{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3GR7IBOPJKBJLJHWBK4HKAHYRC","short_pith_number":"pith:3GR7IBOP","canonical_record":{"source":{"id":"1401.0684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-03T17:28:56Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"69967ee415e92243ab1428d4478cd6274081e2b9f59da439ded6c6a03b04f5f4","abstract_canon_sha256":"99b473aa67d2678d64a27d11646889a3432cb40a108ce8ab0c32627466f15f53"},"schema_version":"1.0"},"canonical_sha256":"d9a3f405cf4a8295a4f60ab87500f888a1999eea03815233d00b5ff0548ae121","source":{"kind":"arxiv","id":"1401.0684","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0684","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0684v1","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0684","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"3GR7IBOPJKBJ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3GR7IBOPJKBJLJHW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3GR7IBOP","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3GR7IBOPJKBJLJHWBK4HKAHYRC","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-03T17:28:56Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"69967ee415e92243ab1428d4478cd6274081e2b9f59da439ded6c6a03b04f5f4","abstract_canon_sha256":"99b473aa67d2678d64a27d11646889a3432cb40a108ce8ab0c32627466f15f53"},"schema_version":"1.0"},"canonical_sha256":"d9a3f405cf4a8295a4f60ab87500f888a1999eea03815233d00b5ff0548ae121","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:21.789265Z","signature_b64":"opD6dhLhtK1TmXR74Rhx8fUe7c6HbaFzgXC+H23/MW4RsBGO+sVHgqFYdxqSgAV6geQ890gCYZXfuQR0dnK+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9a3f405cf4a8295a4f60ab87500f888a1999eea03815233d00b5ff0548ae121","last_reissued_at":"2026-05-18T03:03:21.788627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:21.788627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0684","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xeDwkXs0R9sgcsEA9lik53SJPLm59ucH//sfE4YZsnLVvB3HOhUQJ3kdoe+++JlIHPGQB9qfCfDOyKADEMIJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:06:51.244791Z"},"content_sha256":"a90bff3f06444fa7366a82dd5d38323b092eed1c6ef749d51fe6aabbec50edca","schema_version":"1.0","event_id":"sha256:a90bff3f06444fa7366a82dd5d38323b092eed1c6ef749d51fe6aabbec50edca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3GR7IBOPJKBJLJHWBK4HKAHYRC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-Page Book Embeddings of 4-Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DM","authors_text":"Chrysanthi N. Raftopoulou, Martin Gronemann, Michael A. Bekos","submitted_at":"2014-01-03T17:28:56Z","abstract_excerpt":"Back in the Eighties, Heath showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the class of 4-planar graphs. Our contribution consists of two algorithms: The first one is limited to triconnected graphs, but runs in linear time and uses existing methods for computing hamiltonian cycles in planar graphs. The second one, which solves the general case of the problem, is a quadratic-time algorithm based on the book-embedding viewpoint of the proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0684","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ujJytbOkpxeDHNYMIche1m0xswONJfQdRU1Vu1YHax4jk9/D2HsM4OD66e01cAogpAyRglDNZ2K/zL+MFTT6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:06:51.245130Z"},"content_sha256":"f372d2fd8bb15c5c7763c46843185322844bcf324df90a5002cf8894d0653fc3","schema_version":"1.0","event_id":"sha256:f372d2fd8bb15c5c7763c46843185322844bcf324df90a5002cf8894d0653fc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3GR7IBOPJKBJLJHWBK4HKAHYRC/bundle.json","state_url":"https://pith.science/pith/3GR7IBOPJKBJLJHWBK4HKAHYRC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3GR7IBOPJKBJLJHWBK4HKAHYRC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T22:06:51Z","links":{"resolver":"https://pith.science/pith/3GR7IBOPJKBJLJHWBK4HKAHYRC","bundle":"https://pith.science/pith/3GR7IBOPJKBJLJHWBK4HKAHYRC/bundle.json","state":"https://pith.science/pith/3GR7IBOPJKBJLJHWBK4HKAHYRC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3GR7IBOPJKBJLJHWBK4HKAHYRC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3GR7IBOPJKBJLJHWBK4HKAHYRC","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":"99b473aa67d2678d64a27d11646889a3432cb40a108ce8ab0c32627466f15f53","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-03T17:28:56Z","title_canon_sha256":"69967ee415e92243ab1428d4478cd6274081e2b9f59da439ded6c6a03b04f5f4"},"schema_version":"1.0","source":{"id":"1401.0684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0684","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0684v1","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0684","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"3GR7IBOPJKBJ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3GR7IBOPJKBJLJHW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3GR7IBOP","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:f372d2fd8bb15c5c7763c46843185322844bcf324df90a5002cf8894d0653fc3","target":"graph","created_at":"2026-05-18T03:03:21Z","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":"Back in the Eighties, Heath showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the class of 4-planar graphs. Our contribution consists of two algorithms: The first one is limited to triconnected graphs, but runs in linear time and uses existing methods for computing hamiltonian cycles in planar graphs. The second one, which solves the general case of the problem, is a quadratic-time algorithm based on the book-embedding viewpoint of the proble","authors_text":"Chrysanthi N. Raftopoulou, Martin Gronemann, Michael A. Bekos","cross_cats":["cs.CC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-03T17:28:56Z","title":"Two-Page Book Embeddings of 4-Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0684","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:a90bff3f06444fa7366a82dd5d38323b092eed1c6ef749d51fe6aabbec50edca","target":"record","created_at":"2026-05-18T03:03:21Z","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":"99b473aa67d2678d64a27d11646889a3432cb40a108ce8ab0c32627466f15f53","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-03T17:28:56Z","title_canon_sha256":"69967ee415e92243ab1428d4478cd6274081e2b9f59da439ded6c6a03b04f5f4"},"schema_version":"1.0","source":{"id":"1401.0684","kind":"arxiv","version":1}},"canonical_sha256":"d9a3f405cf4a8295a4f60ab87500f888a1999eea03815233d00b5ff0548ae121","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9a3f405cf4a8295a4f60ab87500f888a1999eea03815233d00b5ff0548ae121","first_computed_at":"2026-05-18T03:03:21.788627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:21.788627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"opD6dhLhtK1TmXR74Rhx8fUe7c6HbaFzgXC+H23/MW4RsBGO+sVHgqFYdxqSgAV6geQ890gCYZXfuQR0dnK+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:21.789265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a90bff3f06444fa7366a82dd5d38323b092eed1c6ef749d51fe6aabbec50edca","sha256:f372d2fd8bb15c5c7763c46843185322844bcf324df90a5002cf8894d0653fc3"],"state_sha256":"89e42b422aa6e9e4514d12ae44c6bc02709efc59fdefb25c682b6c5591544822"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1irzmCTYb8xwpOXwgMGU8GmYmLgRJr7ofFzNDq1RS4Ph+FfEuKM2LT/cPMcLeUuAlLY4CIyNToaTq7TUiEsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:06:51.247025Z","bundle_sha256":"dba883ce51d0296757789ee3d0e6b54bf3b8841ff55979cb930321c114d6bcf4"}}