{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6YQS4JAZ2OIP7IWNLXMSSBZ2S6","short_pith_number":"pith:6YQS4JAZ","canonical_record":{"source":{"id":"1308.2144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-09T14:56:55Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"331dd520592e73483c102164b758c3aa1589f382b2ab8f98e5feb1e60ff5b5c5","abstract_canon_sha256":"ed2b338420b59556c60d802831f449b47a883243b2eebecb6123b7dd0e01658a"},"schema_version":"1.0"},"canonical_sha256":"f6212e2419d390ffa2cd5dd929073a979b68dbced1563c6217f441e79018522c","source":{"kind":"arxiv","id":"1308.2144","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2144","created_at":"2026-05-18T03:16:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2144v2","created_at":"2026-05-18T03:16:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2144","created_at":"2026-05-18T03:16:08Z"},{"alias_kind":"pith_short_12","alias_value":"6YQS4JAZ2OIP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6YQS4JAZ2OIP7IWN","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6YQS4JAZ","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6YQS4JAZ2OIP7IWNLXMSSBZ2S6","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2144","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-09T14:56:55Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"331dd520592e73483c102164b758c3aa1589f382b2ab8f98e5feb1e60ff5b5c5","abstract_canon_sha256":"ed2b338420b59556c60d802831f449b47a883243b2eebecb6123b7dd0e01658a"},"schema_version":"1.0"},"canonical_sha256":"f6212e2419d390ffa2cd5dd929073a979b68dbced1563c6217f441e79018522c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:08.111796Z","signature_b64":"8EzJo8nRSa2uR2UrIw7A1PZQu3t62tpL08do2ibvENh1l8I0D5CahoroSGH2FsdWa5sEnrmTaAnaMO6RtIqyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6212e2419d390ffa2cd5dd929073a979b68dbced1563c6217f441e79018522c","last_reissued_at":"2026-05-18T03:16:08.111229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:08.111229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2144","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":"2026-05-18T03:16:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Q899t+zxA1wGBrPJRKmmSVC8xZNDDO4vCLoh5r37gtDD1iYis5FzoPfDfGmW/ucTCZwxI8iCoBWVNJWlvc9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:27:28.876857Z"},"content_sha256":"2fbf67ab5b745ed532b7177c57982d3e0c73e769d4c9e44ea5adc490944f288a","schema_version":"1.0","event_id":"sha256:2fbf67ab5b745ed532b7177c57982d3e0c73e769d4c9e44ea5adc490944f288a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6YQS4JAZ2OIP7IWNLXMSSBZ2S6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"In-Core Computation of Geometric Centralities with HyperBall: A Hundred Billion Nodes and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"cs.DS","authors_text":"Paolo Boldi, Sebastiano Vigna","submitted_at":"2013-08-09T14:56:55Z","abstract_excerpt":"Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were proposed to account for the importance of the nodes of a network. In this paper, we approach the problem of computing geometric centralities, such as closeness and harmonic centrality, on very large graphs; traditionally this task requires an all-pairs shortest-path computation in the exact case, or a number of breadth-first traversals for approximated computa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2144","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":"2026-05-18T03:16:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b53J4UOkMmxMzjpYnzitJGmBhG5YGjDL1WOUHvs52GG7Uwdb+gZRhR5DwVQ/LXYeEgiM+P9/DggPlJKaOmnkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:27:28.877547Z"},"content_sha256":"b8e646c6408e8925bdb6170e96cc96a7157d74494464e339c349fe62a397f46c","schema_version":"1.0","event_id":"sha256:b8e646c6408e8925bdb6170e96cc96a7157d74494464e339c349fe62a397f46c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YQS4JAZ2OIP7IWNLXMSSBZ2S6/bundle.json","state_url":"https://pith.science/pith/6YQS4JAZ2OIP7IWNLXMSSBZ2S6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YQS4JAZ2OIP7IWNLXMSSBZ2S6/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":"2026-06-10T22:27:28Z","links":{"resolver":"https://pith.science/pith/6YQS4JAZ2OIP7IWNLXMSSBZ2S6","bundle":"https://pith.science/pith/6YQS4JAZ2OIP7IWNLXMSSBZ2S6/bundle.json","state":"https://pith.science/pith/6YQS4JAZ2OIP7IWNLXMSSBZ2S6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YQS4JAZ2OIP7IWNLXMSSBZ2S6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6YQS4JAZ2OIP7IWNLXMSSBZ2S6","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":"ed2b338420b59556c60d802831f449b47a883243b2eebecb6123b7dd0e01658a","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-09T14:56:55Z","title_canon_sha256":"331dd520592e73483c102164b758c3aa1589f382b2ab8f98e5feb1e60ff5b5c5"},"schema_version":"1.0","source":{"id":"1308.2144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2144","created_at":"2026-05-18T03:16:08Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2144v2","created_at":"2026-05-18T03:16:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2144","created_at":"2026-05-18T03:16:08Z"},{"alias_kind":"pith_short_12","alias_value":"6YQS4JAZ2OIP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6YQS4JAZ2OIP7IWN","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6YQS4JAZ","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:b8e646c6408e8925bdb6170e96cc96a7157d74494464e339c349fe62a397f46c","target":"graph","created_at":"2026-05-18T03:16:08Z","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":"Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were proposed to account for the importance of the nodes of a network. In this paper, we approach the problem of computing geometric centralities, such as closeness and harmonic centrality, on very large graphs; traditionally this task requires an all-pairs shortest-path computation in the exact case, or a number of breadth-first traversals for approximated computa","authors_text":"Paolo Boldi, Sebastiano Vigna","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-09T14:56:55Z","title":"In-Core Computation of Geometric Centralities with HyperBall: A Hundred Billion Nodes and Beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2144","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":"sha256:2fbf67ab5b745ed532b7177c57982d3e0c73e769d4c9e44ea5adc490944f288a","target":"record","created_at":"2026-05-18T03:16:08Z","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":"ed2b338420b59556c60d802831f449b47a883243b2eebecb6123b7dd0e01658a","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-08-09T14:56:55Z","title_canon_sha256":"331dd520592e73483c102164b758c3aa1589f382b2ab8f98e5feb1e60ff5b5c5"},"schema_version":"1.0","source":{"id":"1308.2144","kind":"arxiv","version":2}},"canonical_sha256":"f6212e2419d390ffa2cd5dd929073a979b68dbced1563c6217f441e79018522c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6212e2419d390ffa2cd5dd929073a979b68dbced1563c6217f441e79018522c","first_computed_at":"2026-05-18T03:16:08.111229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:08.111229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8EzJo8nRSa2uR2UrIw7A1PZQu3t62tpL08do2ibvENh1l8I0D5CahoroSGH2FsdWa5sEnrmTaAnaMO6RtIqyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:08.111796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fbf67ab5b745ed532b7177c57982d3e0c73e769d4c9e44ea5adc490944f288a","sha256:b8e646c6408e8925bdb6170e96cc96a7157d74494464e339c349fe62a397f46c"],"state_sha256":"74229c50c0c33d86d0c9d9a558b47d6ac9c60c7dd257527be93d6b0343f19382"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGFrJ9stQKAWtsxf5ouTkPI7l1baYyJf7pItMeG2zG5ZSWWueTm9DQJv1rPV/ZcgN7oeIyRSG9Oyhp1tK3c7DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:27:28.881771Z","bundle_sha256":"33100315a8d4245627443c639f32dce0e32547c5fea14ee48a54ada267f59ec2"}}