Large language models (LLMs) have made remarkable progress in generating fluent text, but they still face a critical challenge of contextual misalignment in long-term and dynamic dialogue. When human users omit premises, simplify references, or shift context abruptly during interactions with LLMs, the models may fail to capture their actual intentions, producing mechanical or off-topic responses that weaken the collaborative potential of dialogue. To address this problem, this paper proposes a computational framework called the Context Alignment Pre-processor (C.A.P.). Rather than operating during generation, C.A.P. functions as a pre-processing module between user input and response generation. The framework includes three core processes: (1) semantic expansion, which extends a user instruction to a broader semantic span including its premises, literal meaning, and implications; (2) time-weighted context retrieval, which prioritizes recent dialogue history through a temporal decay function approximating human conversational focus; and (3) alignment verification and decision branching, which evaluates whether the dialogue remains on track by measuring the semantic similarity between the current prompt and the weighted historical context. When a significant deviation is detected, C.A.P. initiates a structured clarification protocol to help users and the system recalibrate the conversation. This study presents the architecture and theoretical basis of C.A.P., drawing on cognitive science and Common Ground theory in human-computer interaction. We argue that C.A.P. is not only a technical refinement but also a step toward shifting human-computer dialogue from one-way command-execution patterns to two-way, self-correcting, partnership-based collaboration. Finally, we discuss implementation paths, evaluation methods, and implications for the future design of interactive intelligent systems.