{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JLEO2JDM3357FEQWAZGTOZEEQ5","short_pith_number":"pith:JLEO2JDM","schema_version":"1.0","canonical_sha256":"4ac8ed246cdefbf29216064d3764848753c65df20639534f7c51add15b363497","source":{"kind":"arxiv","id":"1311.1976","version":1},"attestation_state":"computed","paper":{"title":"On the Number of Edges of Fan-Crossing Free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CG","authors_text":"Heuna Kim, Hyo-Sil Kim, Otfried Cheong, Sariel Har-Peled","submitted_at":"2013-11-08T14:16:56Z","abstract_excerpt":"A graph drawn in the plane with n vertices is k-fan-crossing free for k > 1 if there are no k+1 edges $g,e_1,...e_k$, such that $e_1,e_2,...e_k$ have a common endpoint and $g$ crosses all $e_i$. We prove a tight bound of 4n-8 on the maximum number of edges of a 2-fan-crossing free graph, and a tight 4n-9 bound for a straight-edge drawing. For k > 2, we prove an upper bound of 3(k-1)(n-2) edges. We also discuss generalizations to monotone graph properties."},"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":"1311.1976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-11-08T14:16:56Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"0140d6435ec7aeadd8502b2695ad81309a5bb05df44d2ae8a72b66e093ef77d3","abstract_canon_sha256":"b5dc764740b93c565ee76dc3927ea9e8a3515c43fe39a51015a530a1a85cdc08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:41.829837Z","signature_b64":"irqDA6XaXAeI4lTgNXO6AReUdK3F43AadoqMytshGs49V2vriXz/+LHXR9njCSlmm+1rYKCgIRXmP92xiqvyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ac8ed246cdefbf29216064d3764848753c65df20639534f7c51add15b363497","last_reissued_at":"2026-05-18T03:07:41.829086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:41.829086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Number of Edges of Fan-Crossing Free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CG","authors_text":"Heuna Kim, Hyo-Sil Kim, Otfried Cheong, Sariel Har-Peled","submitted_at":"2013-11-08T14:16:56Z","abstract_excerpt":"A graph drawn in the plane with n vertices is k-fan-crossing free for k > 1 if there are no k+1 edges $g,e_1,...e_k$, such that $e_1,e_2,...e_k$ have a common endpoint and $g$ crosses all $e_i$. We prove a tight bound of 4n-8 on the maximum number of edges of a 2-fan-crossing free graph, and a tight 4n-9 bound for a straight-edge drawing. For k > 2, we prove an upper bound of 3(k-1)(n-2) edges. We also discuss generalizations to monotone graph properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1976","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":"1311.1976","created_at":"2026-05-18T03:07:41.829214+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.1976v1","created_at":"2026-05-18T03:07:41.829214+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1976","created_at":"2026-05-18T03:07:41.829214+00:00"},{"alias_kind":"pith_short_12","alias_value":"JLEO2JDM3357","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JLEO2JDM3357FEQW","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JLEO2JDM","created_at":"2026-05-18T12:27:49.015174+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/JLEO2JDM3357FEQWAZGTOZEEQ5","json":"https://pith.science/pith/JLEO2JDM3357FEQWAZGTOZEEQ5.json","graph_json":"https://pith.science/api/pith-number/JLEO2JDM3357FEQWAZGTOZEEQ5/graph.json","events_json":"https://pith.science/api/pith-number/JLEO2JDM3357FEQWAZGTOZEEQ5/events.json","paper":"https://pith.science/paper/JLEO2JDM"},"agent_actions":{"view_html":"https://pith.science/pith/JLEO2JDM3357FEQWAZGTOZEEQ5","download_json":"https://pith.science/pith/JLEO2JDM3357FEQWAZGTOZEEQ5.json","view_paper":"https://pith.science/paper/JLEO2JDM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.1976&json=true","fetch_graph":"https://pith.science/api/pith-number/JLEO2JDM3357FEQWAZGTOZEEQ5/graph.json","fetch_events":"https://pith.science/api/pith-number/JLEO2JDM3357FEQWAZGTOZEEQ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JLEO2JDM3357FEQWAZGTOZEEQ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JLEO2JDM3357FEQWAZGTOZEEQ5/action/storage_attestation","attest_author":"https://pith.science/pith/JLEO2JDM3357FEQWAZGTOZEEQ5/action/author_attestation","sign_citation":"https://pith.science/pith/JLEO2JDM3357FEQWAZGTOZEEQ5/action/citation_signature","submit_replication":"https://pith.science/pith/JLEO2JDM3357FEQWAZGTOZEEQ5/action/replication_record"}},"created_at":"2026-05-18T03:07:41.829214+00:00","updated_at":"2026-05-18T03:07:41.829214+00:00"}