{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MHT5KTNJMJBT2JWZOOXETHJLI5","short_pith_number":"pith:MHT5KTNJ","schema_version":"1.0","canonical_sha256":"61e7d54da962433d26d973ae499d2b475ced74762ec437ae647aad1f9d18f0d7","source":{"kind":"arxiv","id":"1311.4821","version":8},"attestation_state":"computed","paper":{"title":"On the Complexity of Random Satisfiability Problems with Planted Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.CO","math.PR"],"primary_cat":"cs.CC","authors_text":"Santosh Vempala, Vitaly Feldman, Will Perkins","submitted_at":"2013-11-19T18:13:32Z","abstract_excerpt":"The problem of identifying a planted assignment given a random $k$-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution becomes unique and can be identified given a formula with $O(n\\log n)$ clauses, there are distributions over clauses for which the best known efficient algorithms require $n^{k/2}$ clauses. We propose and study a unified model for planted $k$-SAT, which captures well-known special cases. An instance is described by a planted assignment $\\sigma$ and a distribution on clauses with $k$ literals. We define its distribution comple"},"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":"1311.4821","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-19T18:13:32Z","cross_cats_sorted":["cs.DM","cs.DS","math.CO","math.PR"],"title_canon_sha256":"82dab30ec6f39addee891a9bfd19148bff1b1e27f73ab1da45f17ae407e3d7ef","abstract_canon_sha256":"a48b6ccb85b086b08f909024080890aeeb5a1c89e8171f4b18146156321dbba4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:55.339268Z","signature_b64":"pDlZx4wxS9wTH8fJIdxyXmYpVx0R0vLklOSyUbEsUL6hxIrhXU/YRDDmzSurt+MHY6qXZN4Drmuq3A3AOIxGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61e7d54da962433d26d973ae499d2b475ced74762ec437ae647aad1f9d18f0d7","last_reissued_at":"2026-05-18T00:21:55.338565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:55.338565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Complexity of Random Satisfiability Problems with Planted Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.CO","math.PR"],"primary_cat":"cs.CC","authors_text":"Santosh Vempala, Vitaly Feldman, Will Perkins","submitted_at":"2013-11-19T18:13:32Z","abstract_excerpt":"The problem of identifying a planted assignment given a random $k$-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution becomes unique and can be identified given a formula with $O(n\\log n)$ clauses, there are distributions over clauses for which the best known efficient algorithms require $n^{k/2}$ clauses. We propose and study a unified model for planted $k$-SAT, which captures well-known special cases. An instance is described by a planted assignment $\\sigma$ and a distribution on clauses with $k$ literals. We define its distribution comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4821","kind":"arxiv","version":8},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.4821","created_at":"2026-05-18T00:21:55.338681+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4821v8","created_at":"2026-05-18T00:21:55.338681+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4821","created_at":"2026-05-18T00:21:55.338681+00:00"},{"alias_kind":"pith_short_12","alias_value":"MHT5KTNJMJBT","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MHT5KTNJMJBT2JWZ","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MHT5KTNJ","created_at":"2026-05-18T12:27:52.871228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.09837","citing_title":"Planted-solution SAT and Ising benchmarks from integer factorization","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5","json":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5.json","graph_json":"https://pith.science/api/pith-number/MHT5KTNJMJBT2JWZOOXETHJLI5/graph.json","events_json":"https://pith.science/api/pith-number/MHT5KTNJMJBT2JWZOOXETHJLI5/events.json","paper":"https://pith.science/paper/MHT5KTNJ"},"agent_actions":{"view_html":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5","download_json":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5.json","view_paper":"https://pith.science/paper/MHT5KTNJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4821&json=true","fetch_graph":"https://pith.science/api/pith-number/MHT5KTNJMJBT2JWZOOXETHJLI5/graph.json","fetch_events":"https://pith.science/api/pith-number/MHT5KTNJMJBT2JWZOOXETHJLI5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5/action/storage_attestation","attest_author":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5/action/author_attestation","sign_citation":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5/action/citation_signature","submit_replication":"https://pith.science/pith/MHT5KTNJMJBT2JWZOOXETHJLI5/action/replication_record"}},"created_at":"2026-05-18T00:21:55.338681+00:00","updated_at":"2026-05-18T00:21:55.338681+00:00"}