{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Z2RNZEXNGM2JSOSELC3NRUUDUX","short_pith_number":"pith:Z2RNZEXN","schema_version":"1.0","canonical_sha256":"cea2dc92ed3334993a4458b6d8d283a5fecf441d828efba0ecaa062b19c3be71","source":{"kind":"arxiv","id":"1505.03210","version":1},"attestation_state":"computed","paper":{"title":"Tur\\'an numbers of hypergraph trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tao Jiang, Zolt\\'an F\\\"uredi","submitted_at":"2015-05-13T01:36:19Z","abstract_excerpt":"An $r$-graph is an $r$-uniform hypergraph tree (or $r$-tree) if its edges can be ordered as $E_1,\\ldots, E_m$ such that $\\forall i>1 \\, \\exists \\alpha(i)<i$ such that $E_i\\cap (\\bigcup_{j=1}^{i-1} E_j)\\subseteq E_{\\alpha(i)}$. The Tur\\'an number $ex(n,{\\cal H})$ of an $r$-graph ${\\cal H}$ is the largest size of an $n$-vertex $r$-graph that does not contain ${\\cal H}$. A cross-cut of ${\\cal H}$ is a set of vertices in ${\\cal H}$ that contains exactly one vertex of each edge of ${\\cal H}$. The cross-cut number $\\sigma({\\cal H})$ of ${\\cal H}$ is the minimum size of a cross-cut of ${\\cal H}$. We "},"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":"1505.03210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-13T01:36:19Z","cross_cats_sorted":[],"title_canon_sha256":"5460ef4e8fa802d7167690376c089a2b9def32b98f491c990e2d60845ae2451c","abstract_canon_sha256":"87a40109d6321a36bd3b0c6ddedd2486980eb5bc58daca0022a1a9d21f910196"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:10.121900Z","signature_b64":"7ZmHTM7fsQctFzDTQiG4sajpeMyjPI11OJbRHEMJHXnHGqCgDoD02U138So4oW1+nB0R4BDqGKzplrCGoe5dDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea2dc92ed3334993a4458b6d8d283a5fecf441d828efba0ecaa062b19c3be71","last_reissued_at":"2026-05-18T02:12:10.120949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:10.120949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tur\\'an numbers of hypergraph trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tao Jiang, Zolt\\'an F\\\"uredi","submitted_at":"2015-05-13T01:36:19Z","abstract_excerpt":"An $r$-graph is an $r$-uniform hypergraph tree (or $r$-tree) if its edges can be ordered as $E_1,\\ldots, E_m$ such that $\\forall i>1 \\, \\exists \\alpha(i)<i$ such that $E_i\\cap (\\bigcup_{j=1}^{i-1} E_j)\\subseteq E_{\\alpha(i)}$. The Tur\\'an number $ex(n,{\\cal H})$ of an $r$-graph ${\\cal H}$ is the largest size of an $n$-vertex $r$-graph that does not contain ${\\cal H}$. A cross-cut of ${\\cal H}$ is a set of vertices in ${\\cal H}$ that contains exactly one vertex of each edge of ${\\cal H}$. The cross-cut number $\\sigma({\\cal H})$ of ${\\cal H}$ is the minimum size of a cross-cut of ${\\cal H}$. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03210","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":"1505.03210","created_at":"2026-05-18T02:12:10.121112+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03210v1","created_at":"2026-05-18T02:12:10.121112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03210","created_at":"2026-05-18T02:12:10.121112+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2RNZEXNGM2J","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2RNZEXNGM2JSOSE","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2RNZEXN","created_at":"2026-05-18T12:29:52.810259+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/Z2RNZEXNGM2JSOSELC3NRUUDUX","json":"https://pith.science/pith/Z2RNZEXNGM2JSOSELC3NRUUDUX.json","graph_json":"https://pith.science/api/pith-number/Z2RNZEXNGM2JSOSELC3NRUUDUX/graph.json","events_json":"https://pith.science/api/pith-number/Z2RNZEXNGM2JSOSELC3NRUUDUX/events.json","paper":"https://pith.science/paper/Z2RNZEXN"},"agent_actions":{"view_html":"https://pith.science/pith/Z2RNZEXNGM2JSOSELC3NRUUDUX","download_json":"https://pith.science/pith/Z2RNZEXNGM2JSOSELC3NRUUDUX.json","view_paper":"https://pith.science/paper/Z2RNZEXN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03210&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2RNZEXNGM2JSOSELC3NRUUDUX/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2RNZEXNGM2JSOSELC3NRUUDUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2RNZEXNGM2JSOSELC3NRUUDUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2RNZEXNGM2JSOSELC3NRUUDUX/action/storage_attestation","attest_author":"https://pith.science/pith/Z2RNZEXNGM2JSOSELC3NRUUDUX/action/author_attestation","sign_citation":"https://pith.science/pith/Z2RNZEXNGM2JSOSELC3NRUUDUX/action/citation_signature","submit_replication":"https://pith.science/pith/Z2RNZEXNGM2JSOSELC3NRUUDUX/action/replication_record"}},"created_at":"2026-05-18T02:12:10.121112+00:00","updated_at":"2026-05-18T02:12:10.121112+00:00"}