{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LRZ2L7TZ5QZFOE6QGP7I6HGQWB","short_pith_number":"pith:LRZ2L7TZ","schema_version":"1.0","canonical_sha256":"5c73a5fe79ec325713d033fe8f1cd0b05e87567c343cbd72e4e6e715fc1a5daa","source":{"kind":"arxiv","id":"1510.05891","version":1},"attestation_state":"computed","paper":{"title":"On the Book Thickness of 1-Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Franz J. Brandenburg, Md. Jawaherul Alam, Stephen G. Kobourov","submitted_at":"2015-10-20T13:40:33Z","abstract_excerpt":"In a book embedding of a graph G, the vertices of G are placed in order along a straight-line called spine of the book, and the edges of G are drawn on a set of half-planes, called the pages of the book, such that two edges drawn on a page do not cross each other. The minimum number of pages in which a graph can be embedded is called the book-thickness or the page-number of the graph. It is known that every planar graph has a book embedding on at most four pages. Here we investigate the book-embeddings of 1-planar graphs. A graph is 1-planar if it can be drawn in the plane such that each edge "},"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":"1510.05891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-10-20T13:40:33Z","cross_cats_sorted":[],"title_canon_sha256":"2c2cbb6a1701ae416cba9e2c9d1890824354cbd26cf9e546e5e6304c747e7d47","abstract_canon_sha256":"bbd2c68ad08a0825bb3ae6dbe0cac3df3791b233c5ec7d4624c81fe331365867"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:39.412428Z","signature_b64":"3DqiaiZ95ZT0i8skxrnpT84UIJHDpBpU6TNdQ6KtMGVcoRLa5GP6XpQauL+ZtqDsLLik7jHIIVrS6jfvHDBTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c73a5fe79ec325713d033fe8f1cd0b05e87567c343cbd72e4e6e715fc1a5daa","last_reissued_at":"2026-05-18T01:29:39.411775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:39.411775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Book Thickness of 1-Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Franz J. Brandenburg, Md. Jawaherul Alam, Stephen G. Kobourov","submitted_at":"2015-10-20T13:40:33Z","abstract_excerpt":"In a book embedding of a graph G, the vertices of G are placed in order along a straight-line called spine of the book, and the edges of G are drawn on a set of half-planes, called the pages of the book, such that two edges drawn on a page do not cross each other. The minimum number of pages in which a graph can be embedded is called the book-thickness or the page-number of the graph. It is known that every planar graph has a book embedding on at most four pages. Here we investigate the book-embeddings of 1-planar graphs. A graph is 1-planar if it can be drawn in the plane such that each edge "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05891","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":"1510.05891","created_at":"2026-05-18T01:29:39.411863+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.05891v1","created_at":"2026-05-18T01:29:39.411863+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05891","created_at":"2026-05-18T01:29:39.411863+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRZ2L7TZ5QZF","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRZ2L7TZ5QZFOE6Q","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRZ2L7TZ","created_at":"2026-05-18T12:29:29.992203+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/LRZ2L7TZ5QZFOE6QGP7I6HGQWB","json":"https://pith.science/pith/LRZ2L7TZ5QZFOE6QGP7I6HGQWB.json","graph_json":"https://pith.science/api/pith-number/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/graph.json","events_json":"https://pith.science/api/pith-number/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/events.json","paper":"https://pith.science/paper/LRZ2L7TZ"},"agent_actions":{"view_html":"https://pith.science/pith/LRZ2L7TZ5QZFOE6QGP7I6HGQWB","download_json":"https://pith.science/pith/LRZ2L7TZ5QZFOE6QGP7I6HGQWB.json","view_paper":"https://pith.science/paper/LRZ2L7TZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.05891&json=true","fetch_graph":"https://pith.science/api/pith-number/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/graph.json","fetch_events":"https://pith.science/api/pith-number/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/action/storage_attestation","attest_author":"https://pith.science/pith/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/action/author_attestation","sign_citation":"https://pith.science/pith/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/action/citation_signature","submit_replication":"https://pith.science/pith/LRZ2L7TZ5QZFOE6QGP7I6HGQWB/action/replication_record"}},"created_at":"2026-05-18T01:29:39.411863+00:00","updated_at":"2026-05-18T01:29:39.411863+00:00"}