{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AMK2P2PINN2P6AQMPDLUQUI6XY","short_pith_number":"pith:AMK2P2PI","schema_version":"1.0","canonical_sha256":"0315a7e9e86b74ff020c78d748511ebe0b97715068ff18c1bbccd2922b1248c5","source":{"kind":"arxiv","id":"1403.1288","version":1},"attestation_state":"computed","paper":{"title":"Computational search of small point sets with small rectilinear crossing number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Jorge L\\'opez, Ruy Fabila-Monroy","submitted_at":"2014-03-05T22:42:23Z","abstract_excerpt":"Let $\\crs(K_n)$ be the minimum number of crossings over all rectilinear drawings of the complete graph on $n$ vertices on the plane. In this paper we prove that $\\crs(K_n) < 0.380473\\binom{n}{4}+\\Theta(n^3)$; improving thus on the previous best known upper bound. This is done by obtaining new rectilinear drawings of $K_n$ for small values of $n$, and then using known constructions to obtain arbitrarily large good drawings from smaller ones. The \"small\" sets where found using a simple heuristic detailed in this paper."},"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":"1403.1288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-05T22:42:23Z","cross_cats_sorted":["cs.CG","cs.DM"],"title_canon_sha256":"6881a7a507717f0f676c197d3b8f68ce10321888c2c9b6e565aff03fac4423a7","abstract_canon_sha256":"b984abc8423a8364eabd3d4acaa749c3cc7757e3fa4ab728806b472bcac4899a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:59.347272Z","signature_b64":"MBwkk9F5mxJMwjwyAjZdGeYv9mz+bB3l7ICs+GFn4W3qPqp1f1uWTpOeZpd/v6VieOVygy8QexV2J8M9G1UwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0315a7e9e86b74ff020c78d748511ebe0b97715068ff18c1bbccd2922b1248c5","last_reissued_at":"2026-05-18T02:56:59.346607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:59.346607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computational search of small point sets with small rectilinear crossing number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Jorge L\\'opez, Ruy Fabila-Monroy","submitted_at":"2014-03-05T22:42:23Z","abstract_excerpt":"Let $\\crs(K_n)$ be the minimum number of crossings over all rectilinear drawings of the complete graph on $n$ vertices on the plane. In this paper we prove that $\\crs(K_n) < 0.380473\\binom{n}{4}+\\Theta(n^3)$; improving thus on the previous best known upper bound. This is done by obtaining new rectilinear drawings of $K_n$ for small values of $n$, and then using known constructions to obtain arbitrarily large good drawings from smaller ones. The \"small\" sets where found using a simple heuristic detailed in this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1288","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":"1403.1288","created_at":"2026-05-18T02:56:59.346700+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.1288v1","created_at":"2026-05-18T02:56:59.346700+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1288","created_at":"2026-05-18T02:56:59.346700+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMK2P2PINN2P","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMK2P2PINN2P6AQM","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMK2P2PI","created_at":"2026-05-18T12:28:19.803747+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/AMK2P2PINN2P6AQMPDLUQUI6XY","json":"https://pith.science/pith/AMK2P2PINN2P6AQMPDLUQUI6XY.json","graph_json":"https://pith.science/api/pith-number/AMK2P2PINN2P6AQMPDLUQUI6XY/graph.json","events_json":"https://pith.science/api/pith-number/AMK2P2PINN2P6AQMPDLUQUI6XY/events.json","paper":"https://pith.science/paper/AMK2P2PI"},"agent_actions":{"view_html":"https://pith.science/pith/AMK2P2PINN2P6AQMPDLUQUI6XY","download_json":"https://pith.science/pith/AMK2P2PINN2P6AQMPDLUQUI6XY.json","view_paper":"https://pith.science/paper/AMK2P2PI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.1288&json=true","fetch_graph":"https://pith.science/api/pith-number/AMK2P2PINN2P6AQMPDLUQUI6XY/graph.json","fetch_events":"https://pith.science/api/pith-number/AMK2P2PINN2P6AQMPDLUQUI6XY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMK2P2PINN2P6AQMPDLUQUI6XY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMK2P2PINN2P6AQMPDLUQUI6XY/action/storage_attestation","attest_author":"https://pith.science/pith/AMK2P2PINN2P6AQMPDLUQUI6XY/action/author_attestation","sign_citation":"https://pith.science/pith/AMK2P2PINN2P6AQMPDLUQUI6XY/action/citation_signature","submit_replication":"https://pith.science/pith/AMK2P2PINN2P6AQMPDLUQUI6XY/action/replication_record"}},"created_at":"2026-05-18T02:56:59.346700+00:00","updated_at":"2026-05-18T02:56:59.346700+00:00"}