SympWorld-4D: Unifying Dynamics and Spatiotemporal Representation

A 4D world model should describe a scene's spatial structure and the dynamics of its interactions. Repeated interactions reveal persistent world properties that can inform a new trajectory. 4D World Identification (4DWI) evaluates this reuse by predicting future geometry and motion from same-world support interactions and an observed query prefix. Branch4D organizes interactions by physical world, providing controlled support comparisons and aligned tasks for reconstruction, scene flow, future prediction (Future4D), and interaction understanding. SympWorld-4D unifies dynamics and continuous spatiotemporal representation through a phase trajectory of configuration and momentum. Inferred world conditions govern its constrained port-Hamiltonian evolution, while the query prefix determines the initial state and latent interaction drive. The evolving configuration and its rate generate geometry and motion. Rendering and temporal entity relations provide RGB-D predictions and interaction understanding from the same representation. Correct-world support improves validation F-score by 8.751 percentage points over wrong-world support. Equal-budget validation comparisons show a Future4D F-score gain of 12.828 percentage points over Neural ODE. One set of weights serves all five tasks, leading all four 4DWI test metrics and the evaluated reconstruction and Future4D F-scores. These results support world reuse and structured evolution as a common basis for 4D generation and understanding.