Navigating the deluge of heterogeneous medical data, from academic literature (PubMed) to clinical guidelines (Web) and private knowledge bases remains a critical bottleneck for evidence-based medicine. While commercial black-box tools lack transparency, standard open-source RAG implementations frequently suffer from ``reasoning drift'' when handling complex, long-tail queries. We present DeepMed Search, a fully open-source, agentic platform designed for transparent medical deep research. Built on a high-performance Next.js architecture, DeepMed Search features a source-adaptive router that autonomously dispatches sub-queries to PubMed, web search, or local graph-based knowledge bases based on information density. Crucially, the platform integrates an introspective verification module, powered by a causal-consistent multi-agent debate framework, to validate retrieved evidence against diagnostic logic before synthesis. To demonstrate its robustness, we showcase DeepMed Search's ability to autonomously decompose high-difficulty rare disease queries, filter out confounding noise, and generate structured, citation-backed research reports in minutes. By open-sourcing this software, we provide the community with a robust infrastructure to democratize access to trustworthy, glass-box medical reasoning at a commercial-grade performance level, which is publicly available at: https://www.deepmedsearch.cloud and the demonstration video is available at: https://youtu.be/4U4aok8yLpk.