{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AHOKWTLXMOAVQKQOYUFWXYRNSF","short_pith_number":"pith:AHOKWTLX","canonical_record":{"source":{"id":"1903.07966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-03-19T12:45:04Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"1514aa4a5dd4e5edd2c05ad8e9f1ddc7c45796dbc261fd4a9abd6c1dc9a4ecdf","abstract_canon_sha256":"80542ae0553da6fd7943508a7857c2c82cd0f17511c11c42a00f37c06ad9d65e"},"schema_version":"1.0"},"canonical_sha256":"01dcab4d776381582a0ec50b6be22d914c3bc883e008827f4268155e02be5e94","source":{"kind":"arxiv","id":"1903.07966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07966","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07966v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07966","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"AHOKWTLXMOAV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AHOKWTLXMOAVQKQO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AHOKWTLX","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AHOKWTLXMOAVQKQOYUFWXYRNSF","target":"record","payload":{"canonical_record":{"source":{"id":"1903.07966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-03-19T12:45:04Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"1514aa4a5dd4e5edd2c05ad8e9f1ddc7c45796dbc261fd4a9abd6c1dc9a4ecdf","abstract_canon_sha256":"80542ae0553da6fd7943508a7857c2c82cd0f17511c11c42a00f37c06ad9d65e"},"schema_version":"1.0"},"canonical_sha256":"01dcab4d776381582a0ec50b6be22d914c3bc883e008827f4268155e02be5e94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:53.388542Z","signature_b64":"/gmtWiAGNluf4TA0EIqF3JvSuU1k1yzJjmPRrgUFEos7OHY4TljriJt1qp0R9dR4kxZfSfhRbJctbYW/eC6+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01dcab4d776381582a0ec50b6be22d914c3bc883e008827f4268155e02be5e94","last_reissued_at":"2026-05-17T23:50:53.387808Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:53.387808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.07966","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":"2026-05-17T23:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jR7/FVW1fKpKcnK0M8KeSV3/NCQ+CPXZWipLIBqH7EHMa+T2WvBTo1WZzBqpddJqyUC25IxFsHIBjlQfnakdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:41:32.118249Z"},"content_sha256":"9c36d75a8c8be0ce11b24bba1db3d9d6d339f713e16681e58f86bb156aea4c31","schema_version":"1.0","event_id":"sha256:9c36d75a8c8be0ce11b24bba1db3d9d6d339f713e16681e58f86bb156aea4c31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AHOKWTLXMOAVQKQOYUFWXYRNSF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upward Book Embeddings of st-Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Carla Binucci, Emilio Di Giacomo, Giordano Da Lozzo, Maurizio Patrignani, Tamara Mchedlidze, Walter Didimo","submitted_at":"2019-03-19T12:45:04Z","abstract_excerpt":"We study $k$-page upward book embeddings ($k$UBEs) of $st$-graphs, that is, book embeddings of single-source single-sink directed acyclic graphs on $k$ pages with the additional requirement that the vertices of the graph appear in a topological ordering along the spine of the book. We show that testing whether a graph admits a $k$UBE is NP-complete for $k\\geq 3$. A hardness result for this problem was previously known only for $k = 6$ [Heath and Pemmaraju, 1999]. Motivated by this negative result, we focus our attention on $k=2$. On the algorithmic side, we present polynomial-time algorithms f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07966","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":"2026-05-17T23:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptKhIWcTWwn4x9FQpLT13m1DhXyiOGqKajQS2b4FxDjberQ+jc9IvvAa5Vv7yxXg+UN3x3PrlAX/sxWkxFK/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:41:32.118887Z"},"content_sha256":"0ab886032e492d0d98912d7cf464938d4956c6eb8568658aa689781cd6ab199b","schema_version":"1.0","event_id":"sha256:0ab886032e492d0d98912d7cf464938d4956c6eb8568658aa689781cd6ab199b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHOKWTLXMOAVQKQOYUFWXYRNSF/bundle.json","state