment. This dependency cannot be eliminated by increases in computational power, memory, energy, or architectural complexity. We establish five results: intelligence as sustained process (the Epsilon Law), structural environmental dependency as physical necessity, scaling dependency in distributed systems (the hive mind case), alignment as a physical consequence of dependency in human-containing environments, and identification of physical mechanisms available for alignment engineering. All results are substrate-independent and scale-independent.