We reinterpret NP witness discovery through an information-theoretic lens. Rather than measuring search solely by Turing-machine time, we treat recovery as an information-acquisition process: the hidden witness is the sole source of uncertainty, and identification requires reducing this uncertainty through a rate-limited access interface in the sense of Shannon. To make this perspective explicit, we analyze an extreme regime, the \emph{psocid model}, in which the witness is accessible only via equality probes $[π= w^\star]$ under a uniform, structureless prior. Each probe reveals at most $O(N/2^N)$ bits of mutual information, so polynomially many probes accumulate only $o(1)$ total information. By Fano's inequality, reliable recovery requires $Ω(N)$ bits, creating a fundamental mismatch between required and obtainable information. The psocid setting thus isolates a fully symmetric search regime in which no intermediate computation yields global eliminative leverage, thereby exposing an informational origin of exponential search complexity.

翻译：我们通过信息论的视角重新诠释NP见证发现过程。不同于仅以图灵机时间衡量搜索效率，我们将恢复过程视为信息获取过程：隐藏的见证是唯一的不确定性来源，而识别需要通过香农意义上的速率受限访问接口来减少这种不确定性。为明确阐述这一观点，我们分析了一个极端机制——\emph{伪码模型}，其中见证仅能通过等式探针$[π= w^\star]$在均匀无结构先验下访问。每个探针最多揭示$O(N/2^N)$比特的互信息，因此多项式数量的探针累计仅能获得$o(1)$总信息量。根据法诺不等式，可靠恢复需要$Ω(N)$比特信息，这导致所需信息与可获得信息之间产生根本性不匹配。伪码设定由此隔离出一个完全对称的搜索机制，其中任何中间计算都无法产生全局排除性优势，从而揭示了指数级搜索复杂度的信息论根源。