Using reductions from structured P-matrix violation search to classical NP-complete formulations such as 3-SAT and Subset Sum, we examine the relationship between representational expansion, auxiliary variables, local inferability, and information accessibility. Rather than viewing reductions purely as computational transformations, we interpret them as mechanisms that redistribute hidden witness information across enlarged representations. From this perspective, reductions, gadgets, and auxiliary structures may expose globally encoded witness information to local propagation and inference, while search algorithms act as decoding procedures attempting to recover the original hidden witness. The resulting observations suggest that representational expansion may improve local inferability by introducing auxiliary variables and consistency structures, while preserving the need to recover the underlying witness information. This work is exploratory in nature and proposes a conceptual framework for understanding how reductions reshape information accessibility in NP search.

翻译：基于从结构化P-矩阵违反搜索到经典NP完全表述（如3-SAT和子集和问题）的归约，我们探究了表征扩张、辅助变量、局部可推理性与信息可访问性之间的关系。我们并非将归约纯粹视为计算变换，而是将其解释为在扩展表征中重新分配隐藏见证信息的机制。基于此视角，归约、辅助构造及辅助结构可能使得全局编码的见证信息暴露于局部传播与推理中，而搜索算法则充当试图恢复原始隐藏见证的解码过程。由此产生的观察表明：表征扩张通过引入辅助变量与一致性结构可能提升局部可推理性，同时保持对底层见证信息恢复的需求。本研究属于探索性工作，旨在为理解归约如何重塑NP搜索中的信息可访问性提出概念框架。