{"ID":2858460,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08814","arxiv_id":"2510.08814","title":"A Quantale-Weakness Route to $P \\neq NP$ via CD Evidence Normalization and Gauge-Buffered Locked Ensembles","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_{\\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\\).","short_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 polyn...","url_abs":"https://arxiv.org/abs/2510.08814","url_pdf":"https://arxiv.org/pdf/2510.08814v2","authors":"[\"Ben Goertzel\"]","published":"2025-10-09T21:01:17Z","proceeding":"cs.CC","tasks":"[\"cs.CC\",\"cs.AI\"]","methods":"[]","has_code":false}