{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TNZFNWCMHH2YN5SM5ZO6IDZVDV","short_pith_number":"pith:TNZFNWCM","schema_version":"1.0","canonical_sha256":"9b7256d84c39f586f64cee5de40f351d4e01c543393495ef0b3cbbd0f9067c6e","source":{"kind":"arxiv","id":"1702.08392","version":1},"attestation_state":"computed","paper":{"title":"Combining the $k$-CNF and XOR Phase-Transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jeffrey M. Dudek, Kuldeep S. Meel, Moshe Y. Vardi","submitted_at":"2017-02-27T17:38:31Z","abstract_excerpt":"The runtime performance of modern SAT solvers on random $k$-CNF formulas is deeply connected with the 'phase-transition' phenomenon seen empirically in the satisfiability of random $k$-CNF formulas. Recent universal hashing-based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both $k$-CNF and XOR constraints (known as $k$-CNF-XOR formulas), but the behavior of random $k$-CNF-XOR formulas is unexplored in prior work. In this paper, we present the first study of the satisfiability of random $k$-CNF-XOR fo"},"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":"1702.08392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-27T17:38:31Z","cross_cats_sorted":[],"title_canon_sha256":"b76ce61f3dbbbef9e0ce63e1e6fbe8db4ae6529400da3f6adf34a5acd3b8e0ee","abstract_canon_sha256":"d1edebdb274f897c7728815efe0155a7de35d43b41a828cec229b8bf25d74fc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:54.878929Z","signature_b64":"WliEzAg6LsiPs5OGEzoBXEnLfk6JXwsHnYXqHP7l01XoCDDsEyN/edar4Y/IDCctoJO9SCYjn5knvsUHuTXdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b7256d84c39f586f64cee5de40f351d4e01c543393495ef0b3cbbd0f9067c6e","last_reissued_at":"2026-05-18T00:49:54.878208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:54.878208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combining the $k$-CNF and XOR Phase-Transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jeffrey M. Dudek, Kuldeep S. Meel, Moshe Y. Vardi","submitted_at":"2017-02-27T17:38:31Z","abstract_excerpt":"The runtime performance of modern SAT solvers on random $k$-CNF formulas is deeply connected with the 'phase-transition' phenomenon seen empirically in the satisfiability of random $k$-CNF formulas. Recent universal hashing-based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both $k$-CNF and XOR constraints (known as $k$-CNF-XOR formulas), but the behavior of random $k$-CNF-XOR formulas is unexplored in prior work. In this paper, we present the first study of the satisfiability of random $k$-CNF-XOR fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08392","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":""},"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":"1702.08392","created_at":"2026-05-18T00:49:54.878308+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.08392v1","created_at":"2026-05-18T00:49:54.878308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08392","created_at":"2026-05-18T00:49:54.878308+00:00"},{"alias_kind":"pith_short_12","alias_value":"TNZFNWCMHH2Y","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TNZFNWCMHH2YN5SM","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TNZFNWCM","created_at":"2026-05-18T12:31:46.661854+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV","json":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV.json","graph_json":"https://pith.science/api/pith-number/TNZFNWCMHH2YN5SM5ZO6IDZVDV/graph.json","events_json":"https://pith.science/api/pith-number/TNZFNWCMHH2YN5SM5ZO6IDZVDV/events.json","paper":"https://pith.science/paper/TNZFNWCM"},"agent_actions":{"view_html":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV","download_json":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV.json","view_paper":"https://pith.science/paper/TNZFNWCM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.08392&json=true","fetch_graph":"https://pith.science/api/pith-number/TNZFNWCMHH2YN5SM5ZO6IDZVDV/graph.json","fetch_events":"https://pith.science/api/pith-number/TNZFNWCMHH2YN5SM5ZO6IDZVDV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV/action/storage_attestation","attest_author":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV/action/author_attestation","sign_citation":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV/action/citation_signature","submit_replication":"https://pith.science/pith/TNZFNWCMHH2YN5SM5ZO6IDZVDV/action/replication_record"}},"created_at":"2026-05-18T00:49:54.878308+00:00","updated_at":"2026-05-18T00:49:54.878308+00:00"}