{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E3ENHW4VKOAYSHWV66WEWQNBGD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e2b529c1be608a1bd0b8d50e767b7b5623b0dd8cc39af86a11d1d0236e370f39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-13T11:10:47Z","title_canon_sha256":"d74599497271be1c20c127ff82684b6a393ebc7c5d43b5d2cba711657022d80a"},"schema_version":"1.0","source":{"id":"1807.05008","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05008","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05008v2","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05008","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"E3ENHW4VKOAY","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E3ENHW4VKOAYSHWV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E3ENHW4V","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:a83a2de1f3f7ec78d582247157d8798c0e31d4dd06e2c93e83ba4beda30ad06b","target":"graph","created_at":"2026-05-17T23:54:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"One of the cornerstones of extremal graph theory is a result of F\\\"uredi, later reproved and given due prominence by Alon, Krivelevich and Sudakov, saying that if $H$ is a bipartite graph with maximum degree $r$ on one side, then there is a constant $C$ such that every graph with $n$ vertices and $C n^{2 - 1/r}$ edges contains a copy of $H$. This result is tight up to the constant when $H$ contains a copy of $K_{r,s}$ with $s$ sufficiently large in terms of $r$. We conjecture that this is essentially the only situation in which F\\\"uredi's result can be tight and prove this conjecture for $r = ","authors_text":"David Conlon, Joonkyung Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-13T11:10:47Z","title":"On the extremal number of subdivisions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05008","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d9a786b8dd209e4cbac36fe8debe20f23d964cfdc2716307a833f52cdff792de","target":"record","created_at":"2026-05-17T23:54:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e2b529c1be608a1bd0b8d50e767b7b5623b0dd8cc39af86a11d1d0236e370f39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-13T11:10:47Z","title_canon_sha256":"d74599497271be1c20c127ff82684b6a393ebc7c5d43b5d2cba711657022d80a"},"schema_version":"1.0","source":{"id":"1807.05008","kind":"arxiv","version":2}},"canonical_sha256":"26c8d3db955381891ed5f7ac4b41a130e70b30fdb7c8f2471666970de3f65d14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26c8d3db955381891ed5f7ac4b41a130e70b30fdb7c8f2471666970de3f65d14","first_computed_at":"2026-05-17T23:54:22.781737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:22.781737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EmmOv2dEsJChWGuu7NtPkI9YqnCVPs7kzbiixxaF2U3ftnUR+gvKmGWj0U2wewgQKR3L4TIscGctBU2UAhihAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:22.782402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.05008","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9a786b8dd209e4cbac36fe8debe20f23d964cfdc2716307a833f52cdff792de","sha256:a83a2de1f3f7ec78d582247157d8798c0e31d4dd06e2c93e83ba4beda30ad06b"],"state_sha256":"369c35219d9584fded1f26008ff3ea5f412f8e49899077ecb23d18b8bdb2e806"}