{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WWP7CYZWK3JGQWUI2KOBH7F47W","short_pith_number":"pith:WWP7CYZW","schema_version":"1.0","canonical_sha256":"b59ff1633656d2685a88d29c13fcbcfd85fc28a36bcef330fa7b540bd1c769e5","source":{"kind":"arxiv","id":"1904.07219","version":1},"attestation_state":"computed","paper":{"title":"The Tur\\'an number of blow-ups of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Grzesik, Oliver Janzer, Zolt\\'an L\\'or\\'ant Nagy","submitted_at":"2019-04-15T17:54:30Z","abstract_excerpt":"A conjecture of Erd\\H{o}s from 1967 asserts that any graph on $n$ vertices which does not contain a fixed $r$-degenerate bipartite graph $F$ has at most $Cn^{2-1/r}$ edges, where $C$ is a constant depending only on $F$. We show that this bound holds for a large family of $r$-degenerate bipartite graphs, including all $r$-degenerate blow-ups of trees. Our results generalise many previously proven cases of the Erd\\H{o}s conjecture, including the related results of F\\\"uredi and Alon, Krivelevich and Sudakov. Our proof uses supersaturation and a random walk on an auxiliary graph."},"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":"1904.07219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-15T17:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"0265a991cff83e794be2890060ffe5318634290f7c53de493a83f81e78d52173","abstract_canon_sha256":"790bbfba091cd8d2af66aca0d20ab809a8f1e14c2ae3722a0ab67a9343512450"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:34.884420Z","signature_b64":"+fQHnMIg6vfGMO54jqDrNYS/BG4YY6n/idI0H/8H0vDg3uPOjKNmjf8qcmrEFsDRBZ3CyM4/TNZDfpKRvxz6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b59ff1633656d2685a88d29c13fcbcfd85fc28a36bcef330fa7b540bd1c769e5","last_reissued_at":"2026-05-17T23:48:34.883901Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:34.883901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Tur\\'an number of blow-ups of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Grzesik, Oliver Janzer, Zolt\\'an L\\'or\\'ant Nagy","submitted_at":"2019-04-15T17:54:30Z","abstract_excerpt":"A conjecture of Erd\\H{o}s from 1967 asserts that any graph on $n$ vertices which does not contain a fixed $r$-degenerate bipartite graph $F$ has at most $Cn^{2-1/r}$ edges, where $C$ is a constant depending only on $F$. We show that this bound holds for a large family of $r$-degenerate bipartite graphs, including all $r$-degenerate blow-ups of trees. Our results generalise many previously proven cases of the Erd\\H{o}s conjecture, including the related results of F\\\"uredi and Alon, Krivelevich and Sudakov. Our proof uses supersaturation and a random walk on an auxiliary graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07219","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":"1904.07219","created_at":"2026-05-17T23:48:34.883968+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.07219v1","created_at":"2026-05-17T23:48:34.883968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07219","created_at":"2026-05-17T23:48:34.883968+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWP7CYZWK3JG","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWP7CYZWK3JGQWUI","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWP7CYZW","created_at":"2026-05-18T12:33:33.725879+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/WWP7CYZWK3JGQWUI2KOBH7F47W","json":"https://pith.science/pith/WWP7CYZWK3JGQWUI2KOBH7F47W.json","graph_json":"https://pith.science/api/pith-number/WWP7CYZWK3JGQWUI2KOBH7F47W/graph.json","events_json":"https://pith.science/api/pith-number/WWP7CYZWK3JGQWUI2KOBH7F47W/events.json","paper":"https://pith.science/paper/WWP7CYZW"},"agent_actions":{"view_html":"https://pith.science/pith/WWP7CYZWK3JGQWUI2KOBH7F47W","download_json":"https://pith.science/pith/WWP7CYZWK3JGQWUI2KOBH7F47W.json","view_paper":"https://pith.science/paper/WWP7CYZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.07219&json=true","fetch_graph":"https://pith.science/api/pith-number/WWP7CYZWK3JGQWUI2KOBH7F47W/graph.json","fetch_events":"https://pith.science/api/pith-number/WWP7CYZWK3JGQWUI2KOBH7F47W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWP7CYZWK3JGQWUI2KOBH7F47W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWP7CYZWK3JGQWUI2KOBH7F47W/action/storage_attestation","attest_author":"https://pith.science/pith/WWP7CYZWK3JGQWUI2KOBH7F47W/action/author_attestation","sign_citation":"https://pith.science/pith/WWP7CYZWK3JGQWUI2KOBH7F47W/action/citation_signature","submit_replication":"https://pith.science/pith/WWP7CYZWK3JGQWUI2KOBH7F47W/action/replication_record"}},"created_at":"2026-05-17T23:48:34.883968+00:00","updated_at":"2026-05-17T23:48:34.883968+00:00"}