{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ON6OAAVQLGOUAVHOTLJOU2UEQV","short_pith_number":"pith:ON6OAAVQ","schema_version":"1.0","canonical_sha256":"737ce002b0599d4054ee9ad2ea6a848553515dd157d2c8a958b9cb18e25dd550","source":{"kind":"arxiv","id":"2412.13975","version":1},"attestation_state":"computed","paper":{"title":"The number of descendants in a preferential attachment graph","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Svante Janson, Tiffany Y. Y. Lo","submitted_at":"2024-12-18T15:54:37Z","abstract_excerpt":"We study the number $X^{(n)}$ of vertices that can be reached from the last added vertex $n$ via a directed path (the descendants) in the standard preferential attachment graph. In this model, vertices are sequentially added, each born with outdegree $m\\ge 2$; the endpoint of each outgoing edge is chosen among previously added vertices with probability proportional to the current degree of the vertex plus some number $\\rho$.\n  We show that $X^{(n)}/n^\\nu$ converges in distribution as $n\\to\\infty$, where $\\nu$ depends on both $m$ and $\\rho$, and the limiting distribution is given by a product o"},"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":"2412.13975","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-18T15:54:37Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"aa4a79ad95e15b86848acd6ec17e3faa08e11e6c6ceb879eda173c5a206d9944","abstract_canon_sha256":"5de0b331c286442ea484fd6d6b2fa8721f860eb4f5771791a5052bb7afeb7036"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:51:11.684329Z","signature_b64":"IDjyH3hrNpYpPTYNQviMN/KcFHHtKSXRjnb3FMTWGDh+8YMuX0a1IkdtiBlNpDpvkfEWKAMfaCIGfpuivQTLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"737ce002b0599d4054ee9ad2ea6a848553515dd157d2c8a958b9cb18e25dd550","last_reissued_at":"2026-07-05T09:51:11.683841Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:51:11.683841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of descendants in a preferential attachment graph","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Svante Janson, Tiffany Y. Y. Lo","submitted_at":"2024-12-18T15:54:37Z","abstract_excerpt":"We study the number $X^{(n)}$ of vertices that can be reached from the last added vertex $n$ via a directed path (the descendants) in the standard preferential attachment graph. In this model, vertices are sequentially added, each born with outdegree $m\\ge 2$; the endpoint of each outgoing edge is chosen among previously added vertices with probability proportional to the current degree of the vertex plus some number $\\rho$.\n  We show that $X^{(n)}/n^\\nu$ converges in distribution as $n\\to\\infty$, where $\\nu$ depends on both $m$ and $\\rho$, and the limiting distribution is given by a product o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.13975","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.13975/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.13975","created_at":"2026-07-05T09:51:11.683899+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.13975v1","created_at":"2026-07-05T09:51:11.683899+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.13975","created_at":"2026-07-05T09:51:11.683899+00:00"},{"alias_kind":"pith_short_12","alias_value":"ON6OAAVQLGOU","created_at":"2026-07-05T09:51:11.683899+00:00"},{"alias_kind":"pith_short_16","alias_value":"ON6OAAVQLGOUAVHO","created_at":"2026-07-05T09:51:11.683899+00:00"},{"alias_kind":"pith_short_8","alias_value":"ON6OAAVQ","created_at":"2026-07-05T09:51:11.683899+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.30475","citing_title":"Ancestries in random $d$-DAGs","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV","json":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV.json","graph_json":"https://pith.science/api/pith-number/ON6OAAVQLGOUAVHOTLJOU2UEQV/graph.json","events_json":"https://pith.science/api/pith-number/ON6OAAVQLGOUAVHOTLJOU2UEQV/events.json","paper":"https://pith.science/paper/ON6OAAVQ"},"agent_actions":{"view_html":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV","download_json":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV.json","view_paper":"https://pith.science/paper/ON6OAAVQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.13975&json=true","fetch_graph":"https://pith.science/api/pith-number/ON6OAAVQLGOUAVHOTLJOU2UEQV/graph.json","fetch_events":"https://pith.science/api/pith-number/ON6OAAVQLGOUAVHOTLJOU2UEQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV/action/storage_attestation","attest_author":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV/action/author_attestation","sign_citation":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV/action/citation_signature","submit_replication":"https://pith.science/pith/ON6OAAVQLGOUAVHOTLJOU2UEQV/action/replication_record"}},"created_at":"2026-07-05T09:51:11.683899+00:00","updated_at":"2026-07-05T09:51:11.683899+00:00"}