{"paper":{"title":"On the $K$-sat model with large number of clauses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Dmitry Panchenko","submitted_at":"2016-08-22T18:28:44Z","abstract_excerpt":"We show that in the $K$-sat model with $N$ variables and $\\alpha N$ clauses, the expected ratio of the smallest number of unsatisfied clauses to the number of variables is $\\alpha/2^K - \\sqrt{\\alpha} c_*(N)/2^K$ up to smaller order terms $o(\\sqrt{\\alpha})$ as $\\alpha\\to\\infty$ uniformly in $N$, where $c_*(N)$ is the expected normalized maximum energy of some specific mixed $p$-spin spin glass model. The formula for the limit of $c_*(N)$ is well known in the theory of spin glasses."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06256","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}