Abstract: This article discusses the theoretical boundary of large language models from a systems and statistical perspective. Rather than treating an LLM as a complete intelligent agent, we view it as a high-dimensional conditional distribution estimator and candidate-generation module embedded in a human-AI system. Under this view, the strength of LLMs lies in expressive approximation, cross-task transfer, and efficient generation of candidate solutions, whereas their structural limitations arise from distribution dependence, miscalibrated uncertainty, and the mismatch between training objectives and real-world decision losses. This article further interprets retrieval augmentation, output calibration, conformal prediction, logical verification, watermarking, and governance constraints as a control layer operating on model outputs. Examples from medical diagnosis, financial risk control, scientific writing, legal assistance, and statistical modeling illustrate why such a layer is necessary. The article argues that the next stage of AI development should focus not only on training larger models, but also on designing reliable systems that can diagnose distribution shifts, quantify uncertainty, support abstention, and remain auditable by humans.