{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZU7FI3OSX5TTIGZI2UQLGSMTFX","short_pith_number":"pith:ZU7FI3OS","canonical_record":{"source":{"id":"1510.08274","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-28T12:00:16Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"16753505fc6755d9f1e194f24133751fddc586b58a6a246c0917a19ce44e4597","abstract_canon_sha256":"3db2d16ded01bcc42b14c7e605efd2e05080b0e918116a807fe20f6e77e2279c"},"schema_version":"1.0"},"canonical_sha256":"cd3e546dd2bf67341b28d520b349932defe2d9683261585c77596d7d6a1cc1de","source":{"kind":"arxiv","id":"1510.08274","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08274","created_at":"2026-05-18T01:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08274v4","created_at":"2026-05-18T01:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08274","created_at":"2026-05-18T01:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"ZU7FI3OSX5TT","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZU7FI3OSX5TTIGZI","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZU7FI3OS","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZU7FI3OSX5TTIGZI2UQLGSMTFX","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08274","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-28T12:00:16Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"16753505fc6755d9f1e194f24133751fddc586b58a6a246c0917a19ce44e4597","abstract_canon_sha256":"3db2d16ded01bcc42b14c7e605efd2e05080b0e918116a807fe20f6e77e2279c"},"schema_version":"1.0"},"canonical_sha256":"cd3e546dd2bf67341b28d520b349932defe2d9683261585c77596d7d6a1cc1de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:51.097471Z","signature_b64":"TZav5yv9Q0A+W7TNorqf6C3OR5E/IsXgFo1EDTYaPHc41/DkUzgQXCnPT6F0xwm1XI4lvDbyTH1vif46hZGkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd3e546dd2bf67341b28d520b349932defe2d9683261585c77596d7d6a1cc1de","last_reissued_at":"2026-05-18T01:07:51.096994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:51.096994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08274","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:07:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKJty1xvMW0iG1tTpEdF0VMM77RXMsTuH+UXgcLhTtqL9O/1iPrX/vIwDa8i4018tLaP8Z/aYiJTJwHsOW6VBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T23:44:39.948854Z"},"content_sha256":"bf3c77b2c00bc334759156a1558cf8f7e466abcff2c9b8075054dc041f0e1979","schema_version":"1.0","event_id":"sha256:bf3c77b2c00bc334759156a1558cf8f7e466abcff2c9b8075054dc041f0e1979"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZU7FI3OSX5TTIGZI2UQLGSMTFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond Level Planarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Fabrizio Frati, Giordano Da Lozzo, Giuseppe Di Battista, Ignaz Rutter, Maurizio Patrignani, Patrizio Angelini","submitted_at":"2015-10-28T12:00:16Z","abstract_excerpt":"In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level embedding of a level graph on the surface of the rolling cylinder or on the surface of the torus, respectively known by the name of $\\textit{Cyclic Level Planarity}$ and $\\textit{Torus Level Planarity}$, are polynomial-time solvable.\n  Moreover, we show a complexity dichotomy for testing the $\\textit{Simultaneous Level Planarity}$ of a set of level graphs, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08274","kind":"arxiv","version":4},"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":"2026-05-18T01:07:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUDEjZdEFShWrpGEGPz9fANrNJgeZEstQd/q0TIs76hQ+ShCFFZxC6H1eGAH5icWjfrqHpQIiVF8g2fKvFlpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T23:44:39.949568Z"},"content_sha256":"dd465006bb4d304af893c278219a0f7644511284cfc4e1e8b5c4d830a0a5932b","schema_version":"1.0","event_id":"sha256:dd465006bb4d304af893c278219a0f7644511284cfc4e1e8b5c4d830a0a5932b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZU7FI3OSX5TTIGZI2UQLGSMTFX/bundle.json","state_url":"https://pith.science/pith/ZU7FI3OSX5TTIGZI2UQLGSMTFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZU7FI3OSX5TTIGZI2UQLGSMTFX/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":"2026-05-29T23:44:39Z","links":{"resolver":"https://pith.science/pith/ZU7FI3OSX5TTIGZI2UQLGSMTFX","bundle":"https://pith.science/pith/ZU7FI3OSX5TTIGZI2UQLGSMTFX/bundle.json","state":"https://pith.science/pith/ZU7FI3OSX5TTIGZI2UQLGSMTFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZU7FI3OSX5TTIGZI2UQLGSMTFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZU7FI3OSX5TTIGZI2UQLGSMTFX","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":"3db2d16ded01bcc42b14c7e605efd2e05080b0e918116a807fe20f6e77e2279c","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-28T12:00:16Z","title_canon_sha256":"16753505fc6755d9f1e194f24133751fddc586b58a6a246c0917a19ce44e4597"},"schema_version":"1.0","source":{"id":"1510.08274","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08274","created_at":"2026-05-18T01:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08274v4","created_at":"2026-05-18T01:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08274","created_at":"2026-05-18T01:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"ZU7FI3OSX5TT","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZU7FI3OSX5TTIGZI","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZU7FI3OS","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:dd465006bb4d304af893c278219a0f7644511284cfc4e1e8b5c4d830a0a5932b","target":"graph","created_at":"2026-05-18T01:07:51Z","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":"In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level embedding of a level graph on the surface of the rolling cylinder or on the surface of the torus, respectively known by the name of $\\textit{Cyclic Level Planarity}$ and $\\textit{Torus Level Planarity}$, are polynomial-time solvable.\n  Moreover, we show a complexity dichotomy for testing the $\\textit{Simultaneous Level Planarity}$ of a set of level graphs, w","authors_text":"Fabrizio Frati, Giordano Da Lozzo, Giuseppe Di Battista, Ignaz Rutter, Maurizio Patrignani, Patrizio Angelini","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-28T12:00:16Z","title":"Beyond Level Planarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08274","kind":"arxiv","version":4},"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:bf3c77b2c00bc334759156a1558cf8f7e466abcff2c9b8075054dc041f0e1979","target":"record","created_at":"2026-05-18T01:07:51Z","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":"3db2d16ded01bcc42b14c7e605efd2e05080b0e918116a807fe20f6e77e2279c","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-28T12:00:16Z","title_canon_sha256":"16753505fc6755d9f1e194f24133751fddc586b58a6a246c0917a19ce44e4597"},"schema_version":"1.0","source":{"id":"1510.08274","kind":"arxiv","version":4}},"canonical_sha256":"cd3e546dd2bf67341b28d520b349932defe2d9683261585c77596d7d6a1cc1de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd3e546dd2bf67341b28d520b349932defe2d9683261585c77596d7d6a1cc1de","first_computed_at":"2026-05-18T01:07:51.096994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:51.096994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZav5yv9Q0A+W7TNorqf6C3OR5E/IsXgFo1EDTYaPHc41/DkUzgQXCnPT6F0xwm1XI4lvDbyTH1vif46hZGkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:51.097471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08274","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf3c77b2c00bc334759156a1558cf8f7e466abcff2c9b8075054dc041f0e1979","sha256:dd465006bb4d304af893c278219a0f7644511284cfc4e1e8b5c4d830a0a5932b"],"state_sha256":"8fd7dcec2b798268e17c70f25b67f5b0c5b9400b18efc5e2fefcbb52740e3083"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lGOgJLihfDSrBsU2TlUYkoU8ybntpc8jatG/DxKv009A6GFgoA7eeH+43zVzfpd1rIPr2UndnYikXP77NXNiCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T23:44:39.953770Z","bundle_sha256":"1f93a0246e7846caf8f47d3569d4df2151a177538861d6fed97f32dc6eae5813"}}