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It coincides with the analogous formula for the 3-uniform triangle $C^3_3$, obtained earlier by Frankl and F\\\"uredi for $n\\ge 75$ and Cs\\'ak\\'any and Kahn for all $n$. In view of this coincidence, we also determine a `conditional' Tur\\'an number, defined as the maximum number of edges in a $P^3_3$-free 3-uniform hypergraph on $n$ vertices which is \\emph{not} $C^3_3$-free."},"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":"1506.03759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-11T18:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"3e67b3d09b476b45ce8b4d37138d18962c04bc8a5ee98ab921c7d9e43a4d9508","abstract_canon_sha256":"86de6c3f8c7d0f66cf9dd750b466eac764a8eb9ac83c82b8a1f947aadae90ea1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:03.376935Z","signature_b64":"OY60ixEVVqn9akEZSLy+SSFcw56Eyd5OA/o6IgcMh+poJkLOB8f308xGP+erJQN+Mouk/BPhWjKAUVnFrc34Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cc2b368eedc075a92fb8b35ca7495ac5d262893355c7d43c4cec482efc808d5","last_reissued_at":"2026-05-18T01:53:03.376350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:03.376350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tur\\'an numbers for 3-uniform linear paths of length 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Ruci\\'nski, Eliza Jackowska, Joanna Polcyn","submitted_at":"2015-06-11T18:01:43Z","abstract_excerpt":"In this paper we confirm a conjecture of F\\\"uredi, Jiang, and Seiver, and determine an exact formula for the Tur\\'an number $ex_3(n; P_3^3)$ of the 3-uniform linear path $P^3_3$ of length 3, valid for all $n$. It coincides with the analogous formula for the 3-uniform triangle $C^3_3$, obtained earlier by Frankl and F\\\"uredi for $n\\ge 75$ and Cs\\'ak\\'any and Kahn for all $n$. In view of this coincidence, we also determine a `conditional' Tur\\'an number, defined as the maximum number of edges in a $P^3_3$-free 3-uniform hypergraph on $n$ vertices which is \\emph{not} $C^3_3$-free."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03759","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":"1506.03759","created_at":"2026-05-18T01:53:03.376432+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03759v1","created_at":"2026-05-18T01:53:03.376432+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03759","created_at":"2026-05-18T01:53:03.376432+00:00"},{"alias_kind":"pith_short_12","alias_value":"DTBLG2HO3QDV","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DTBLG2HO3QDVVEX3","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DTBLG2HO","created_at":"2026-05-18T12:29:17.054201+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/DTBLG2HO3QDVVEX3RM24U5EVVR","json":"https://pith.science/pith/DTBLG2HO3QDVVEX3RM24U5EVVR.json","graph_json":"https://pith.science/api/pith-number/DTBLG2HO3QDVVEX3RM24U5EVVR/graph.json","events_json":"https://pith.science/api/pith-number/DTBLG2HO3QDVVEX3RM24U5EVVR/events.json","paper":"https://pith.science/paper/DTBLG2HO"},"agent_actions":{"view_html":"https://pith.science/pith/DTBLG2HO3QDVVEX3RM24U5EVVR","download_json":"https://pith.science/pith/DTBLG2HO3QDVVEX3RM24U5EVVR.json","view_paper":"https://pith.science/paper/DTBLG2HO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03759&json=true","fetch_graph":"https://pith.science/api/pith-number/DTBLG2HO3QDVVEX3RM24U5EVVR/graph.json","fetch_events":"https://pith.science/api/pith-number/DTBLG2HO3QDVVEX3RM24U5EVVR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DTBLG2HO3QDVVEX3RM24U5EVVR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DTBLG2HO3QDVVEX3RM24U5EVVR/action/storage_attestation","attest_author":"https://pith.science/pith/DTBLG2HO3QDVVEX3RM24U5EVVR/action/author_attestation","sign_citation":"https://pith.science/pith/DTBLG2HO3QDVVEX3RM24U5EVVR/action/citation_signature","submit_replication":"https://pith.science/pith/DTBLG2HO3QDVVEX3RM24U5EVVR/action/replication_record"}},"created_at":"2026-05-18T01:53:03.376432+00:00","updated_at":"2026-05-18T01:53:03.376432+00:00"}