{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JQLAVWJRE7OVGAMS372UAECAEY","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":"4b2b46ebcf200457a2c751fe17e42be39c3a1c2768282771e3524a300844561c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-28T22:37:42Z","title_canon_sha256":"8bc0da19a68f1802ed9c07ef1700829d86c8173ecb508bf1298e5295747bef9a"},"schema_version":"1.0","source":{"id":"1404.7189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7189","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7189v1","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7189","created_at":"2026-05-18T02:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"JQLAVWJRE7OV","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JQLAVWJRE7OVGAMS","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JQLAVWJR","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:92f5f690af9465c9c9b05918c923e595908a0ab661e7c7af86b23c33b1145e9f","target":"graph","created_at":"2026-05-18T02:52:57Z","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":"We prove logarithmic upper bounds for the diameters of the random-surfer Webgraph model and the PageRank-based selection Webgraph model, confirming the small world phenomenon holds for them. In the special case when the generated graph is a tree, we provide close lower and upper bounds for the diameters of both models.","authors_text":"Abbas Mehrabian, Nick Wormald","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-28T22:37:42Z","title":"It's a Small World for Random Surfers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7189","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":"sha256:8308d21e7ef804cf7933797c5051155b39dcd6f24e5522fd3c76631c1eb0da1e","target":"record","created_at":"2026-05-18T02:52:57Z","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":"4b2b46ebcf200457a2c751fe17e42be39c3a1c2768282771e3524a300844561c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-28T22:37:42Z","title_canon_sha256":"8bc0da19a68f1802ed9c07ef1700829d86c8173ecb508bf1298e5295747bef9a"},"schema_version":"1.0","source":{"id":"1404.7189","kind":"arxiv","version":1}},"canonical_sha256":"4c160ad93127dd530192dff5401040263b0e73680782fb27408bb3c5c0beb400","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c160ad93127dd530192dff5401040263b0e73680782fb27408bb3c5c0beb400","first_computed_at":"2026-05-18T02:52:57.308779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:57.308779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fvBY1xWCrM+Hl9DjHuTezgeGFl2zV6wdOGs3SNQcxvwFPexuWCm7MRlQJuMh3oXfC9yO1ijBrg5noCn3SjScBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:57.309481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8308d21e7ef804cf7933797c5051155b39dcd6f24e5522fd3c76631c1eb0da1e","sha256:92f5f690af9465c9c9b05918c923e595908a0ab661e7c7af86b23c33b1145e9f"],"state_sha256":"57c2c3e9331eb44bff22951701053df2045bfe2a1a8c87e2fff00973ccbff265"}