Connected physical systems fuse observations from robots, IoT sensors, and edge-AI modules into a shared account of the world, yet most evaluations score only the final answer or action and cannot tell whether a method attributed the evidence, updated its belief, handled contradictions, and justified its decision. We argue that shared reasoning in Connected Robotics should be evaluated as an evidence-to-belief trajectory, and introduce the Connected Robotics Evidence Graph (CREG) Benchmark to make that trajectory measurable.

CREG comprises 350 deterministically generated scenarios across seven regimes (justified revision, belief preservation, relation association, contradiction onset and resolution, stale/delayed evidence, and source reliability), each exposing a normative posterior reference at every evidence prefix, validated by an independent log-odds checker and screened by a blinded expert audit. Nine representation conditions separate relation content from serialization, ordering, and metadata.

Evaluating four open-weight instruction models and six transparent fusion baselines yields three findings. First, entity grounding accounts for a substantial part of the weak-model deficit.

Second, deleting semantic relations costs 15.3 points of strict belief-state accuracy on relation-dependent scenarios (Holm-corrected p<0.001), but an information-matched structured list outperforms the full graph and shuffling the graph does not hurt: relation content matters where required, while graph serialization confers no consistent advantage. Third, belief accuracy is strongly non-monotonic along the evidence sequence, with mid-trajectory failures that endpoint-only evaluation cannot detect.

All scenarios, references, prompts, metrics, and analysis code are released for offline, hardware-free reproduction.