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A Quantale-Weakness Route to P neq NP via CD Evidence Normalization and Gauge-Buffered Locked Ensembles
arXiv:2510.08814v2 Announce Type: replace-cross Abstract: We present a proof architecture for (P neq NP) based on an upper--lower clash in polytime-capped conditional description length. We construct
arXiv:2510.08814v2 Announce Type: replace-cross Abstract: 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_{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_{poly}(M(Y)mid Y)ge Omega(t) ] with high probability. This contradicts the constant upper bound from (P=NP). Therefore (P neq NP).
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Source: arXiv cs.AI | 2026-04-24