{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:WSBJEJVD246R5QYONXMEHWJBEZ","short_pith_number":"pith:WSBJEJVD","schema_version":"1.0","canonical_sha256":"b4829226a3d73d1ec30e6dd843d921266d5b569dc9bc03dec93bd1894d38ed65","source":{"kind":"arxiv","id":"0906.0152","version":1},"attestation_state":"computed","paper":{"title":"Long and short paths in uniform random recursive dags","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luc Devroye, Svante Janson","submitted_at":"2009-05-31T12:51:46Z","abstract_excerpt":"In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \\sigma such that S_n/log(n) tends to \\sigma in probability as n tends to infinity. We also show that max_{1 \\le i \\le n} S_i/log(n) tends to \\sigma in probability."},"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":"0906.0152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-31T12:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"8be1edbb07a2130fc0014750386900ff9b1d8778fb7e334ad4f9f7807b0025f4","abstract_canon_sha256":"6fb429bd6f6222bbea72e477996ee979631dbe85d28db1bc1fb53c3299ea187f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:30.283220Z","signature_b64":"76Z1jxGEWdcg7k6D+9LLOUAVU4Hsft1aEPG1MQXkYJV/mOwBePs+Ar8ZSPJb0stVKLXtNZQeDbqaUJhTALcJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4829226a3d73d1ec30e6dd843d921266d5b569dc9bc03dec93bd1894d38ed65","last_reissued_at":"2026-05-18T02:13:30.282518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:30.282518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long and short paths in uniform random recursive dags","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luc Devroye, Svante Janson","submitted_at":"2009-05-31T12:51:46Z","abstract_excerpt":"In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \\sigma such that S_n/log(n) tends to \\sigma in probability as n tends to infinity. We also show that max_{1 \\le i \\le n} S_i/log(n) tends to \\sigma in probability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0152","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0906.0152","created_at":"2026-05-18T02:13:30.282628+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.0152v1","created_at":"2026-05-18T02:13:30.282628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0152","created_at":"2026-05-18T02:13:30.282628+00:00"},{"alias_kind":"pith_short_12","alias_value":"WSBJEJVD246R","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"WSBJEJVD246R5QYO","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"WSBJEJVD","created_at":"2026-05-18T12:26:02.257875+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/WSBJEJVD246R5QYONXMEHWJBEZ","json":"https://pith.science/pith/WSBJEJVD246R5QYONXMEHWJBEZ.json","graph_json":"https://pith.science/api/pith-number/WSBJEJVD246R5QYONXMEHWJBEZ/graph.json","events_json":"https://pith.science/api/pith-number/WSBJEJVD246R5QYONXMEHWJBEZ/events.json","paper":"https://pith.science/paper/WSBJEJVD"},"agent_actions":{"view_html":"https://pith.science/pith/WSBJEJVD246R5QYONXMEHWJBEZ","download_json":"https://pith.science/pith/WSBJEJVD246R5QYONXMEHWJBEZ.json","view_paper":"https://pith.science/paper/WSBJEJVD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.0152&json=true","fetch_graph":"https://pith.science/api/pith-number/WSBJEJVD246R5QYONXMEHWJBEZ/graph.json","fetch_events":"https://pith.science/api/pith-number/WSBJEJVD246R5QYONXMEHWJBEZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WSBJEJVD246R5QYONXMEHWJBEZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WSBJEJVD246R5QYONXMEHWJBEZ/action/storage_attestation","attest_author":"https://pith.science/pith/WSBJEJVD246R5QYONXMEHWJBEZ/action/author_attestation","sign_citation":"https://pith.science/pith/WSBJEJVD246R5QYONXMEHWJBEZ/action/citation_signature","submit_replication":"https://pith.science/pith/WSBJEJVD246R5QYONXMEHWJBEZ/action/replication_record"}},"created_at":"2026-05-18T02:13:30.282628+00:00","updated_at":"2026-05-18T02:13:30.282628+00:00"}