Despite rapid progress, embodied reasoning under real-world variability remains challenging. Existing approaches rely on demonstration-driven sequential biases, limiting flexibility in open-ended and long-horizon tasks that require structured reasoning over evolving states. We introduce RoBoSR, an intermediate structural representation that formulates manipulation as step-wise state transitions over semantically grounded, object-centric scene graphs. By modeling object states and their spatial relations at the perception-action interface, RoBoSR disentangles high-level task reasoning from raw inputs and enables structured reasoning over preconditions, effects, and goal states. This representation endows the agent with causal reasoning capability, enforcing subtask dependencies and supporting coherent long-horizon task planning. To learn such structure-aware reasoning, we construct Manip-Cognition-1.6M, an open-world dataset that jointly supervises scene understanding, instruction interpretation, and subtask planning across diverse tasks. Across several benchmarks and real-world demonstrations, our method consistently outperforms prompting-based methods and classical TAMP baselines in zero-shot generalization and long-horizon tasks. The results underscore structured intermediate representations as a critical inductive bias for scalable embodied reasoning.

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