{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TRB6WJK4GD2XFBGERQ7SHYRHUT","short_pith_number":"pith:TRB6WJK4","canonical_record":{"source":{"id":"1210.2918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-10T13:48:13Z","cross_cats_sorted":[],"title_canon_sha256":"2f5c00ddbf3e52dfe92c846f5419dfca9ad56a3e3fef69a45dd31f1c7f31c9b3","abstract_canon_sha256":"7650cf89345f698e81b7bdaeb7f95a7f947d263bb5c0bc8c5f45f2d62fe62feb"},"schema_version":"1.0"},"canonical_sha256":"9c43eb255c30f57284c48c3f23e227a4d5f30ada23449e4c75bf98efc90241cb","source":{"kind":"arxiv","id":"1210.2918","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2918","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2918v1","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2918","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"TRB6WJK4GD2X","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TRB6WJK4GD2XFBGE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TRB6WJK4","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TRB6WJK4GD2XFBGERQ7SHYRHUT","target":"record","payload":{"canonical_record":{"source":{"id":"1210.2918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-10T13:48:13Z","cross_cats_sorted":[],"title_canon_sha256":"2f5c00ddbf3e52dfe92c846f5419dfca9ad56a3e3fef69a45dd31f1c7f31c9b3","abstract_canon_sha256":"7650cf89345f698e81b7bdaeb7f95a7f947d263bb5c0bc8c5f45f2d62fe62feb"},"schema_version":"1.0"},"canonical_sha256":"9c43eb255c30f57284c48c3f23e227a4d5f30ada23449e4c75bf98efc90241cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:59.023883Z","signature_b64":"mNpGukSxFBfEJPh+Aeoz9rAdnkeqArsWHyaZZ6XaDw4YYI1hEI3duFouTjsCgU1LClltYabhBcf9nNJiaM+lAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c43eb255c30f57284c48c3f23e227a4d5f30ada23449e4c75bf98efc90241cb","last_reissued_at":"2026-05-18T02:37:59.023507Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:59.023507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.2918","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":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WUYVlsB+sRlZXf2ydBNdiogEcTe2IQytLSR/Dhj62kYN2pJfRH6zs8VkzT3qNY9LcoAtOZGQinuXuYDAAcb9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:13:08.536685Z"},"content_sha256":"5aa0672a26efffd494d09de0685947dc4ba3f4f706b7896a95a1415bf4299a25","schema_version":"1.0","event_id":"sha256:5aa0672a26efffd494d09de0685947dc4ba3f4f706b7896a95a1415bf4299a25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TRB6WJK4GD2XFBGERQ7SHYRHUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Book drawings of complete bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dmitrii V. Pasechnik, Etienne de Klerk, Gelasio Salazar","submitted_at":"2012-10-10T13:48:13Z","abstract_excerpt":"A \"book\" with k pages consists of a straight line (the \"spine\") and k half-planes (the \"pages\"), such that the boundary of each page is the spine. If a graph is drawn on a book with k pages in such a way that the vertices lie on the spine, and each edge is contained in a page, the result is a k-page book drawing (or simply a k-page drawing). The pagenumber of a graph G is the minimum k such that G admits a k-page embedding (that is, a k-page drawing with no edge crossings). The k-page crossing number nu_k(G) of G is the minimum number of crossings in a k-page drawing of G. We investigate the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2918","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":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"20NIstiCwppetE0pXdnIEPWxsj5iMQlRAGrsLAf6i1cFWtRsgyVoQHzhki38QTpxF5Jzj93+NbggzZtQFSebDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:13:08.537029Z"},"content_sha256":"e9da18dbc21128384aad633a6238100576966e5d6a2c0fb7381398f6d2a07ba2","schema_version":"1.0","event_id":"sha256:e9da18dbc21128384aad633a6238100576966e5d6a2c0fb7381398f6d2a07ba2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRB6WJK4GD2XFBGERQ7SHYRHUT/bundle.json","state_url":"https://pith.science/pith/TRB6WJK4GD2