{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LC232NKXOT7KCPAFU37V2G257M","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":"2c727d2069f999cc83dd840c323ce4094d93fdcb688b30327c268c443d7496ae","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-26T01:15:44Z","title_canon_sha256":"0447c1d8bebd62aa869bcf5d7ca27546468646c79899e8c4f19883119e0f6a40"},"schema_version":"1.0","source":{"id":"1201.5421","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5421","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5421v1","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5421","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"LC232NKXOT7K","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LC232NKXOT7KCPAF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LC232NKX","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:2626e94e73c853fa712d20176f0a80fd9c26565bcaf427021c8c6e5d61b9ec2a","target":"graph","created_at":"2026-05-18T03:16:40Z","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":"We prove that the crossing number of a graph decays in a continuous fashion in the following sense. For any epsilon>0 there is a delta>0 such that for a sufficiently large n, every graph G with n vertices and m > n^{1+epsilon} edges, has a subgraph G' of at most (1-delta)m edges and crossing number at least (1-epsilon)cr(G). This generalizes the result of J. Fox and Cs. Toth.","authors_text":"G\\'eza T\\'oth, Jakub \\v{C}ern\\'y, Jan Kyn\\v{c}l","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-26T01:15:44Z","title":"Improvement on the decay of crossing numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5421","kind":"arxiv","version":1},"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":"sha256:4e7191170c8bf9c3f30170a480b0d0cb717ff728bdf4bd02cb92bea0f45b910b","target":"record","created_at":"2026-05-18T03:16:40Z","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":"2c727d2069f999cc83dd840c323ce4094d93fdcb688b30327c268c443d7496ae","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-26T01:15:44Z","title_canon_sha256":"0447c1d8bebd62aa869bcf5d7ca27546468646c79899e8c4f19883119e0f6a40"},"schema_version":"1.0","source":{"id":"1201.5421","kind":"arxiv","version":1}},"canonical_sha256":"58b5bd355774fea13c05a6ff5d1b5dfb3ec75a1cf7bfbe985697c66e4251436a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58b5bd355774fea13c05a6ff5d1b5dfb3ec75a1cf7bfbe985697c66e4251436a","first_computed_at":"2026-05-18T03:16:40.602244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:40.602244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kPMP41H91biLb2ezSymW0JukeH/OmvgZ0T0gbwOkvjhOTVGD/RttwJ4nietmCegPX7TgseA6cwyqBlviMZhUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:40.603965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5421","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e7191170c8bf9c3f30170a480b0d0cb717ff728bdf4bd02cb92bea0f45b910b","sha256:2626e94e73c853fa712d20176f0a80fd9c26565bcaf427021c8c6e5d61b9ec2a"],"state_sha256":"018a038211d8aaadf0e82e71c13870b33bb8864491a054185e8fa0147a9ac7ba"}