{"paper":{"title":"The Proof Analysis Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO","math.LO"],"primary_cat":"cs.CC","authors_text":"Albert Atserias, Erfan Khaniki, Noel Arteche, Susanna F. de Rezende","submitted_at":"2025-06-20T12:44:03Z","abstract_excerpt":"Atserias and M\\\"uller (JACM, 2020) proved that for every unsatisfiable CNF formula $\\varphi$, the formula $\\operatorname{Ref}(\\varphi)$, stating \"$\\varphi$ has small Resolution refutations\", does not have subexponential-size Resolution refutations. Conversely, when $\\varphi$ is satisfiable, Pudl\\'ak (TCS, 2003) showed how to construct a polynomial-size Resolution refutation of $\\operatorname{Ref}(\\varphi)$ given a satisfying assignment of $\\varphi$. A question that remained open is: do all short Resolution refutations of $\\operatorname{Ref}(\\varphi)$ explicitly leak a satisfying assignment of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16956","kind":"arxiv","version":2},"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/2506.16956/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"}