We present a proof architecture for \(P \neq NP\) based on an upper--lower clash in polytime-capped conditional description length. We construct an efficiently samplable family of SAT instances \(Y\) such that every satisfying witness for \(Y\) yields the same global message \(M(Y)\). If \(P=NP\), then a standard polynomial-time SAT self-reduction recovers \(M(Y)\) from \(Y\), so \[ K_{\mathrm{poly}}(M(Y)\mid Y)=O(1). \] The lower-bound side shows the opposite. For the same ensemble, no fixed polynomial-time observer can gain substantial predictive advantage on a linear number of selected message coordinates. The argument treats computation as an evidence-producing process: predictive advantage is converted into constructible-dual evidence skew and then into pairwise distinctions between message-opposite worlds. A normalization theorem shows that every target-relevant non-neutral evidence leaf is either a safe-buffer observation or a hidden-gauge observation. Safe-buffer observations have negligible leakage, while hidden-gauge observations are limited by gauge-rank accounting. This yields an atomic evidence budget implying that total message-resolving advantage is \(o(t)\) across \(t\) selected coordinates. Boundary-law mixing gives the near-random baseline for the visible surface. Combining this with the evidence budget gives product small-success and then, by Compression-from-Success, \[ K_{\mathrm{poly}}(M(Y)\mid Y)\ge Ω(t) \] with high probability. This contradicts the constant upper bound from \(P=NP\). Therefore \(P \neq NP\).

翻译：我们提出了一种基于多项式时间限制条件描述长度的上下界冲突的 \(P \neq NP\) 证明体系。构造了一个高效可采样的SAT实例族 \(Y\)，使得 \(Y\) 的所有满足性见证均产生同一全局消息 \(M(Y)\)。若 \(P=NP\)，则标准多项式时间SAT自归约可从 \(Y\) 恢复 \(M(Y)\)，故 \[ K_{\mathrm{poly}}(M(Y)\mid Y)=O(1) \]。下界侧则呈现相反结果：对于同一集成体，任何固定多项式时间观测器在线性数量的选定消息坐标上均无法获得显著预测优势。该论证将计算视为证据产生过程：预测优势可转化为可构造对偶证据偏斜，进而转化为消息对立世界间的成对区分。归一化定理表明：每个目标相关非中性证据叶节点要么属于安全缓冲区观测，要么属于隐藏规范观测。安全缓冲区观测的泄漏可忽略不计，而隐藏规范观测受规范秩核算限制。由此得到原子证据预算，表明在 \(t\) 个选定坐标上的总消息解析优势为 \(o(t)\)。边界律混合给出了可见表面的近随机基线。结合证据预算可得乘积小成功概率，进而通过成功压缩定理得到：\[ K_{\mathrm{poly}}(M(Y)\mid Y)\ge Ω(t) \] 以高概率成立。这与 \(P=NP\) 假设下的常数上界矛盾，因此 \(P \neq NP\)。