{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SQBSWSXFGQJGLIDWC5PUZBRJJR","short_pith_number":"pith:SQBSWSXF","schema_version":"1.0","canonical_sha256":"94032b4ae5341265a076175f4c86294c67d186f5d6bf433d4c95e34da168c7ae","source":{"kind":"arxiv","id":"1702.01275","version":1},"attestation_state":"computed","paper":{"title":"Geometric Biplane Graphs I: Maximal Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alfredo Garc\\'ia, Csaba D. T\\'oth, Ferran Hurtado, In\\^es Matos, Javier Tejel, Maria Saumell, Matias Korman, Rodrigo I. Silveira","submitted_at":"2017-02-04T11:51:44Z","abstract_excerpt":"We study biplane graphs drawn on a finite planar point set $S$ in general position. This is the family of geometric graphs whose vertex set is $S$ and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the sense that no edge can be added while staying biplane---may differ in the number of edges, and we provide an efficient algorithm for adding edges to a biplane graph to make it maximal. We also study extremal properties of maximal biplane graphs such as the maximum number of edges and the largest maximum connectivity over $n$-element point sets."},"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":"1702.01275","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-02-04T11:51:44Z","cross_cats_sorted":[],"title_canon_sha256":"1d2613dd6ab43b50ef60f77c0a08b943378ad911c2aa899f3ae290d03c385f2b","abstract_canon_sha256":"e7185c813f0ecf354249f28b2c9daa2220ce3bd86cbc61cb712ecfda3f7a0a8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:20.973961Z","signature_b64":"I2+8Vdaw8c+Ulmy4U+uoqxh1fncNFQtfA8Qc6A6crfrtsNZSG4jtWQA5fJYcXx5JvhamV0LCmxoqblrNBkrgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94032b4ae5341265a076175f4c86294c67d186f5d6bf433d4c95e34da168c7ae","last_reissued_at":"2026-05-18T00:38:20.973476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:20.973476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Biplane Graphs I: Maximal Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alfredo Garc\\'ia, Csaba D. T\\'oth, Ferran Hurtado, In\\^es Matos, Javier Tejel, Maria Saumell, Matias Korman, Rodrigo I. Silveira","submitted_at":"2017-02-04T11:51:44Z","abstract_excerpt":"We study biplane graphs drawn on a finite planar point set $S$ in general position. This is the family of geometric graphs whose vertex set is $S$ and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the sense that no edge can be added while staying biplane---may differ in the number of edges, and we provide an efficient algorithm for adding edges to a biplane graph to make it maximal. We also study extremal properties of maximal biplane graphs such as the maximum number of edges and the largest maximum connectivity over $n$-element point sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01275","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":"1702.01275","created_at":"2026-05-18T00:38:20.973552+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.01275v1","created_at":"2026-05-18T00:38:20.973552+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01275","created_at":"2026-05-18T00:38:20.973552+00:00"},{"alias_kind":"pith_short_12","alias_value":"SQBSWSXFGQJG","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SQBSWSXFGQJGLIDW","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SQBSWSXF","created_at":"2026-05-18T12:31:43.269735+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/SQBSWSXFGQJGLIDWC5PUZBRJJR","json":"https://pith.science/pith/SQBSWSXFGQJGLIDWC5PUZBRJJR.json","graph_json":"https://pith.science/api/pith-number/SQBSWSXFGQJGLIDWC5PUZBRJJR/graph.json","events_json":"https://pith.science/api/pith-number/SQBSWSXFGQJGLIDWC5PUZBRJJR/events.json","paper":"https://pith.science/paper/SQBSWSXF"},"agent_actions":{"view_html":"https://pith.science/pith/SQBSWSXFGQJGLIDWC5PUZBRJJR","download_json":"https://pith.science/pith/SQBSWSXFGQJGLIDWC5PUZBRJJR.json","view_paper":"https://pith.science/paper/SQBSWSXF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.01275&json=true","fetch_graph":"https://pith.science/api/pith-number/SQBSWSXFGQJGLIDWC5PUZBRJJR/graph.json","fetch_events":"https://pith.science/api/pith-number/SQBSWSXFGQJGLIDWC5PUZBRJJR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SQBSWSXFGQJGLIDWC5PUZBRJJR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SQBSWSXFGQJGLIDWC5PUZBRJJR/action/storage_attestation","attest_author":"https://pith.science/pith/SQBSWSXFGQJGLIDWC5PUZBRJJR/action/author_attestation","sign_citation":"https://pith.science/pith/SQBSWSXFGQJGLIDWC5PUZBRJJR/action/citation_signature","submit_replication":"https://pith.science/pith/SQBSWSXFGQJGLIDWC5PUZBRJJR/action/replication_record"}},"created_at":"2026-05-18T00:38:20.973552+00:00","updated_at":"2026-05-18T00:38:20.973552+00:00"}