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We show that for large $n$, the unique largest $\\mc{K}_{3,3}^3$-free 3-graph on $n$ vertices is a balanced blow-up of the complete 3-graph on 5 vertices. Our proof uses the stability method and a result on lagrangians of intersecting families that has independent interest."},"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":"1307.8423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-31T18:53:10Z","cross_cats_sorted":[],"title_canon_sha256":"ad6259da365e6b75f5c420cd0ccb46c697325b83e6340478b15a578ea45f8235","abstract_canon_sha256":"73a8dd09b2e1585782330743b7871c1dd266f3262bce543728dfbf59af0f315f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:01.186722Z","signature_b64":"9Qsk7vI5HIPBrubZoYl6Sg7o573Oj5GCtdC4Cx5q3PNlkR625ZrLytjzVdHUWBWmcIP2al2OINEiBGtYhhHcBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15475f52eb5aec13af057973d494385d4f773007e8789651fc0bce728a7b035d","last_reissued_at":"2026-05-18T03:17:01.185991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:01.185991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A hypergraph Tur\\'an theorem via lagrangians of intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Hefetz, Peter Keevash","submitted_at":"2013-07-31T18:53:10Z","abstract_excerpt":"Let $\\mc{K}_{3,3}^3$ be the 3-graph with 15 vertices $\\{x_i, y_i: 1 \\le i \\le 3\\}$ and $\\{z_{ij}: 1 \\le i,j \\le 3\\}$, and 11 edges $\\{x_1, x_2, x_3\\}$, $\\{y_1, y_2, y_3\\}$ and $\\{\\{x_i, y_j, z_{ij}\\}: 1 \\le i,j \\le 3\\}$. We show that for large $n$, the unique largest $\\mc{K}_{3,3}^3$-free 3-graph on $n$ vertices is a balanced blow-up of the complete 3-graph on 5 vertices. Our proof uses the stability method and a result on lagrangians of intersecting families that has independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8423","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":"1307.8423","created_at":"2026-05-18T03:17:01.186110+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.8423v1","created_at":"2026-05-18T03:17:01.186110+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8423","created_at":"2026-05-18T03:17:01.186110+00:00"},{"alias_kind":"pith_short_12","alias_value":"CVDV6UXLLLWB","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CVDV6UXLLLWBHLYF","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CVDV6UXL","created_at":"2026-05-18T12:27:40.988391+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/CVDV6UXLLLWBHLYFPFZ5JFBYLV","json":"https://pith.science/pith/CVDV6UXLLLWBHLYFPFZ5JFBYLV.json","graph_json":"https://pith.science/api/pith-number/CVDV6UXLLLWBHLYFPFZ5JFBYLV/graph.json","events_json":"https://pith.science/api/pith-number/CVDV6UXLLLWBHLYFPFZ5JFBYLV/events.json","paper":"https://pith.science/paper/CVDV6UXL"},"agent_actions":{"view_html":"https://pith.science/pith/CVDV6UXLLLWBHLYFPFZ5JFBYLV","download_json":"https://pith.science/pith/CVDV6UXLLLWBHLYFPFZ5JFBYLV.json","view_paper":"https://pith.science/paper/CVDV6UXL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.8423&json=true","fetch_graph":"https://pith.science/api/pith-number/CVDV6UXLLLWBHLYFPFZ5JFBYLV/graph.json","fetch_events":"https://pith.science/api/pith-number/CVDV6UXLLLWBHLYFPFZ5JFBYLV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CVDV6UXLLLWBHLYFPFZ5JFBYLV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CVDV6UXLLLWBHLYFPFZ5JFBYLV/action/storage_attestation","attest_author":"https://pith.science/pith/CVDV6UXLLLWBHLYFPFZ5JFBYLV/action/author_attestation","sign_citation":"https://pith.science/pith/CVDV6UXLLLWBHLYFPFZ5JFBYLV/action/citation_signature","submit_replication":"https://pith.science/pith/CVDV6UXLLLWBHLYFPFZ5JFBYLV/action/replication_record"}},"created_at":"2026-05-18T03:17:01.186110+00:00","updated_at":"2026-05-18T03:17:01.186110+00:00"}