{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:VKZ5TXZQ7KVLRUET5C5RT426HJ","short_pith_number":"pith:VKZ5TXZQ","schema_version":"1.0","canonical_sha256":"aab3d9df30faaab8d093e8bb19f35e3a75130b606068be6605d8d6382ee66697","source":{"kind":"arxiv","id":"1201.4326","version":1},"attestation_state":"computed","paper":{"title":"Tur\\'an H-densities for 3-graphs","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":"2012-01-20T16:02:34Z","abstract_excerpt":"Given an $r$-graph $H$ on $h$ vertices, and a family $\\mathcal{F}$ of forbidden subgraphs, we define $\\ex_{H}(n, \\mathcal{F})$ to be the maximum number of induced copies of $H$ in an $\\mathcal{F}$-free $r$-graph on $n$ vertices.\n  Then the \\emph{Tur\\'an $H$-density} of $\\mathcal{F}$ is the limit \\[\\pi_{H}(\\mathcal{F})= \\lim_{n\\rightarrow \\infty}\\ex_{H}(n, \\mathcal{F})/\\binom{n}{h}. \\]\n  This generalises the notions of \\emph{Tur\\'an density} (when $H$ is an $r$-edge), and \\emph{inducibility} (when $\\mathcal{F}$ is empty). Although problems of this kind have received some attention, very few res"},"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":"1201.4326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-20T16:02:34Z","cross_cats_sorted":[],"title_canon_sha256":"40fe4c88bda62f944571f549d299691d20a03d06618c6221630f4835cc13d102","abstract_canon_sha256":"1b14930d2fa8a7db74872a78ab2bb025cb26a7c4b6813b780a27aadd3a7e81ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:11.245401Z","signature_b64":"Gzj74vKyr7dSYohFPDYpnwkEaHHCzAU0obbqkbkeI3J5aANGPBfgchomaaLbzYH1qwTuQT8W1Wp3wkbM6ykxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aab3d9df30faaab8d093e8bb19f35e3a75130b606068be6605d8d6382ee66697","last_reissued_at":"2026-05-18T02:25:11.244963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:11.244963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tur\\'an H-densities for 3-graphs","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":"2012-01-20T16:02:34Z","abstract_excerpt":"Given an $r$-graph $H$ on $h$ vertices, and a family $\\mathcal{F}$ of forbidden subgraphs, we define $\\ex_{H}(n, \\mathcal{F})$ to be the maximum number of induced copies of $H$ in an $\\mathcal{F}$-free $r$-graph on $n$ vertices.\n  Then the \\emph{Tur\\'an $H$-density} of $\\mathcal{F}$ is the limit \\[\\pi_{H}(\\mathcal{F})= \\lim_{n\\rightarrow \\infty}\\ex_{H}(n, \\mathcal{F})/\\binom{n}{h}. \\]\n  This generalises the notions of \\emph{Tur\\'an density} (when $H$ is an $r$-edge), and \\emph{inducibility} (when $\\mathcal{F}$ is empty). Although problems of this kind have received some attention, very few res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4326","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":"1201.4326","created_at":"2026-05-18T02:25:11.245022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.4326v1","created_at":"2026-05-18T02:25:11.245022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4326","created_at":"2026-05-18T02:25:11.245022+00:00"},{"alias_kind":"pith_short_12","alias_value":"VKZ5TXZQ7KVL","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"VKZ5TXZQ7KVLRUET","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"VKZ5TXZQ","created_at":"2026-05-18T12:27:25.539911+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/VKZ5TXZQ7KVLRUET5C5RT426HJ","json":"https://pith.science/pith/VKZ5TXZQ7KVLRUET5C5RT426HJ.json","graph_json":"https://pith.science/api/pith-number/VKZ5TXZQ7KVLRUET5C5RT426HJ/graph.json","events_json":"https://pith.science/api/pith-number/VKZ5TXZQ7KVLRUET5C5RT426HJ/events.json","paper":"https://pith.science/paper/VKZ5TXZQ"},"agent_actions":{"view_html":"https://pith.science/pith/VKZ5TXZQ7KVLRUET5C5RT426HJ","download_json":"https://pith.science/pith/VKZ5TXZQ7KVLRUET5C5RT426HJ.json","view_paper":"https://pith.science/paper/VKZ5TXZQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.4326&json=true","fetch_graph":"https://pith.science/api/pith-number/VKZ5TXZQ7KVLRUET5C5RT426HJ/graph.json","fetch_events":"https://pith.science/api/pith-number/VKZ5TXZQ7KVLRUET5C5RT426HJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VKZ5TXZQ7KVLRUET5C5RT426HJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VKZ5TXZQ7KVLRUET5C5RT426HJ/action/storage_attestation","attest_author":"https://pith.science/pith/VKZ5TXZQ7KVLRUET5C5RT426HJ/action/author_attestation","sign_citation":"https://pith.science/pith/VKZ5TXZQ7KVLRUET5C5RT426HJ/action/citation_signature","submit_replication":"https://pith.science/pith/VKZ5TXZQ7KVLRUET5C5RT426HJ/action/replication_record"}},"created_at":"2026-05-18T02:25:11.245022+00:00","updated_at":"2026-05-18T02:25:11.245022+00:00"}