{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JLEO2JDM3357FEQWAZGTOZEEQ5","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":"b5dc764740b93c565ee76dc3927ea9e8a3515c43fe39a51015a530a1a85cdc08","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-11-08T14:16:56Z","title_canon_sha256":"0140d6435ec7aeadd8502b2695ad81309a5bb05df44d2ae8a72b66e093ef77d3"},"schema_version":"1.0","source":{"id":"1311.1976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1976","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1976v1","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1976","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"pith_short_12","alias_value":"JLEO2JDM3357","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JLEO2JDM3357FEQW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JLEO2JDM","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:a9bf2c5f6a073df5de85d0ff08e7ca888765d028129ca0a4a5f515bcf81eaac7","target":"graph","created_at":"2026-05-18T03:07:41Z","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":"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.","authors_text":"Heuna Kim, Hyo-Sil Kim, Otfried Cheong, Sariel Har-Peled","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-11-08T14:16:56Z","title":"On the Number of Edges of Fan-Crossing Free Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1976","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:f006133392287192eab962bba461a211e2b75d6b32f1728cb82f16362a67ad0e","target":"record","created_at":"2026-05-18T03:07:41Z","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":"b5dc764740b93c565ee76dc3927ea9e8a3515c43fe39a51015a530a1a85cdc08","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-11-08T14:16:56Z","title_canon_sha256":"0140d6435ec7aeadd8502b2695ad81309a5bb05df44d2ae8a72b66e093ef77d3"},"schema_version":"1.0","source":{"id":"1311.1976","kind":"arxiv","version":1}},"canonical_sha256":"4ac8ed246cdefbf29216064d3764848753c65df20639534f7c51add15b363497","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ac8ed246cdefbf29216064d3764848753c65df20639534f7c51add15b363497","first_computed_at":"2026-05-18T03:07:41.829086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:41.829086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"irqDA6XaXAeI4lTgNXO6AReUdK3F43AadoqMytshGs49V2vriXz/+LHXR9njCSlmm+1rYKCgIRXmP92xiqvyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:41.829837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f006133392287192eab962bba461a211e2b75d6b32f1728cb82f16362a67ad0e","sha256:a9bf2c5f6a073df5de85d0ff08e7ca888765d028129ca0a4a5f515bcf81eaac7"],"state_sha256":"83c544deb55601b7aeb2325754441ee48f714002ac3d762b119248b87ce20962"}