{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VSHHZAZONYYGTVNB2CKMWN7VXM","short_pith_number":"pith:VSHHZAZO","canonical_record":{"source":{"id":"1602.07816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-02-25T06:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"698fb3414e64218b9cb01f025127da8f2c2d91dc3f0c02f852f557b58dfef2c2","abstract_canon_sha256":"4b1836db2bd272638a9aa768f8c7a168e93eff521e354c11450674496d6a2523"},"schema_version":"1.0"},"canonical_sha256":"ac8e7c832e6e3069d5a1d094cb37f5bb2b91a904dbd2f70b6ba6ce743cd6be25","source":{"kind":"arxiv","id":"1602.07816","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07816","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07816v2","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07816","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"VSHHZAZONYYG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VSHHZAZONYYGTVNB","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VSHHZAZO","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VSHHZAZONYYGTVNB2CKMWN7VXM","target":"record","payload":{"canonical_record":{"source":{"id":"1602.07816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-02-25T06:14:19Z","cross_cats_sorted":[],"title_canon_sha256":"698fb3414e64218b9cb01f025127da8f2c2d91dc3f0c02f852f557b58dfef2c2","abstract_canon_sha256":"4b1836db2bd272638a9aa768f8c7a168e93eff521e354c11450674496d6a2523"},"schema_version":"1.0"},"canonical_sha256":"ac8e7c832e6e3069d5a1d094cb37f5bb2b91a904dbd2f70b6ba6ce743cd6be25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:02.420102Z","signature_b64":"kp2+tcbqPmlyQUB9xFAZ/BeP3/JvnlaYyUinvGtr8uwGapA0LhiBEJL1mdvVTaGZ8n+H02AloLYsAKsjSfCbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac8e7c832e6e3069d5a1d094cb37f5bb2b91a904dbd2f70b6ba6ce743cd6be25","last_reissued_at":"2026-05-18T01:16:02.419311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:02.419311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.07816","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"us70nurVKla0INW5X6L5yvNB0vQfsqHVdJ64qEdLMZ1vWx4rMr6O/nZFghiJbKeU0S6nVMWpm/ggQ8GH1B3NBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:48:02.020631Z"},"content_sha256":"5726ad06c4267ab7a9e50385cb2d3d1e8429ee049902558ce09b0bf58da93896","schema_version":"1.0","event_id":"sha256:5726ad06c4267ab7a9e50385cb2d3d1e8429ee049902558ce09b0bf58da93896"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VSHHZAZONYYGTVNB2CKMWN7VXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relating Graph Thickness to Planar Layers and Bend Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Debajyoti Mondal, Stephane Durocher","submitted_at":"2016-02-25T06:14:19Z","abstract_excerpt":"The thickness of a graph $G=(V,E)$ with $n$ vertices is the minimum number of planar subgraphs of $G$ whose union is $G$. A polyline drawing of $G$ in $\\mathbb{R}^2$ is a drawing $\\Gamma$ of $G$, where each vertex is mapped to a point and each edge is mapped to a polygonal chain. Bend and layer complexities are two important aesthetics of such a drawing. The bend complexity of $\\Gamma$ is the maximum number of bends per edge in $\\Gamma$, and the layer complexity of $\\Gamma$ is the minimum integer $r$ such that the set of polygonal chains in $\\Gamma$ can be partitioned into $r$ disjoint sets, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07816","kind":"arxiv","version":2},"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":"2026-05-18T01:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C5MsV/H7W1wgf7MqMsflJjyvNF0lbuQWZj410XmRuWgify5k2MSuxrjBZtEoDdr9a7C8OdNv0GAlJLYUfAOoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:48:02.020985Z"},"content_sha256":"cb25a7e51bd3b430bd6a14edcfcb5e47bd258e7333cd2926a81e1ceb50262084","schema_version":"1.0","event_id":"sha256:cb25a7e51bd3b430bd6a14edcfcb5e47bd258e7333cd2926a81e1ceb50262084"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSHHZAZONYYGTVNB2CKMWN7VXM/bundle.json","state_url":"https://pith.science/pith/VSHHZAZONYYGTVNB2CKMWN7VXