{"paper":{"title":"A Better Analysis For PPSZ For 3-SAT","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Shaowei Cai, Tao Jiang","submitted_at":"2026-07-12T10:40:39Z","abstract_excerpt":"We revisit Scheder's analysis of the original PPSZ algorithm. Keeping his regular and irregular estimates unchanged, we express them in common structural coordinates and replace only their final recombination by an explicit linear-programming dual certificate. The old and new running-time bounds are \\[ \\begin{array}{c|cc}\n  & \\text{Unique-$3$-SAT} & \\text{general $3$-SAT} \\\\ \\hline \\text{Scheder's analysis} & O^*(1.306972377^n) & O^*(1.307031594^n) \\\\ \\text{this work} & O^*(1.306969598^n) & O^*(1.307031578^n). \\end{array} \\] In both rows, the general-case bound is obtained by applying the same"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10697","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10697/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}