_url":"https://pith.science/pith/AHOKWTLXMOAVQKQOYUFWXYRNSF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHOKWTLXMOAVQKQOYUFWXYRNSF/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":"2026-05-26T14:41:32Z","links":{"resolver":"https://pith.science/pith/AHOKWTLXMOAVQKQOYUFWXYRNSF","bundle":"https://pith.science/pith/AHOKWTLXMOAVQKQOYUFWXYRNSF/bundle.json","state":"https://pith.science/pith/AHOKWTLXMOAVQKQOYUFWXYRNSF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHOKWTLXMOAVQKQOYUFWXYRNSF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AHOKWTLXMOAVQKQOYUFWXYRNSF","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":"80542ae0553da6fd7943508a7857c2c82cd0f17511c11c42a00f37c06ad9d65e","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-03-19T12:45:04Z","title_canon_sha256":"1514aa4a5dd4e5edd2c05ad8e9f1ddc7c45796dbc261fd4a9abd6c1dc9a4ecdf"},"schema_version":"1.0","source":{"id":"1903.07966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07966","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07966v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07966","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"AHOKWTLXMOAV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AHOKWTLXMOAVQKQO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AHOKWTLX","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:0ab886032e492d0d98912d7cf464938d4956c6eb8568658aa689781cd6ab199b","target":"graph","created_at":"2026-05-17T23:50:53Z","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":"We study $k$-page upward book embeddings ($k$UBEs) of $st$-graphs, that is, book embeddings of single-source single-sink directed acyclic graphs on $k$ pages with the additional requirement that the vertices of the graph appear in a topological ordering along the spine of the book. We show that testing whether a graph admits a $k$UBE is NP-complete for $k\\geq 3$. A hardness result for this problem was previously known only for $k = 6$ [Heath and Pemmaraju, 1999]. Motivated by this negative result, we focus our attention on $k=2$. On the algorithmic side, we present polynomial-time algorithms f","authors_text":"Carla Binucci, Emilio Di Giacomo, Giordano Da Lozzo, Maurizio Patrignani, Tamara Mchedlidze, Walter Didimo","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-03-19T12:45:04Z","title":"Upward Book Embeddings of st-Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07966","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":"sha256:9c36d75a8c8be0ce11b24bba1db3d9d6d339f713e16681e58f86bb156aea4c31","target":"record","created_at":"2026-05-17T23:50:53Z","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":"80542ae0553da6fd7943508a7857c2c82cd0f17511c11c42a00f37c06ad9d65e","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-03-19T12:45:04Z","title_canon_sha256":"1514aa4a5dd4e5edd2c05ad8e9f1ddc7c45796dbc261fd4a9abd6c1dc9a4ecdf"},"schema_version":"1.0","source":{"id":"1903.07966","kind":"arxiv","version":1}},"canonical_sha256":"01dcab4d776381582a0ec50b6be22d914c3bc883e008827f4268155e02be5e94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01dcab4d776381582a0ec50b6be22d914c3bc883e008827f4268155e02be5e94","first_computed_at":"2026-05-17T23:50:53.387808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:53.387808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/gmtWiAGNluf4TA0EIqF3JvSuU1k1yzJjmPRrgUFEos7OHY4TljriJt1qp0R9dR4kxZfSfhRbJctbYW/eC6+Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:53.388542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c36d75a8c8be0ce11b24bba1db3d9d6d339f713e16681e58f86bb156aea4c31","sha256:0ab886032e492d0d98912d7cf464938d4956c6eb8568658aa689781cd6ab199b"],"state_sha256":"5bce6ccfcdaccf13717b27dcad812fa66134b33ed2ca937203b4167d9067dfed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xL18ZTEBmK1RWIXfmE1WFf4zVmo5uYOzccjCZo5gHzwL0Vhb+fvT136zqYgQcs0wYeFqpnmjcLXDSb2+h3+5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:41:32.122157Z","bundle_sha256":"7080be1a615037e4c6f1126a1c869b2879ac104b92ff9b8c40b2eff346bff995"}}