Diagnostic error is a major threat to patient safety, yet current large language model (LLM) systems often treat diagnosis as a one-shot prediction task, lacking safeguards against missed high-risk alternatives or rigorous verification of their reasoning. Here, we present AegisDx, a safety-oriented framework for hypothetico-deductive clinical reasoning. AegisDx coordinates specialized LLM components through role-specific contracts, structured intermediate outputs, evidence-retrieval interfaces, and verification gates to generate broad differential diagnoses, enforce explicit screening for dangerous "must-not-miss" conditions, verify reasoning against grounded medical evidence, and structure actionable next steps. We evaluated AegisDx across three layers. On literature-derived case reports from NEJM and JAMA, with GPT-oss-120B as the shared backbone, Top-3 diagnostic accuracy was 59.9% versus 52.1% for the standalone LLM on JAMA cases and 62.7% versus 51.4% on NEJM cases. On cases from Annals of Emergency Medicine, Top-3 accuracy was 85.7% versus 68.6%; against physician-consensus must-not-miss diagnosis sets, AegisDx captured at least one such condition among its top three diagnoses in 78.0% of cases versus 52.0%. In a blinded physician evaluation of 43 real-world emergency department notes from the Yale New Haven Health System compared against GPT-5, AegisDx improved the physician-rated composite safety score from 4.31 to 4.55 on a 5-point scale (adjusted p = 2.1x10^-4), with qualitative gains in must-not-miss identification and reasoning safety. Our findings suggest that engineering diagnostic AI as a safety-oriented reasoning framework, rather than optimizing raw predictive accuracy alone, can provide a safer, more transparent, and clinically meaningful layer of bedside decision support for acute care workflows.

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