{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:5V4WRCIYLRWIEDEHV6OGCMBDM3","short_pith_number":"pith:5V4WRCIY","schema_version":"1.0","canonical_sha256":"ed796889185c6c820c87af9c61302366f57b520edac9fcca412d8622a4be1023","source":{"kind":"arxiv","id":"physics/0604203","version":2},"attestation_state":"computed","paper":{"title":"Random Walks on Directed Networks: the Case of PageRank","license":"","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Alessandro Flammini, Santo Fortunato","submitted_at":"2006-04-25T17:16:57Z","abstract_excerpt":"PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability of being visited. We give some exact results on the distribution of PageRank in the cases in which the damping factor q approaches the two limit values 0 and 1. When q -> 0 and for several classes of graphs the distribution is a power law with exponent 2, regardless of the in-degree distribution. When q -> 1 it can always be derived from the in-degree distrib"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"physics/0604203","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"physics.soc-ph","submitted_at":"2006-04-25T17:16:57Z","cross_cats_sorted":[],"title_canon_sha256":"6f2a92ddd062f554736660524258c1c5235bddf8863dd3aecd6390d796bd0c5a","abstract_canon_sha256":"dd6491f82d8579c78d1ae09b6b1f524be4d3d43157c78db4aaa81e1a1a6493b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:07.050643Z","signature_b64":"Hy1vLuPW/Kzek1iW9LYvLKOp3dYS4zhjYsaVx28e7FOeMjRw/SfndCLwL/nLt/5Eyie2zgjKkd0qyV0XE0dBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed796889185c6c820c87af9c61302366f57b520edac9fcca412d8622a4be1023","last_reissued_at":"2026-05-18T01:38:07.050014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:07.050014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random Walks on Directed Networks: the Case of PageRank","license":"","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Alessandro Flammini, Santo Fortunato","submitted_at":"2006-04-25T17:16:57Z","abstract_excerpt":"PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability of being visited. We give some exact results on the distribution of PageRank in the cases in which the damping factor q approaches the two limit values 0 and 1. When q -> 0 and for several classes of graphs the distribution is a power law with exponent 2, regardless of the in-degree distribution. When q -> 1 it can always be derived from the in-degree distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0604203","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"physics/0604203","created_at":"2026-05-18T01:38:07.050113+00:00"},{"alias_kind":"arxiv_version","alias_value":"physics/0604203v2","created_at":"2026-05-18T01:38:07.050113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0604203","created_at":"2026-05-18T01:38:07.050113+00:00"},{"alias_kind":"pith_short_12","alias_value":"5V4WRCIYLRWI","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"5V4WRCIYLRWIEDEH","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"5V4WRCIY","created_at":"2026-05-18T12:25:53.939244+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3","json":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3.json","graph_json":"https://pith.science/api/pith-number/5V4WRCIYLRWIEDEHV6OGCMBDM3/graph.json","events_json":"https://pith.science/api/pith-number/5V4WRCIYLRWIEDEHV6OGCMBDM3/events.json","paper":"https://pith.science/paper/5V4WRCIY"},"agent_actions":{"view_html":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3","download_json":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3.json","view_paper":"https://pith.science/paper/5V4WRCIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=physics/0604203&json=true","fetch_graph":"https://pith.science/api/pith-number/5V4WRCIYLRWIEDEHV6OGCMBDM3/graph.json","fetch_events":"https://pith.science/api/pith-number/5V4WRCIYLRWIEDEHV6OGCMBDM3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3/action/storage_attestation","attest_author":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3/action/author_attestation","sign_citation":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3/action/citation_signature","submit_replication":"https://pith.science/pith/5V4WRCIYLRWIEDEHV6OGCMBDM3/action/replication_record"}},"created_at":"2026-05-18T01:38:07.050113+00:00","updated_at":"2026-05-18T01:38:07.050113+00:00"}