{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UFZDTUEX6GJLW7P3EPADFSRXHN","short_pith_number":"pith:UFZDTUEX","schema_version":"1.0","canonical_sha256":"a17239d097f192bb7dfb23c032ca373b77a806393b23f1ba9e093ffba94b6a87","source":{"kind":"arxiv","id":"1212.3822","version":2},"attestation_state":"computed","paper":{"title":"The Satisfiability Threshold for $k$-XORSAT, using an alternative proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Boris Pittel, Gregory B. Sorkin","submitted_at":"2012-12-16T19:37:15Z","abstract_excerpt":"We consider \"unconstrained\" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-homogeneous equations in $\\mathbb{F}_2$ over $n$ variables, each equation containing $k \\ge 3$ variables, and also consider a \"constrained\" model where every variable appears in at least two equations. Dubois and Mandler proved that $m/n=1$ is a sharp threshold for satisfiability of constrained 3-XORSAT, and analyzed the 2-core of a random 3-uniform hypergraph to extend this result to find the threshold for unconstrained 3-XORSAT.\n  We show that $m/n=1$ remains a sharp threshold for satisfiabili"},"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":"1212.3822","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-16T19:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"5fe7d47340cd45d4f27ef09c988414642aebad10d56b1422ba023e0fd6e78d71","abstract_canon_sha256":"3e8509096df0b60f8880271b51e4abd6c6dcbadfd45926d1f5e43c9cda291ca7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:57.819490Z","signature_b64":"C2Y77Yvj783mz/nnsJ2TjPnq1wfmnGSAwWjR8+xKyqlfQD/clRLtvLgWulifEzkRKO3s+jzjHzG+CuqdWedmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a17239d097f192bb7dfb23c032ca373b77a806393b23f1ba9e093ffba94b6a87","last_reissued_at":"2026-05-18T03:11:57.818546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:57.818546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Satisfiability Threshold for $k$-XORSAT, using an alternative proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Boris Pittel, Gregory B. Sorkin","submitted_at":"2012-12-16T19:37:15Z","abstract_excerpt":"We consider \"unconstrained\" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-homogeneous equations in $\\mathbb{F}_2$ over $n$ variables, each equation containing $k \\ge 3$ variables, and also consider a \"constrained\" model where every variable appears in at least two equations. Dubois and Mandler proved that $m/n=1$ is a sharp threshold for satisfiability of constrained 3-XORSAT, and analyzed the 2-core of a random 3-uniform hypergraph to extend this result to find the threshold for unconstrained 3-XORSAT.\n  We show that $m/n=1$ remains a sharp threshold for satisfiabili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3822","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":""},"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":"1212.3822","created_at":"2026-05-18T03:11:57.818692+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.3822v2","created_at":"2026-05-18T03:11:57.818692+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3822","created_at":"2026-05-18T03:11:57.818692+00:00"},{"alias_kind":"pith_short_12","alias_value":"UFZDTUEX6GJL","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"UFZDTUEX6GJLW7P3","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"UFZDTUEX","created_at":"2026-05-18T12:27:23.164592+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/UFZDTUEX6GJLW7P3EPADFSRXHN","json":"https://pith.science/pith/UFZDTUEX6GJLW7P3EPADFSRXHN.json","graph_json":"https://pith.science/api/pith-number/UFZDTUEX6GJLW7P3EPADFSRXHN/graph.json","events_json":"https://pith.science/api/pith-number/UFZDTUEX6GJLW7P3EPADFSRXHN/events.json","paper":"https://pith.science/paper/UFZDTUEX"},"agent_actions":{"view_html":"https://pith.science/pith/UFZDTUEX6GJLW7P3EPADFSRXHN","download_json":"https://pith.science/pith/UFZDTUEX6GJLW7P3EPADFSRXHN.json","view_paper":"https://pith.science/paper/UFZDTUEX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.3822&json=true","fetch_graph":"https://pith.science/api/pith-number/UFZDTUEX6GJLW7P3EPADFSRXHN/graph.json","fetch_events":"https://pith.science/api/pith-number/UFZDTUEX6GJLW7P3EPADFSRXHN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UFZDTUEX6GJLW7P3EPADFSRXHN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UFZDTUEX6GJLW7P3EPADFSRXHN/action/storage_attestation","attest_author":"https://pith.science/pith/UFZDTUEX6GJLW7P3EPADFSRXHN/action/author_attestation","sign_citation":"https://pith.science/pith/UFZDTUEX6GJLW7P3EPADFSRXHN/action/citation_signature","submit_replication":"https://pith.science/pith/UFZDTUEX6GJLW7P3EPADFSRXHN/action/replication_record"}},"created_at":"2026-05-18T03:11:57.818692+00:00","updated_at":"2026-05-18T03:11:57.818692+00:00"}