Supporting public-safety Mission Critical Services (MCX) over a shared Open radio access network (O-RAN) requires service assurance over finite incident horizons, while ordinary mobile traffic competes for the same resources and heterogeneous E2 domains expose different observations, control actions, and actuation latencies. Existing RAN key performance indicators are retrospective, whereas conventional effective capacity characterizes an asymptotic stationary regime and therefore suppresses both the initial E2-observed condition and the finite selection-to-actuation transient. To solve this problem, in this paper we develop an E2-conditioned finite-horizon effective capacity (FH-EC) framework for public-safety MCX over shared O-RAN. Specifically, we first establish a finite-horizon O-RAN MCX-based service model that incorporates E2-observed network states, control actuation latency, and correlation-aware connectivity diversity. Based on this model, we derive an FH-EC formulation that characterizes the executable service capability within a finite mission horizon. Furthermore, we transform FH-EC into confidence-calibrated capability profiles and develop an MCX orchestration framework with contract certification, shared-resource protection, and FH-EC-driven profile selection at the Near-RT RAN Intelligent Controller (RIC). Coupled MATLAB/ns-3 evaluations demonstrate the predicted short-horizon state and actuation effects and show that adaptive connectivity selection improves MCX supportability under O-DU degradation while satisfying the configured multi-QoS and non-MCX protection requirements.

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