{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JGQYVJC3Y2GG3IZA76GQEPDSWI","short_pith_number":"pith:JGQYVJC3","schema_version":"1.0","canonical_sha256":"49a18aa45bc68c6da320ff8d023c72b22c2ddb06ef93258ba71b4077019db902","source":{"kind":"arxiv","id":"1307.0075","version":3},"attestation_state":"computed","paper":{"title":"The codegree threshold for 3-graphs with independent neighbourhoods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edward Marchant, Emil Vaughan, Oleg Pikhurko, Victor Falgas-Ravry","submitted_at":"2013-06-29T08:30:05Z","abstract_excerpt":"Given a family of 3-graphs $F$, we define its codegree threshold $\\mathrm{coex}(n, F)$ to be the largest number $d=d(n)$ such that there exists an $n$-vertex 3-graph in which every pair of vertices is contained in at least $d$ 3-edges but which contains no member of $F$ as a subgraph. Let $F_{3,2}$ be the 3-graph on $\\{a,b,c,d,e\\}$ with 3-edges $\\{abc,abd,abe,cde\\}$.\n  In this paper, we give two proofs that $\\mathrm{coex}(n, F_{3,2})= n/3 +o(n)$, the first by a direct combinatorial argument and the second via a flag algebra computation. Information extracted from the latter proof is then used "},"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":"1307.0075","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-29T08:30:05Z","cross_cats_sorted":[],"title_canon_sha256":"08cebec65bb57324626a87000e9cf33dd376268ddf49c982728dbbb5089548ac","abstract_canon_sha256":"df58788263b011d9f5871f4c5ffba2ae6882c6efa483b0408f3d76733d9ce83c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:43.419642Z","signature_b64":"kj6ABa2BDFpYBXrSQHHb5DfaE0g4bpsebA0SwPWpyAi+SIPHS5Dd0XSh+rQfLaw+OueGja0ijW+Xhu7PV3LHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49a18aa45bc68c6da320ff8d023c72b22c2ddb06ef93258ba71b4077019db902","last_reissued_at":"2026-05-18T01:55:43.418824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:43.418824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The codegree threshold for 3-graphs with independent neighbourhoods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edward Marchant, Emil Vaughan, Oleg Pikhurko, Victor Falgas-Ravry","submitted_at":"2013-06-29T08:30:05Z","abstract_excerpt":"Given a family of 3-graphs $F$, we define its codegree threshold $\\mathrm{coex}(n, F)$ to be the largest number $d=d(n)$ such that there exists an $n$-vertex 3-graph in which every pair of vertices is contained in at least $d$ 3-edges but which contains no member of $F$ as a subgraph. Let $F_{3,2}$ be the 3-graph on $\\{a,b,c,d,e\\}$ with 3-edges $\\{abc,abd,abe,cde\\}$.\n  In this paper, we give two proofs that $\\mathrm{coex}(n, F_{3,2})= n/3 +o(n)$, the first by a direct combinatorial argument and the second via a flag algebra computation. Information extracted from the latter proof is then used "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0075","kind":"arxiv","version":3},"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":"1307.0075","created_at":"2026-05-18T01:55:43.418970+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.0075v3","created_at":"2026-05-18T01:55:43.418970+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0075","created_at":"2026-05-18T01:55:43.418970+00:00"},{"alias_kind":"pith_short_12","alias_value":"JGQYVJC3Y2GG","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JGQYVJC3Y2GG3IZA","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JGQYVJC3","created_at":"2026-05-18T12:27:49.015174+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/JGQYVJC3Y2GG3IZA76GQEPDSWI","json":"https://pith.science/pith/JGQYVJC3Y2GG3IZA76GQEPDSWI.json","graph_json":"https://pith.science/api/pith-number/JGQYVJC3Y2GG3IZA76GQEPDSWI/graph.json","events_json":"https://pith.science/api/pith-number/JGQYVJC3Y2GG3IZA76GQEPDSWI/events.json","paper":"https://pith.science/paper/JGQYVJC3"},"agent_actions":{"view_html":"https://pith.science/pith/JGQYVJC3Y2GG3IZA76GQEPDSWI","download_json":"https://pith.science/pith/JGQYVJC3Y2GG3IZA76GQEPDSWI.json","view_paper":"https://pith.science/paper/JGQYVJC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.0075&json=true","fetch_graph":"https://pith.science/api/pith-number/JGQYVJC3Y2GG3IZA76GQEPDSWI/graph.json","fetch_events":"https://pith.science/api/pith-number/JGQYVJC3Y2GG3IZA76GQEPDSWI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JGQYVJC3Y2GG3IZA76GQEPDSWI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JGQYVJC3Y2GG3IZA76GQEPDSWI/action/storage_attestation","attest_author":"https://pith.science/pith/JGQYVJC3Y2GG3IZA76GQEPDSWI/action/author_attestation","sign_citation":"https://pith.science/pith/JGQYVJC3Y2GG3IZA76GQEPDSWI/action/citation_signature","submit_replication":"https://pith.science/pith/JGQYVJC3Y2GG3IZA76GQEPDSWI/action/replication_record"}},"created_at":"2026-05-18T01:55:43.418970+00:00","updated_at":"2026-05-18T01:55:43.418970+00:00"}