XFBGERQ7SHYRHUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRB6WJK4GD2XFBGERQ7SHYRHUT/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":"2026-06-11T12:13:08Z","links":{"resolver":"https://pith.science/pith/TRB6WJK4GD2XFBGERQ7SHYRHUT","bundle":"https://pith.science/pith/TRB6WJK4GD2XFBGERQ7SHYRHUT/bundle.json","state":"https://pith.science/pith/TRB6WJK4GD2XFBGERQ7SHYRHUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRB6WJK4GD2XFBGERQ7SHYRHUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TRB6WJK4GD2XFBGERQ7SHYRHUT","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":"7650cf89345f698e81b7bdaeb7f95a7f947d263bb5c0bc8c5f45f2d62fe62feb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-10T13:48:13Z","title_canon_sha256":"2f5c00ddbf3e52dfe92c846f5419dfca9ad56a3e3fef69a45dd31f1c7f31c9b3"},"schema_version":"1.0","source":{"id":"1210.2918","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2918","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2918v1","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2918","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"TRB6WJK4GD2X","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TRB6WJK4GD2XFBGE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TRB6WJK4","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:e9da18dbc21128384aad633a6238100576966e5d6a2c0fb7381398f6d2a07ba2","target":"graph","created_at":"2026-05-18T02:37:59Z","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 \"book\" with k pages consists of a straight line (the \"spine\") and k half-planes (the \"pages\"), such that the boundary of each page is the spine. If a graph is drawn on a book with k pages in such a way that the vertices lie on the spine, and each edge is contained in a page, the result is a k-page book drawing (or simply a k-page drawing). The pagenumber of a graph G is the minimum k such that G admits a k-page embedding (that is, a k-page drawing with no edge crossings). The k-page crossing number nu_k(G) of G is the minimum number of crossings in a k-page drawing of G. We investigate the p","authors_text":"Dmitrii V. Pasechnik, Etienne de Klerk, Gelasio Salazar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-10T13:48:13Z","title":"Book drawings of complete bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2918","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":"sha256:5aa0672a26efffd494d09de0685947dc4ba3f4f706b7896a95a1415bf4299a25","target":"record","created_at":"2026-05-18T02:37:59Z","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":"7650cf89345f698e81b7bdaeb7f95a7f947d263bb5c0bc8c5f45f2d62fe62feb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-10T13:48:13Z","title_canon_sha256":"2f5c00ddbf3e52dfe92c846f5419dfca9ad56a3e3fef69a45dd31f1c7f31c9b3"},"schema_version":"1.0","source":{"id":"1210.2918","kind":"arxiv","version":1}},"canonical_sha256":"9c43eb255c30f57284c48c3f23e227a4d5f30ada23449e4c75bf98efc90241cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c43eb255c30f57284c48c3f23e227a4d5f30ada23449e4c75bf98efc90241cb","first_computed_at":"2026-05-18T02:37:59.023507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:59.023507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mNpGukSxFBfEJPh+Aeoz9rAdnkeqArsWHyaZZ6XaDw4YYI1hEI3duFouTjsCgU1LClltYabhBcf9nNJiaM+lAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:59.023883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2918","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5aa0672a26efffd494d09de0685947dc4ba3f4f706b7896a95a1415bf4299a25","sha256:e9da18dbc21128384aad633a6238100576966e5d6a2c0fb7381398f6d2a07ba2"],"state_sha256":"36b49e6413307d0fb8671495ac3f7c4551bc8932d9c6c2f971b9ba0334a1dce0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oc7FP36evLmGx2KwUAkbmdtRkbXqcDWlVL5Aqk6ipDVdI4ZlFuHSqttZuegIxa55Ot3ydr5xkL8MPbiB1Oo9Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:13:08.538954Z","bundle_sha256":"1879575652982b0e06a2a265a8ccb15308d640d7ec8ebdf7530a59ecd7b24be2"}}