{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CJOT3LL3F6FQEKFADTBXSHI7RJ","short_pith_number":"pith:CJOT3LL3","canonical_record":{"source":{"id":"2104.02764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-04-06T20:08:58Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"6a9b505b8be54d01797fcad485e2fba0ab6db1503f425d6983b0fe2644f5c66a","abstract_canon_sha256":"83d249c1da748d2867675451db817b3fcaaa27604176af89d2470c7df73d35a3"},"schema_version":"1.0"},"canonical_sha256":"125d3dad7b2f8b0228a01cc3791d1f8a4302776dc76d067ce46db72b8b4eeccc","source":{"kind":"arxiv","id":"2104.02764","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.02764","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"2104.02764v2","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.02764","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"CJOT3LL3F6FQ","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"pith_short_16","alias_value":"CJOT3LL3F6FQEKFA","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"pith_short_8","alias_value":"CJOT3LL3","created_at":"2026-07-05T02:40:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CJOT3LL3F6FQEKFADTBXSHI7RJ","target":"record","payload":{"canonical_record":{"source":{"id":"2104.02764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-04-06T20:08:58Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"6a9b505b8be54d01797fcad485e2fba0ab6db1503f425d6983b0fe2644f5c66a","abstract_canon_sha256":"83d249c1da748d2867675451db817b3fcaaa27604176af89d2470c7df73d35a3"},"schema_version":"1.0"},"canonical_sha256":"125d3dad7b2f8b0228a01cc3791d1f8a4302776dc76d067ce46db72b8b4eeccc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:40:33.868838Z","signature_b64":"RHHz3wtFs3vsaHK6JQ7COd5UqZ3mqh48uBbeRFbVG29RlCCQKUQOBA7wrL8JYZSddkgtacB7Iyc0k28wRoqzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"125d3dad7b2f8b0228a01cc3791d1f8a4302776dc76d067ce46db72b8b4eeccc","last_reissued_at":"2026-07-05T02:40:33.868259Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:40:33.868259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.02764","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":"2026-07-05T02:40:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qgs4+LCzapWwF14M1K4V60OAKb2+VAjKywgrgjJYBcqLbV3EzEZaOervCiCKTAaovfPTAJBqZyfpRf+0zil4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:35:22.459036Z"},"content_sha256":"8251780877f4241caff95f587f4d16af3788745b11816666c3416bfef9a0ca37","schema_version":"1.0","event_id":"sha256:8251780877f4241caff95f587f4d16af3788745b11816666c3416bfef9a0ca37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CJOT3LL3F6FQEKFADTBXSHI7RJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PageRank centrality and algorithms for weighted, directed networks with applications to World Input-Output Tables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"physics.soc-ph","authors_text":"Jun Yan, Panpan Zhang, Tiandong Wang","submitted_at":"2021-04-06T20:08:58Z","abstract_excerpt":"PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible non-uniform node-specific information that is dependent or independent of network structure. A tuning parameter leveraging node degree and strength is introduced. An efficient algorithm based on R program has been developed for computing WPR in large-scale networks. We have tested the proposed WPR on widely used simulated network models, and found it outperf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.02764","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.02764/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:40:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"af1V5H3JZBAu3+h3H73AmAQOzUHns4iK+6VSgYP00OgLyGmagkZtRiN8oN+oxP0Mi8Nla4E0rY+RT09NEksbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:35:22.459706Z"},"content_sha256":"8cf53f795822d95b3a301d16ddcea8c888e3e369915ea39168ece13d6ef77b26","schema_version":"1.0","event_id":"sha256:8cf53f795822d95b3a301d16ddcea8c888e3e369915ea39168ece13d6ef77b26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJOT3LL3F6FQEKFADTBXSHI7RJ/bundle.json","state_url":"https://pith.science/pith/CJOT3LL3F6FQEKFADTBXSHI7RJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJOT3LL3F6FQEKFADTBXSHI7RJ/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":"2026-07-07T06:35:22Z","links":{"resolver":"https://pith.science/pith/CJOT3LL3F6FQEKFADTBXSHI7RJ","bundle":"https://pith.science/pith/CJOT3LL3F6FQEKFADTBXSHI7RJ/bundle.json","state":"https://pith.science/pith/CJOT3LL3F6FQEKFADTBXSHI7RJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJOT3LL3F6FQEKFADTBXSHI7RJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CJOT3LL3F6FQEKFADTBXSHI7RJ","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":"83d249c1da748d2867675451db817b3fcaaa27604176af89d2470c7df73d35a3","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-04-06T20:08:58Z","title_canon_sha256":"6a9b505b8be54d01797fcad485e2fba0ab6db1503f425d6983b0fe2644f5c66a"},"schema_version":"1.0","source":{"id":"2104.02764","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.02764","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"arxiv_version","alias_value":"2104.02764v2","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.02764","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"pith_short_12","alias_value":"CJOT3LL3F6FQ","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"pith_short_16","alias_value":"CJOT3LL3F6FQEKFA","created_at":"2026-07-05T02:40:33Z"},{"alias_kind":"pith_short_8","alias_value":"CJOT3LL3","created_at":"2026-07-05T02:40:33Z"}],"graph_snapshots":[{"event_id":"sha256:8cf53f795822d95b3a301d16ddcea8c888e3e369915ea39168ece13d6ef77b26","target":"graph","created_at":"2026-07-05T02:40:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2104.02764/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible non-uniform node-specific information that is dependent or independent of network structure. A tuning parameter leveraging node degree and strength is introduced. An efficient algorithm based on R program has been developed for computing WPR in large-scale networks. We have tested the proposed WPR on widely used simulated network models, and found it outperf","authors_text":"Jun Yan, Panpan Zhang, Tiandong Wang","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-04-06T20:08:58Z","title":"PageRank centrality and algorithms for weighted, directed networks with applications to World Input-Output Tables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.02764","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":"sha256:8251780877f4241caff95f587f4d16af3788745b11816666c3416bfef9a0ca37","target":"record","created_at":"2026-07-05T02:40:33Z","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":"83d249c1da748d2867675451db817b3fcaaa27604176af89d2470c7df73d35a3","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-04-06T20:08:58Z","title_canon_sha256":"6a9b505b8be54d01797fcad485e2fba0ab6db1503f425d6983b0fe2644f5c66a"},"schema_version":"1.0","source":{"id":"2104.02764","kind":"arxiv","version":2}},"canonical_sha256":"125d3dad7b2f8b0228a01cc3791d1f8a4302776dc76d067ce46db72b8b4eeccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"125d3dad7b2f8b0228a01cc3791d1f8a4302776dc76d067ce46db72b8b4eeccc","first_computed_at":"2026-07-05T02:40:33.868259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:40:33.868259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RHHz3wtFs3vsaHK6JQ7COd5UqZ3mqh48uBbeRFbVG29RlCCQKUQOBA7wrL8JYZSddkgtacB7Iyc0k28wRoqzBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:40:33.868838Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.02764","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8251780877f4241caff95f587f4d16af3788745b11816666c3416bfef9a0ca37","sha256:8cf53f795822d95b3a301d16ddcea8c888e3e369915ea39168ece13d6ef77b26"],"state_sha256":"c5c4c5d54b8437829dadc1c28659267b734fdc586d0819222003828ff4caf66f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RzYQ+YzxzlYr4ohZC8CnL4lK3OR2btbrIOXS5FvKJMlqWQmnTSjC/+95+SliUOu5C+VVlFZZShg1k6qUZAxwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T06:35:22.463421Z","bundle_sha256":"df0fef84ec7b96a83cafe05372d8bef2b99fbe71530d44e4741c6b1cfb25634b"}}