Predicting and Unpredicting: Anchor Choice in Joint Inference

How can dynamics learned by prediction help explain hidden states from later evidence? We reuse a frozen library of locally invertible mechanisms to propose trajectories on unseen compositions, then weight them under a joint posterior when innovations and observations are uncertain. A conditional bound separates inverse execution, model error and uncertainty in the missing inputs. In a predeclared 24-world held-out study with terminal and midpoint observations, the tested midpoint-anchored proposal lowers effective sample size and the fraction of runs meeting full-trajectory quality criteria in expanding chains relative to terminal anchoring, but improves both in contracting chains. Both proposals target the same learned posterior. At matched full-trajectory posterior quality, a direct-inverse policy selected on separate development worlds lowers complete query cost against continuous-grid smoothing in expanding chains with both observations at both tested horizons. The result identifies where direct recovery helps joint inference and where unresolved uncertainty still governs the answer.