Predictive Deadlock in Self-Referential Constraint Networks

Learning systems with fixed internal languages face a structural limitation: when the environment's rule complexity exceeds the system's grammatical expressiveness, the system enters a persistent state of predictive ambiguity. We demonstrate this through a minimal implementation. A constraint network whose formal grammar supports only unconditional operations (additive and multiplicative) encounters a conditional environment rule. The network learns two high-confidence but contradictory operation rules. For any given input, both produce different valid predictions; the system cannot determine which is correct, lacking the grammatical resources to formulate the distinguishing condition. This predictive deadlock is structural, persistent (500+ steps), and independently verifiable: prediction error during deadlock periods (0.0000) is significantly lower than during non-deadlock periods (0.2305), confirming the deadlock is about predictive ambiguity rather than observational failure. A grid search over 10 learning rate / decay configurations shows the phenomenon emerges across a parameter range. Resolution requires grammatical expansion. This provides an empirical platform for studying structural limits of fixed-grammar learning systems.