Recent advances in artificial intelligence-radio access network (AI-RAN) are placing large language model (LLM)-driven agents within the open RAN (O-RAN) control hierarchy. A promising deployment for this agentic AI-RAN co-locates LLM inference with physical-layer (PHY) communication processing over the same accelerated compute pool for infrastructure sharing, data locality, and low control latency. However, this co-location induces bidirectional control-compute coupling, as the agent competes with PHY processing for compute, while its reasoned gNB control actions may alter future PHY workload and hence the compute available to its next inference. To this end, this article proposes the control-compute contract, a coordination protocol linking AI-RAN workload governance with O-RAN control execution. Specifically, we first expose direct compute contention on an over-the-air (OTA) O-RAN testbed, where continuous LLM inference increases the PHY decoding time approximately eightfold. We then formulate the contract as three protocol rules with operator-requirement protection, and map it onto O-RAN and AI-RAN functions as a five-stage workflow. Afterward, an OTA-calibrated case study of simulated uplink gNB control indicates that the contract keeps the proportion of slots violating the PHY time budget below $0.9\%$, against $20.7\%$ under ungoverned co-location, while achieving faster gNB control than a fixed compute reservation benchmark. Finally, we identify several open issues and outlooks for its practical deployment.

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