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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2510.08814 |
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| _version_ | 1866917430115172352 |
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| author | Goertzel, Ben |
| author_facet | Goertzel, Ben |
| contents | 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 \(P \neq NP\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Quantale-Weakness Route to $P \neq NP$ via CD Evidence Normalization and Gauge-Buffered Locked Ensembles Goertzel, Ben Computational Complexity Artificial Intelligence 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 \(P \neq NP\). |
| title | A Quantale-Weakness Route to $P \neq NP$ via CD Evidence Normalization and Gauge-Buffered Locked Ensembles |
| topic | Computational Complexity Artificial Intelligence |
| url | https://arxiv.org/abs/2510.08814 |