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSHHZAZONYYGTVNB2CKMWN7VXM/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":"2026-06-02T02:48:02Z","links":{"resolver":"https://pith.science/pith/VSHHZAZONYYGTVNB2CKMWN7VXM","bundle":"https://pith.science/pith/VSHHZAZONYYGTVNB2CKMWN7VXM/bundle.json","state":"https://pith.science/pith/VSHHZAZONYYGTVNB2CKMWN7VXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSHHZAZONYYGTVNB2CKMWN7VXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VSHHZAZONYYGTVNB2CKMWN7VXM","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":"4b1836db2bd272638a9aa768f8c7a168e93eff521e354c11450674496d6a2523","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-02-25T06:14:19Z","title_canon_sha256":"698fb3414e64218b9cb01f025127da8f2c2d91dc3f0c02f852f557b58dfef2c2"},"schema_version":"1.0","source":{"id":"1602.07816","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07816","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07816v2","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07816","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"VSHHZAZONYYG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VSHHZAZONYYGTVNB","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VSHHZAZO","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:cb25a7e51bd3b430bd6a14edcfcb5e47bd258e7333cd2926a81e1ceb50262084","target":"graph","created_at":"2026-05-18T01:16:02Z","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":"The thickness of a graph $G=(V,E)$ with $n$ vertices is the minimum number of planar subgraphs of $G$ whose union is $G$. A polyline drawing of $G$ in $\\mathbb{R}^2$ is a drawing $\\Gamma$ of $G$, where each vertex is mapped to a point and each edge is mapped to a polygonal chain. Bend and layer complexities are two important aesthetics of such a drawing. The bend complexity of $\\Gamma$ is the maximum number of bends per edge in $\\Gamma$, and the layer complexity of $\\Gamma$ is the minimum integer $r$ such that the set of polygonal chains in $\\Gamma$ can be partitioned into $r$ disjoint sets, w","authors_text":"Debajyoti Mondal, Stephane Durocher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-02-25T06:14:19Z","title":"Relating Graph Thickness to Planar Layers and Bend Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07816","kind":"arxiv","version":2},"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":"sha256:5726ad06c4267ab7a9e50385cb2d3d1e8429ee049902558ce09b0bf58da93896","target":"record","created_at":"2026-05-18T01:16:02Z","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":"4b1836db2bd272638a9aa768f8c7a168e93eff521e354c11450674496d6a2523","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-02-25T06:14:19Z","title_canon_sha256":"698fb3414e64218b9cb01f025127da8f2c2d91dc3f0c02f852f557b58dfef2c2"},"schema_version":"1.0","source":{"id":"1602.07816","kind":"arxiv","version":2}},"canonical_sha256":"ac8e7c832e6e3069d5a1d094cb37f5bb2b91a904dbd2f70b6ba6ce743cd6be25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac8e7c832e6e3069d5a1d094cb37f5bb2b91a904dbd2f70b6ba6ce743cd6be25","first_computed_at":"2026-05-18T01:16:02.419311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:02.419311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kp2+tcbqPmlyQUB9xFAZ/BeP3/JvnlaYyUinvGtr8uwGapA0LhiBEJL1mdvVTaGZ8n+H02AloLYsAKsjSfCbDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:02.420102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07816","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5726ad06c4267ab7a9e50385cb2d3d1e8429ee049902558ce09b0bf58da93896","sha256:cb25a7e51bd3b430bd6a14edcfcb5e47bd258e7333cd2926a81e1ceb50262084"],"state_sha256":"51d8f4b4ba2a815bdd4c943d6605df514af09bfe82b2acf6d79701b685df1795"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tukL7KgCDkhLqreE8lOgFculIa7eV4e8H++909o6/z2zhkBe/esaBjDmqjSrewDEMsEmJe58Z1xEjB862H8sCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:48:02.022935Z","bundle_sha256":"25fba4946fa463b57a5db673f4860f23667848929f6f82c0d99fd6e41e654b87"}}