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解释NP见证的发现过程。与其仅用量子图灵机时间衡量搜索，我们将恢复过程视为信息获取：隐藏见证是唯一的不确定性来源，而识别需要通过对香农意义上的速率受限访问接口来降低这种不确定性。为明确这一视角，我们分析了一个极端场景——\emph{psocid模型}，其中见证仅能通过均匀无结构先验下的等式探测$[π= w^\star]$来访问。每次探测最多揭示$O(N/2^N)$比特的互信息，因此多项式次探测累积的信息总量仅为$o(1)$。根据法诺不等式，可靠恢复需要$Ω(N)$比特，这造成了所需与可获得信息之间的根本性不匹配。因此，psocid场景隔离了一个完全对称的搜索机制，其中中间计算无法产生全局消除杠杆，从而揭示了指数级搜索复杂度的信息论根源。