{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4JPEX7JIZYFYPTYAEX2YCY45I2","short_pith_number":"pith:4JPEX7JI","schema_version":"1.0","canonical_sha256":"e25e4bfd28ce0b87cf0025f581639d46a8f4b49d911cf7aa3dad8ccc45b48a90","source":{"kind":"arxiv","id":"1110.1623","version":2},"attestation_state":"computed","paper":{"title":"On applications of Razborov's flag algebra calculus to extremal 3-graph theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emil R. Vaughan, Victor Falgas-Ravry","submitted_at":"2011-10-07T19:56:43Z","abstract_excerpt":"In this paper, we prove several new Tur\\'an density results for 3-graphs with independent neighbourhoods. We show:\n  \\pi(K_4^-, C_5, F_{3,2})=12/49, \\pi(K_4^-, F_{3,2})=5/18, and\n  \\pi(J_4, F_{3,2})=\\pi(J_5, F_{3,2})=3/8, where J_t is the 3-graph consisting of a single vertex x together with a disjoint set A of size t and all $\\binom{|A|}{2}$ 3-edges containing x.\n  We also prove two Tur\\'an density results where we forbid certain induced subgraphs:\n  \\pi(F_{3,2}, induced K_4^-)=3/8 and\n  \\pi(K_5, 5-set spanning 8 edges)=3/4.\n  The latter result is an analogue for K_5 of Razborov's result that"},"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":"1110.1623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-07T19:56:43Z","cross_cats_sorted":[],"title_canon_sha256":"641dd76d8c9b06fd39ac11f5ccf0175220052518c77c7857c5f609c8707ccbd7","abstract_canon_sha256":"2610e96cbbf06d1d7446aa1fd8f4f75bad298a7897dd0dd836311087d05db57a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:11.705038Z","signature_b64":"BCnpq57Z11570ksvq/GgJ5zCQ7QeuRr46fVmr1AXGKNHyp/EIzIcLIJfsI4zdYg1RvjFqagqW+kAL4iAPiJABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e25e4bfd28ce0b87cf0025f581639d46a8f4b49d911cf7aa3dad8ccc45b48a90","last_reissued_at":"2026-05-18T02:25:11.704605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:11.704605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On applications of Razborov's flag algebra calculus to extremal 3-graph theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emil R. Vaughan, Victor Falgas-Ravry","submitted_at":"2011-10-07T19:56:43Z","abstract_excerpt":"In this paper, we prove several new Tur\\'an density results for 3-graphs with independent neighbourhoods. We show:\n  \\pi(K_4^-, C_5, F_{3,2})=12/49, \\pi(K_4^-, F_{3,2})=5/18, and\n  \\pi(J_4, F_{3,2})=\\pi(J_5, F_{3,2})=3/8, where J_t is the 3-graph consisting of a single vertex x together with a disjoint set A of size t and all $\\binom{|A|}{2}$ 3-edges containing x.\n  We also prove two Tur\\'an density results where we forbid certain induced subgraphs:\n  \\pi(F_{3,2}, induced K_4^-)=3/8 and\n  \\pi(K_5, 5-set spanning 8 edges)=3/4.\n  The latter result is an analogue for K_5 of Razborov's result that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1623","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":"1110.1623","created_at":"2026-05-18T02:25:11.704671+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.1623v2","created_at":"2026-05-18T02:25:11.704671+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1623","created_at":"2026-05-18T02:25:11.704671+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JPEX7JIZYFY","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JPEX7JIZYFYPTYA","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JPEX7JI","created_at":"2026-05-18T12:26:20.644004+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/4JPEX7JIZYFYPTYAEX2YCY45I2","json":"https://pith.science/pith/4JPEX7JIZYFYPTYAEX2YCY45I2.json","graph_json":"https://pith.science/api/pith-number/4JPEX7JIZYFYPTYAEX2YCY45I2/graph.json","events_json":"https://pith.science/api/pith-number/4JPEX7JIZYFYPTYAEX2YCY45I2/events.json","paper":"https://pith.science/paper/4JPEX7JI"},"agent_actions":{"view_html":"https://pith.science/pith/4JPEX7JIZYFYPTYAEX2YCY45I2","download_json":"https://pith.science/pith/4JPEX7JIZYFYPTYAEX2YCY45I2.json","view_paper":"https://pith.science/paper/4JPEX7JI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.1623&json=true","fetch_graph":"https://pith.science/api/pith-number/4JPEX7JIZYFYPTYAEX2YCY45I2/graph.json","fetch_events":"https://pith.science/api/pith-number/4JPEX7JIZYFYPTYAEX2YCY45I2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JPEX7JIZYFYPTYAEX2YCY45I2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JPEX7JIZYFYPTYAEX2YCY45I2/action/storage_attestation","attest_author":"https://pith.science/pith/4JPEX7JIZYFYPTYAEX2YCY45I2/action/author_attestation","sign_citation":"https://pith.science/pith/4JPEX7JIZYFYPTYAEX2YCY45I2/action/citation_signature","submit_replication":"https://pith.science/pith/4JPEX7JIZYFYPTYAEX2YCY45I2/action/replication_record"}},"created_at":"2026-05-18T02:25:11.704671+00:00","updated_at":"2026-05-18T02:25:11.704671+00:00"}