{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AN4EDQFPUJ3PL47KIRJCYL56DY","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":"16cda382e16c21fbb4dd1e87c6a4523f2e01875236bbdf5707309dc0070a1dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-22T13:53:12Z","title_canon_sha256":"fc7c57070b4f85056070924f0f33c67e662f20cf6089a1ce061a9446a49718e4"},"schema_version":"1.0","source":{"id":"1801.07097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07097","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07097v1","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07097","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"pith_short_12","alias_value":"AN4EDQFPUJ3P","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AN4EDQFPUJ3PL47K","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AN4EDQFP","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:4c38fdbb020e90a9ac9981034970b1878fe569c0bdd6a8383a3f097017407fe7","target":"graph","created_at":"2026-05-18T00:25:22Z","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 \\emph{book-embedding} of a graph $G$ is an embedding of vertices of $G$ along the spine of a book, and edges of $G$ on the pages so that no two edges on the same page intersect. the minimum number of pages in which a graph can be embedded is called the \\emph{page number}. The book-embedding of graphs may be important in several technical applications, e.g., sorting with parallel stacks, fault-tolerant processor arrays design, and layout problems with application to very large scale integration (VLSI). Bernhart and Kainen firstly considered the book-embedding of the planar graph and conjectur","authors_text":"Weihua Yang, Xiaxia Guan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-22T13:53:12Z","title":"Embedding 5-planar graphs in three pages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07097","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":"sha256:6949aca157f2350b1d47a698983d61d32e92f485a72e174f74ed68003a3ce47c","target":"record","created_at":"2026-05-18T00:25:22Z","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":"16cda382e16c21fbb4dd1e87c6a4523f2e01875236bbdf5707309dc0070a1dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-22T13:53:12Z","title_canon_sha256":"fc7c57070b4f85056070924f0f33c67e662f20cf6089a1ce061a9446a49718e4"},"schema_version":"1.0","source":{"id":"1801.07097","kind":"arxiv","version":1}},"canonical_sha256":"037841c0afa276f5f3ea44522c2fbe1e0c20019f5d42d3f0cf779b9e5369211c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"037841c0afa276f5f3ea44522c2fbe1e0c20019f5d42d3f0cf779b9e5369211c","first_computed_at":"2026-05-18T00:25:22.277834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:22.277834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PVaZUimMRMw+3qdq3ExA8moMGx8xwn82ERjk7MMJru4Y+VGOpUBZfGD/XcqduOrX2sD8O6RMFyhc9izHNQIbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:22.278522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6949aca157f2350b1d47a698983d61d32e92f485a72e174f74ed68003a3ce47c","sha256:4c38fdbb020e90a9ac9981034970b1878fe569c0bdd6a8383a3f097017407fe7"],"state_sha256":"10bea0337920d842bf38ed64eef1e34b64256a05633b8bc71f4389daae80824f"}