\section{Conclusion}

An autoregressive model can represent a globally reward-tilted trajectory distribution without thereby solving a stochastic control problem. In typed action--event sequences, the difference is one operator at chance nodes: exponential tilting for generation versus expectation under the environment law for control. That small formal change has three consequences. It yields an exact recursion for how chance optimism is created and propagated; it clarifies when event typicality contaminates an interpretation of sequence energy; and it supports a pathwise separation of controllable advantages from exogenous innovations.

The experiments follow the logical order of the paper. Exhaustive code tests validate the equalities, an independent factorial design identifies the relevant return-dispersion mechanism, finite estimators reveal coverage limits, and a causal Transformer demonstrates that an observational model and a decision readout can be trained and evaluated as separate components. The operational rule is therefore precise: learn what actions and events occurred, preserve exogenous chance under its supported conditional law, optimize only controllable choices relative to an explicit reference, and abstain when the model cannot support the comparison.

