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In an era of escalating healthcare demands, hospitals face persistent challenges in maintaining operational resilience amid fluctuating patient volumes, resource constraints, and unforeseen disruptions. This conceptual manuscript introduces a novel framework for real-time hospital capacity intelligence, designed to enhance decision-making through integrated AI-driven analytics and interoperable data ecosystems. Drawing on theoretical foundations from clinical AI architectures, healthcare analytics infrastructures, and decision support pipelines, the proposed system emphasizes seamless integration with electronic health records (EHRs), governance mechanisms for AI deployment, and dynamic monitoring to mitigate risks such as capacity overloads. The framework outlines a layered architecture that orchestrates data exchange, predictive analytics, and adaptive resource allocation, ensuring interoperability across clinical workflows. Key conceptual formulas are presented to interpret risk propagation in capacity management, decision confidence in real-time intelligence, and governance load in system operations. By synthesizing recent peer-reviewed literature on AI governance and clinical interoperability, this work highlights the potential for such frameworks to foster resilient hospital operations without relying on empirical data or model evaluations. Implications for healthcare systems include improved preparedness for surges, ethical AI integration, and scalable intelligence ecosystems. This theoretical exploration underscores the need for robust, AI-augmented infrastructures to support sustainable healthcare delivery.