{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:O5FRTMYEF2J4BTD5OGQMET2JOG","short_pith_number":"pith:O5FRTMYE","schema_version":"1.0","canonical_sha256":"774b19b3042e93c0cc7d71a0c24f4971927a8647d910952ea9d3928c1190825d","source":{"kind":"arxiv","id":"1305.6945","version":1},"attestation_state":"computed","paper":{"title":"Infinite Tur\\'an problems for bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons, Xing Peng","submitted_at":"2013-05-29T20:42:47Z","abstract_excerpt":"We consider an infinite version of the bipartite Tur\\'{a}n problem. Let $G$ be an infinite graph with $V(G) = \\mathbb{N}$ and let $G_n$ be the $n$-vertex subgraph of $G$ induced by the vertices $\\{1,2, \\dots, n \\}$. We show that if $G$ is $K_{2,t+1}$-free then for infinitely many $n$, $e(G_n) \\leq 0.471 \\sqrt{t} n^{3/2}$. Using the $K_{2,t+1}$-free graphs constructed by F\\\"{u}redi, we construct an infinite $K_{2,t+1}$-free graph with $e(G_n) \\geq 0.23 \\sqrt{t}n^{3/2}$ for all $n \\geq n_0$."},"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":"1305.6945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-29T20:42:47Z","cross_cats_sorted":[],"title_canon_sha256":"432f9ac3610345998641c8d72141133906426cfd8eafc893af66a95d3d868681","abstract_canon_sha256":"3f55802f25ac3be9d7e7c1ac71efd8716e97ca80f092b89f15c3b166ad9cbb05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:16.808636Z","signature_b64":"vbv3jWNR2Wi3KR/UIo2C7oQGyEF7pgbpleojXiNcfOrmSEs5dw0MBwOFZgao0MyMTEdEwXkdjkmYFLWuTMt3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"774b19b3042e93c0cc7d71a0c24f4971927a8647d910952ea9d3928c1190825d","last_reissued_at":"2026-05-18T03:22:16.808204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:16.808204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite Tur\\'an problems for bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Timmons, Xing Peng","submitted_at":"2013-05-29T20:42:47Z","abstract_excerpt":"We consider an infinite version of the bipartite Tur\\'{a}n problem. Let $G$ be an infinite graph with $V(G) = \\mathbb{N}$ and let $G_n$ be the $n$-vertex subgraph of $G$ induced by the vertices $\\{1,2, \\dots, n \\}$. We show that if $G$ is $K_{2,t+1}$-free then for infinitely many $n$, $e(G_n) \\leq 0.471 \\sqrt{t} n^{3/2}$. Using the $K_{2,t+1}$-free graphs constructed by F\\\"{u}redi, we construct an infinite $K_{2,t+1}$-free graph with $e(G_n) \\geq 0.23 \\sqrt{t}n^{3/2}$ for all $n \\geq n_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6945","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":"1305.6945","created_at":"2026-05-18T03:22:16.808262+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6945v1","created_at":"2026-05-18T03:22:16.808262+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6945","created_at":"2026-05-18T03:22:16.808262+00:00"},{"alias_kind":"pith_short_12","alias_value":"O5FRTMYEF2J4","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"O5FRTMYEF2J4BTD5","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"O5FRTMYE","created_at":"2026-05-18T12:27:54.935989+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/O5FRTMYEF2J4BTD5OGQMET2JOG","json":"https://pith.science/pith/O5FRTMYEF2J4BTD5OGQMET2JOG.json","graph_json":"https://pith.science/api/pith-number/O5FRTMYEF2J4BTD5OGQMET2JOG/graph.json","events_json":"https://pith.science/api/pith-number/O5FRTMYEF2J4BTD5OGQMET2JOG/events.json","paper":"https://pith.science/paper/O5FRTMYE"},"agent_actions":{"view_html":"https://pith.science/pith/O5FRTMYEF2J4BTD5OGQMET2JOG","download_json":"https://pith.science/pith/O5FRTMYEF2J4BTD5OGQMET2JOG.json","view_paper":"https://pith.science/paper/O5FRTMYE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6945&json=true","fetch_graph":"https://pith.science/api/pith-number/O5FRTMYEF2J4BTD5OGQMET2JOG/graph.json","fetch_events":"https://pith.science/api/pith-number/O5FRTMYEF2J4BTD5OGQMET2JOG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O5FRTMYEF2J4BTD5OGQMET2JOG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O5FRTMYEF2J4BTD5OGQMET2JOG/action/storage_attestation","attest_author":"https://pith.science/pith/O5FRTMYEF2J4BTD5OGQMET2JOG/action/author_attestation","sign_citation":"https://pith.science/pith/O5FRTMYEF2J4BTD5OGQMET2JOG/action/citation_signature","submit_replication":"https://pith.science/pith/O5FRTMYEF2J4BTD5OGQMET2JOG/action/replication_record"}},"created_at":"2026-05-18T03:22:16.808262+00:00","updated_at":"2026-05-18T03:22:16.808262+00:00"}