Full-stack human-robot collaboration (HRC) can become brittle when replacing a planner, partner model, coordination policy, or controller changes the physical meaning of cross-layer signals. We introduce C2C, an object-centric cognition-to-control architecture that preserves these meanings through physical contracts. Rather than standardizing individual modules, C2C standardizes the physical semantics exchanged between them: task intent is represented by a geometrically verified payload path, partner information by a source-independent physical state, learned coordination by bounded 11-D task-space commands, and robot-specific feasibility remains inside whole-body control (WBC). The reference system combines a vision-language model with deterministic geometric verification and multi-agent reinforcement learning (MARL) for partner-aware coordination. Across nine transport scenarios, adaptive MARL variants achieve 77.1-82.1% mean success under unchanged interfaces, compared with 56.5% for a scripted-partner reference. The same contracts further support neural and interpretable hard-tree actors, two- and three-carrier teams, and simulated-to-human partner substitution. Physical Unitree G1-human tests achieve 100% success in spatially confined transport and 80% in super-long-object handling, while a three-carrier system with two G1 humanoids and one human validates the same interface structure on hardware. Together, these results show that C2C converts a tightly coupled HRC stack into a plug-compatible system in which key components can change without redefining the physical collaboration task.

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