AI RESEARCH
A Quantale-Weakness Route to $P \neq NP$ via CD Evidence Normalization and Gauge-Buffered Locked Ensembles
arXiv CS.AI
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ArXi:2510.08814v2 Announce Type: replace-cross 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.