{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5QACEPNIWRVUB35YRFW3RWY2YG","short_pith_number":"pith:5QACEPNI","schema_version":"1.0","canonical_sha256":"ec00223da8b46b40efb8896db8db1ac184577b3b5b34724d7dd4b7ca66f1362b","source":{"kind":"arxiv","id":"1903.10631","version":2},"attestation_state":"computed","paper":{"title":"More on the extremal number of subdivisions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Conlon, Joonkyung Lee, Oliver Janzer","submitted_at":"2019-03-25T23:16:03Z","abstract_excerpt":"Given a graph $H$, the extremal number $\\mathrm{ex}(n,H)$ is the largest number of edges in an $H$-free graph on $n$ vertices. We make progress on a number of conjectures about the extremal number of bipartite graphs. First, writing $K'_{s,t}$ for the subdivision of the bipartite graph $K_{s,t}$, we show that $\\mathrm{ex}(n, K'_{s,t}) = O(n^{3/2 - \\frac{1}{2s}})$. This proves a conjecture of Kang, Kim and Liu and is tight up to the implied constant for $t$ sufficiently large in terms of $s$. Second, for any integers $s, k \\geq 1$, we show that $\\mathrm{ex}(n, L) = \\Theta(n^{1 + \\frac{s}{sk+1}}"},"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":"1903.10631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-25T23:16:03Z","cross_cats_sorted":[],"title_canon_sha256":"3c595052045f0bdb550d265cb3b42a73be2fc31ff06b4b7b1efbf7b658aca8a5","abstract_canon_sha256":"00b0a5a044fb2c79d6d9868c29ca7b84695cfd59f3e1ba5b763dde3034657c6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:58:02.609484Z","signature_b64":"URZWaRkoYGDuAO/mbBYsQEZBj14iX3VS9mu4SW80LDzZZFghYdbG1csW0Syvn1vJpasfFv6miR4s9+Zcf/WbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec00223da8b46b40efb8896db8db1ac184577b3b5b34724d7dd4b7ca66f1362b","last_reissued_at":"2026-07-05T00:58:02.609029Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:58:02.609029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"More on the extremal number of subdivisions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Conlon, Joonkyung Lee, Oliver Janzer","submitted_at":"2019-03-25T23:16:03Z","abstract_excerpt":"Given a graph $H$, the extremal number $\\mathrm{ex}(n,H)$ is the largest number of edges in an $H$-free graph on $n$ vertices. We make progress on a number of conjectures about the extremal number of bipartite graphs. First, writing $K'_{s,t}$ for the subdivision of the bipartite graph $K_{s,t}$, we show that $\\mathrm{ex}(n, K'_{s,t}) = O(n^{3/2 - \\frac{1}{2s}})$. This proves a conjecture of Kang, Kim and Liu and is tight up to the implied constant for $t$ sufficiently large in terms of $s$. Second, for any integers $s, k \\geq 1$, we show that $\\mathrm{ex}(n, L) = \\Theta(n^{1 + \\frac{s}{sk+1}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10631","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.10631/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1903.10631","created_at":"2026-07-05T00:58:02.609097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.10631v2","created_at":"2026-07-05T00:58:02.609097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10631","created_at":"2026-07-05T00:58:02.609097+00:00"},{"alias_kind":"pith_short_12","alias_value":"5QACEPNIWRVU","created_at":"2026-07-05T00:58:02.609097+00:00"},{"alias_kind":"pith_short_16","alias_value":"5QACEPNIWRVUB35Y","created_at":"2026-07-05T00:58:02.609097+00:00"},{"alias_kind":"pith_short_8","alias_value":"5QACEPNI","created_at":"2026-07-05T00:58:02.609097+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.02385","citing_title":"Many Turan exponents via subdivisions","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG","json":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG.json","graph_json":"https://pith.science/api/pith-number/5QACEPNIWRVUB35YRFW3RWY2YG/graph.json","events_json":"https://pith.science/api/pith-number/5QACEPNIWRVUB35YRFW3RWY2YG/events.json","paper":"https://pith.science/paper/5QACEPNI"},"agent_actions":{"view_html":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG","download_json":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG.json","view_paper":"https://pith.science/paper/5QACEPNI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.10631&json=true","fetch_graph":"https://pith.science/api/pith-number/5QACEPNIWRVUB35YRFW3RWY2YG/graph.json","fetch_events":"https://pith.science/api/pith-number/5QACEPNIWRVUB35YRFW3RWY2YG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG/action/storage_attestation","attest_author":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG/action/author_attestation","sign_citation":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG/action/citation_signature","submit_replication":"https://pith.science/pith/5QACEPNIWRVUB35YRFW3RWY2YG/action/replication_record"}},"created_at":"2026-07-05T00:58:02.609097+00:00","updated_at":"2026-07-05T00:58:02.609097+00:00"}