{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YZPLIML54V5K4ZUO4WVW5BKNN5","short_pith_number":"pith:YZPLIML5","canonical_record":{"source":{"id":"1702.06503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-21T18:13:40Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"d5df67d8c5e77deac0748417aef6d35243e48653487987da1e66acf6e718f379","abstract_canon_sha256":"29fdb2e233c26bf1ca52828106e271648c073a6e9a71662638785c7ed5e77880"},"schema_version":"1.0"},"canonical_sha256":"c65eb4317de57aae668ee5ab6e854d6f5afb6637625e9e9b6598b0241da3fa1e","source":{"kind":"arxiv","id":"1702.06503","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06503","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06503v1","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06503","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"YZPLIML54V5K","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZPLIML54V5K4ZUO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZPLIML5","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YZPLIML54V5K4ZUO4WVW5BKNN5","target":"record","payload":{"canonical_record":{"source":{"id":"1702.06503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-21T18:13:40Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"d5df67d8c5e77deac0748417aef6d35243e48653487987da1e66acf6e718f379","abstract_canon_sha256":"29fdb2e233c26bf1ca52828106e271648c073a6e9a71662638785c7ed5e77880"},"schema_version":"1.0"},"canonical_sha256":"c65eb4317de57aae668ee5ab6e854d6f5afb6637625e9e9b6598b0241da3fa1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:13.984983Z","signature_b64":"F1NXa6xHveELdt+r4M/3sHs2/FkPJcxK7gywdmK3iXodAO9EFA5FbO3S6SszjL725WVVoZYIobLafv0c40pnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65eb4317de57aae668ee5ab6e854d6f5afb6637625e9e9b6598b0241da3fa1e","last_reissued_at":"2026-05-18T00:50:13.984528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:13.984528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.06503","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":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vd3eIrUqWlvXQcGqbqcrv3e4h6qVqeTnm6n0qFltePmGMTmJNRx+EFSTTebGMVG1Wb4elyfhxEEx7h0qh8JRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:34:40.057368Z"},"content_sha256":"9464e5baa904c49c857becceb91c4a4917fbd1df3068d5463294d3d1283d14f2","schema_version":"1.0","event_id":"sha256:9464e5baa904c49c857becceb91c4a4917fbd1df3068d5463294d3d1283d14f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YZPLIML54V5K4ZUO4WVW5BKNN5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When can Graph Hyperbolicity be computed in Linear Time?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Andr\\'e Nichterlein, Christian Komusiewicz, George B. Mertzios, Nimrod Talmon, Rolf Niedermeier, Till Fluschnik","submitted_at":"2017-02-21T18:13:40Z","abstract_excerpt":"Hyperbolicity measures, in terms of (distance) metrics, how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last years. Unfortunately, the best known algorithms for computing the hyperbolicity number of a graph (the smaller, the more tree-like) have running time $O(n^4)$, where $n$ is the number of graph vertices. Exploiting the framework of parameterized complexity analysis, we explore possibilities for \"linear-time FPT\" algorithms to compute hyperbolicity. For instance, we show that hyperbolicity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06503","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":"2026-05-18T00:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M9RmBUkl+RKEAsCAzrRU2HvyltfXNkdgLsWLQTSM2a8N6gDzbsjn5StWOMhJPIzes/PcMekX4KOd7ATeUr1fDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:34:40.057724Z"},"content_sha256":"247fc7553e9a554bb04dea0685446f0a19af34b9ad7cbf5ec0ffa17da2dc7029","schema_version":"1.0","event_id":"sha256:247fc7553e9a554bb04dea0685446f0a19af34b9ad7cbf5ec0ffa17da2dc7029"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZPLIML54V5K4ZUO4WVW5BKNN5/bundle.json","state_url":"https://pith.science/pith/YZPLIML54V5K4ZUO4WVW5BKNN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZPLIML54V5K4ZUO4WVW5BKNN5/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":"2026-06-01T21:34:40Z","links":{"resolver":"https://pith.science/pith/YZPLIML54V5K4ZUO4WVW5BKNN5","bundle":"https://pith.science/pith/YZPLIML54V5K4ZUO4WVW5BKNN5/bundle.json","state":"https://pith.science/pith/YZPLIML54V5K4ZUO4WVW5BKNN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZPLIML54V5K4ZUO4WVW5BKNN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YZPLIML54V5K4ZUO4WVW5BKNN5","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":"29fdb2e233c26bf1ca52828106e271648c073a6e9a71662638785c7ed5e77880","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-21T18:13:40Z","title_canon_sha256":"d5df67d8c5e77deac0748417aef6d35243e48653487987da1e66acf6e718f379"},"schema_version":"1.0","source":{"id":"1702.06503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06503","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06503v1","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06503","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"YZPLIML54V5K","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZPLIML54V5K4ZUO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZPLIML5","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:247fc7553e9a554bb04dea0685446f0a19af34b9ad7cbf5ec0ffa17da2dc7029","target":"graph","created_at":"2026-05-18T00:50:13Z","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":"Hyperbolicity measures, in terms of (distance) metrics, how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last years. Unfortunately, the best known algorithms for computing the hyperbolicity number of a graph (the smaller, the more tree-like) have running time $O(n^4)$, where $n$ is the number of graph vertices. Exploiting the framework of parameterized complexity analysis, we explore possibilities for \"linear-time FPT\" algorithms to compute hyperbolicity. For instance, we show that hyperbolicity","authors_text":"Andr\\'e Nichterlein, Christian Komusiewicz, George B. Mertzios, Nimrod Talmon, Rolf Niedermeier, Till Fluschnik","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-21T18:13:40Z","title":"When can Graph Hyperbolicity be computed in Linear Time?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06503","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":"sha256:9464e5baa904c49c857becceb91c4a4917fbd1df3068d5463294d3d1283d14f2","target":"record","created_at":"2026-05-18T00:50:13Z","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":"29fdb2e233c26bf1ca52828106e271648c073a6e9a71662638785c7ed5e77880","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-21T18:13:40Z","title_canon_sha256":"d5df67d8c5e77deac0748417aef6d35243e48653487987da1e66acf6e718f379"},"schema_version":"1.0","source":{"id":"1702.06503","kind":"arxiv","version":1}},"canonical_sha256":"c65eb4317de57aae668ee5ab6e854d6f5afb6637625e9e9b6598b0241da3fa1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c65eb4317de57aae668ee5ab6e854d6f5afb6637625e9e9b6598b0241da3fa1e","first_computed_at":"2026-05-18T00:50:13.984528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:13.984528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F1NXa6xHveELdt+r4M/3sHs2/FkPJcxK7gywdmK3iXodAO9EFA5FbO3S6SszjL725WVVoZYIobLafv0c40pnBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:13.984983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9464e5baa904c49c857becceb91c4a4917fbd1df3068d5463294d3d1283d14f2","sha256:247fc7553e9a554bb04dea0685446f0a19af34b9ad7cbf5ec0ffa17da2dc7029"],"state_sha256":"0226d58b4a31a0eac70f7a03261c713f83a0e9cfb6c2fba9f813bfcd778fb28c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1vIFRZaYUldNkxLnCvFK5d1aNkyk/KjlMZrgw+EpgqSFERV6nhr98/OFMLL10TjqBspfN8BZsh92L4mWngzvCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:34:40.060021Z","bundle_sha256":"dfced3308fd080aa121e7485f651836e976582c2922706b7f81fe1bba8b4a052"}}