Synthetic Hospital is an open, synthetic longitudinal EHR benchmark built from public medical-education material with 1,268 patients and 5,602 encounters, designed to overcome privacy barriers while providing verifiable ground truth grounded in standard medical ontologies. Physician reviewers distinguished synthetic records from real charts at near-chance rates, and frontier language models achieve at best a severity-weighted F1 of 0.73 on patient problem list reconstruction, revealing significant gaps in clinical AI performance.