When to Trust Your Rollouts? A Boundary Map for Long-Horizon Action-Conditional World Models

Closed-loop rollout, feeding a temporal model its own predictions while forcing an action sequence, turns a one-step predictor into a simulator of long-horizon consequences. It is also where such a model can silently stop being trustworthy, with no prior criterion for deciding when. We show that trustworthiness here is a property of the \emph{environment}, not the estimator, and that two measurable coordinates predict it: targeting strength, how strongly the environment assigns actions from the same state that drives the outcome (measured as a propensity AUC), and path ratio, how much effects compound through state over the horizon rather than simply add up. Sweeping both in a controllable event-stream generator yields a boundary map for whether rollout still ranks units by their true long-horizon effect. The map has three readings. Above targeting AUC $\approx0.75$–$0.79$, rollout does not merely degrade: it ranks counterfactuals backwards. Path dependence shields against this inversion, but gradually, moving the boundary rightward as compounding strengthens; full immunity needs roughly $8\times$. Weak targeting is not safe either: with little state-dependent assignment there is little state-linked heterogeneity to recover, so recovery peaks at intermediate targeting, an inverted U. The map transfers: an independently built public benchmark (tumour-growth PK/PD) lands on the uphill of the same curve and reproduces its rank levels at the same AUC. A real transaction panel then marks the map's limit: its coordinates predict usable rankings, yet a time-shifted placebo matches the real campaign, because the confounding there lies between units, while the coordinates chart only confounding that varies along a unit's trajectory.