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Artificial intelligence and autonomous robotics are entering hospitals. This is no longer a question of whether but of when, how fast, and — most critically — under whose governance. This paper proposes SMART-H 3.0 (Smart Medical Autonomous Robotics Technology for Hospitals), a governance-native architecture for AI-enabled hospitals that places infection prevention for immunocompromised patients as its primary constitutional objective. The architecture builds upon two prior published frameworks by the present author: the RAH-SPINE (Recursive Agentic-Human Governance Spine) twelve-layer governance stack, which provides the foundational layered architecture for embedding governance rules into autonomous AI systems; and the Computable Governance Notation (CGN) formalism, which enables machine-readable regulatory policies to compile into executable operational constraints across diverse jurisdictions. Together, these frameworks serve as the proposed central nervous system of the hospital-as-organism. At the heart of the architecture lies a six-phase recursive governance loop — Sense, Score, Simulate, Act, Review, Learn — through which every autonomous decision is continuously evaluated, validated against constitutional constraints, and subject to medical-led human review. The paper introduces the Constitutional Autonomous Hospital Spine (CAH-SPINE), a fourteen-layer governance stack extending RAH-SPINE with hospital-specific components including digital twin simulation, autonomous swarm robotics coordination, sovereign AI processing, and post-quantum cryptographic identity. A constitutional zone model classifies hospital areas by immunocompromised patient vulnerability, with non-optimisable safety floors that cannot be overridden by AI optimisation. The proposal is explicitly conceptual (TRL 1-2): no prototype exists, no clinical validation has been conducted, and all quantitative parameters are illustrative governance modelling constructs. The paper contributes an architectural hypothesis — that the hospital of 2035 may be defined less by the sophistication of its robots or the power of its AI than by the maturity of its governance.