The integration of Large Language Models (LLMs) into scientific discovery is currently hindered by the Implicit Context problem, where governing equations extracted from literature contain invisible thermodynamic assumptions (e.g., undrained conditions) that standard generative models fail to recognize. This leads to Physical Hallucination: the generation of syntactically correct solvers that faithfully execute physically invalid laws. Here, we introduce a Neuro-Symbolic Generative Agent that functions as a cognitive supervisor atop traditional numerical engines. By encapsulating physical laws into modular Constitutive Skills and leveraging latent intrinsic priors, the Agent employs a Chain-of-Thought reasoning workflow to autonomously validate, prune, and complete physical mechanisms. We demonstrate this capability on the challenge of thermal pressurization in low-permeability sandstone. While a standard literature-retrieval baseline erroneously predicts catastrophic material failure by blindly adopting a rigid "undrained" simplification, our Agent autonomously identifies the system as operating in a drained regime (Deborah number De << 1) via dimensionless scaling analysis. Consequently, it inductively completes the missing dissipation mechanism (Darcy flow) required to satisfy boundary constraints, predicting a stable stress path consistent with experimental reality. This work establishes a paradigm where AI agents transcend the role of coding assistants to act as epistemic partners, capable of reasoning about and correcting the theoretical assumptions embedded in scientific data.

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