This paper introduces ARCADIA, an agentic AI framework for causal discovery that integrates large-language-model reasoning with statistical diagnostics to construct valid, temporally coherent causal structures. Unlike traditional algorithms, ARCADIA iteratively refines candidate DAGs through constraint-guided prompting and causal-validity feedback, leading to stable and interpretable models for real-world high-stakes domains. Experiments on corporate bankruptcy data show that ARCADIA produces more reliable causal graphs than NOTEARS, GOLEM, and DirectLiNGAM while offering a fully explainable, intervention-ready pipeline. The framework advances AI by demonstrating how agentic LLMs can participate in autonomous scientific modeling and structured causal inference.