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 support and material-response conditions governing excavation outcomes. 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. Completed interactions update measured belief, while hypothetical actions advance a separate imagined state with fixed deployment weights. Experiments show that interaction history resolves current-view ambiguity, remains useful across delayed revisits, and improves observation-free multi-step prediction. Offline candidate ranking reduces action-selection regret by 65.5% relative to the current-observation-only Local baseline. Target-domain studies in Newton/MPM and real excavation demonstrate the value of interaction history across dynamics and sensing conditions. These results identify persistent physical belief as a useful representation for world models of environments that robots continually reshape.