{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:X4XRNNPJVUAMUIJBSA3VJFPIOT","short_pith_number":"pith:X4XRNNPJ","schema_version":"1.0","canonical_sha256":"bf2f16b5e9ad00ca212190375495e874fe58265652ffa26f94454b245e49f1ac","source":{"kind":"arxiv","id":"2507.14504","version":1},"attestation_state":"computed","paper":{"title":"New Algorithms for #2-SAT and #3-SAT","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Junqiang Peng, Mingyu Xiao, Zimo Sheng","submitted_at":"2025-07-19T06:32:36Z","abstract_excerpt":"The #2-SAT and #3-SAT problems involve counting the number of satisfying assignments (also called models) for instances of 2-SAT and 3-SAT, respectively. In 2010, Zhou et al. proposed an $\\mathcal{O}^*(1.1892^m)$-time algorithm for #2-SAT and an efficient approach for #3-SAT, where $m$ denotes the number of clauses. In this paper, we show that the weighted versions of #2-SAT and #3-SAT can be solved in $\\mathcal{O}^*(1.1082^m)$ and $\\mathcal{O}^*(1.4423^m)$ time, respectively. These results directly apply to the unweighted cases and achieve substantial improvements over the previous results. T"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.14504","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-07-19T06:32:36Z","cross_cats_sorted":[],"title_canon_sha256":"d6bbcbcc06d1afb78f8777dc4003088d63b818d95a1a5276d9c30d8d79c76bb8","abstract_canon_sha256":"fd4f719c6e02e5e8f52be08010658476f6de6f4216084e94e3015ba2a70e4f64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:08.523843Z","signature_b64":"fyBoTz2zCUxr596igGlmSNS0V3Enqog8ZC5G3NTwEpbBlS2n0Vl7mF4WuPlP8MmCSETvedBY8vjUGPU/63b3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf2f16b5e9ad00ca212190375495e874fe58265652ffa26f94454b245e49f1ac","last_reissued_at":"2026-07-05T11:40:08.523341Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:08.523341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Algorithms for #2-SAT and #3-SAT","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Junqiang Peng, Mingyu Xiao, Zimo Sheng","submitted_at":"2025-07-19T06:32:36Z","abstract_excerpt":"The #2-SAT and #3-SAT problems involve counting the number of satisfying assignments (also called models) for instances of 2-SAT and 3-SAT, respectively. In 2010, Zhou et al. proposed an $\\mathcal{O}^*(1.1892^m)$-time algorithm for #2-SAT and an efficient approach for #3-SAT, where $m$ denotes the number of clauses. In this paper, we show that the weighted versions of #2-SAT and #3-SAT can be solved in $\\mathcal{O}^*(1.1082^m)$ and $\\mathcal{O}^*(1.4423^m)$ time, respectively. These results directly apply to the unweighted cases and achieve substantial improvements over the previous results. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14504","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/2507.14504/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.14504","created_at":"2026-07-05T11:40:08.523401+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.14504v1","created_at":"2026-07-05T11:40:08.523401+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14504","created_at":"2026-07-05T11:40:08.523401+00:00"},{"alias_kind":"pith_short_12","alias_value":"X4XRNNPJVUAM","created_at":"2026-07-05T11:40:08.523401+00:00"},{"alias_kind":"pith_short_16","alias_value":"X4XRNNPJVUAMUIJB","created_at":"2026-07-05T11:40:08.523401+00:00"},{"alias_kind":"pith_short_8","alias_value":"X4XRNNPJ","created_at":"2026-07-05T11:40:08.523401+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.15031","citing_title":"A Hypergraph Container Method for Spread SAT: Approximation and Speedup","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT","json":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT.json","graph_json":"https://pith.science/api/pith-number/X4XRNNPJVUAMUIJBSA3VJFPIOT/graph.json","events_json":"https://pith.science/api/pith-number/X4XRNNPJVUAMUIJBSA3VJFPIOT/events.json","paper":"https://pith.science/paper/X4XRNNPJ"},"agent_actions":{"view_html":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT","download_json":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT.json","view_paper":"https://pith.science/paper/X4XRNNPJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.14504&json=true","fetch_graph":"https://pith.science/api/pith-number/X4XRNNPJVUAMUIJBSA3VJFPIOT/graph.json","fetch_events":"https://pith.science/api/pith-number/X4XRNNPJVUAMUIJBSA3VJFPIOT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT/action/storage_attestation","attest_author":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT/action/author_attestation","sign_citation":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT/action/citation_signature","submit_replication":"https://pith.science/pith/X4XRNNPJVUAMUIJBSA3VJFPIOT/action/replication_record"}},"created_at":"2026-07-05T11:40:08.523401+00:00","updated_at":"2026-07-05T11:40:08.523401+00:00"}