Large language model (LLM) agents extend generative models with reasoning, tool use, and persistent memory, thereby enabling the automation of complex tasks. In healthcare, such systems could support documentation, care coordination, and clinical decision making. Their reliable deployment in hospitals, however, remains constrained by safety risks, limited transparency, and inadequate mechanisms for handling longitudinal clinical context. Here we propose an architecture that adapts LLM agents to hospital environments. The design comprises four components: a restricted execution environment inspired by multi-user operating systems, a document-centric interaction model linking patient and clinician agents, a page-indexed memory architecture for longitudinal context management, and a curated library of composable medical skills. Implemented on top of OpenClaw, an open-source agent orchestration framework, this design provides the basis for an Agentic Operating System for Hospitals: a computing layer for coordinating clinical workflows while preserving safety, transparency, and auditability. To evaluate the memory component, we introduce manifest-guided retrieval for hierarchical navigation of longitudinal patient records. In a benchmark derived from the MIMIC-IV dataset (v2.2) comprising 100 de-identified patient records and 300 clinical queries stratified across three difficulty tiers (100 per tier), manifest-guided retrieval matched a metadata-filtered RAG baseline on overall recall (0.877 versus 0.876) while achieving 2.2x higher precision (0.779 versus 0.352) and retrieving fewer documents; on tier-3 longitudinal queries, manifest recall was 21% higher (0.846 versus 0.701), confirming that LLM-guided hierarchical navigation is most valuable when queries span multiple care episodes. These results outline a practical path toward hospital-scale agentic infrastructure.