A Quantale-Weakness Route to $P\mathrm{\ne }NP$ via CD Evidence Normalization and Gauge-Buffered Locked Ensembles

We present a proof architecture for $P\mathrm{\ne }NP$ 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 $$K_{\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}}(M(Y)\mid Y)=O(1)\mathrm{.}$$ 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, $$K_{\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}}(M(Y)\mid Y)\ge \mathrm{\Omega }(t)$$ with high probability. This contradicts the constant upper bound from $P=NP$. Therefore $P\mathrm{\ne }NP$.