PileBelief: Persistent Physical State for Interaction-Driven World Modeling

World models allow robots to anticipate action consequences before execution. This capability is especially valuable in excavation, where each scoop reshapes the terrain and affects subsequent actions. Local observations, however, cannot fully reveal the underlying support and material conditions. We present PileBelief, an interaction-driven persistent world model for partially observed excavation that retains physical evidence beyond the visible surface. It combines an observation-conditioned physical prior with world-addressed deformation memory and physical-response memory. Action-aligned reads and gated residual corrections refine terrain-change and outcome predictions. With deployment weights fixed, completed interactions update measured belief, while hypothetical actions advance a separate imagined state. Compared with a current-observation-only baseline, PileBelief reduces five-step joint prediction error by 10.8% and offline action-selection regret by 65.5%. Experiments on Newton/MPM and real excavation datasets further demonstrate improved terrain-change and bucket-volume prediction. Our method enables multi-step prediction and candidate-action ranking from local observations, even when the underlying soil state is unknown. These results identify persistent physical belief as a useful representation for world models of environments that robots continually reshape.