{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:D6BKTNIJ34GDZITXZDIPG6ZQUL","short_pith_number":"pith:D6BKTNIJ","schema_version":"1.0","canonical_sha256":"1f82a9b509df0c3ca277c8d0f37b30a2d264af8addf3c6db597c39427a068429","source":{"kind":"arxiv","id":"1703.09908","version":4},"attestation_state":"computed","paper":{"title":"A probabilistic approach to the leader problem in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Louigi Addario-Berry, Sanchayan Sen, Shankar Bhamidi","submitted_at":"2017-03-29T07:04:15Z","abstract_excerpt":"We study the fixation time of the identity of the leader, i.e., the most massive component, in the general setting of Aldous's multiplicative coalescent [4, 5], which in an asymptotic sense describes the evolution of the component sizes of a wide array of near-critical coalescent processes, including the classical Erd\\H{o}s-R\\'enyi process.\n  We show tightness of the fixation time in the \"Brownian\" regime, explicitly determining the median value of the fixation time to within an optimal $O(1)$ window. This generalizes {\\L}uczak's result [31] for the Erd\\H{o}s-R\\'enyi random graph using complet"},"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":"1703.09908","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-29T07:04:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d40332a1ee4ed6e403e8fb5425de2499b5bd1c860d7426c94093496d9f68836","abstract_canon_sha256":"8319c238040d57570c6088736a6f5b8d6c3bf410710f29ba115ad7221bf8d62b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:06:05.942345Z","signature_b64":"sU5UXZvEZatEhlqXu+xLJaHZlqgSM0/TotTWMIfEaOdTeZU2BdQfUa263FAgXyX3zIB329buyLXlT3Sv0a9HBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f82a9b509df0c3ca277c8d0f37b30a2d264af8addf3c6db597c39427a068429","last_reissued_at":"2026-07-05T01:06:05.941978Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:06:05.941978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A probabilistic approach to the leader problem in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Louigi Addario-Berry, Sanchayan Sen, Shankar Bhamidi","submitted_at":"2017-03-29T07:04:15Z","abstract_excerpt":"We study the fixation time of the identity of the leader, i.e., the most massive component, in the general setting of Aldous's multiplicative coalescent [4, 5], which in an asymptotic sense describes the evolution of the component sizes of a wide array of near-critical coalescent processes, including the classical Erd\\H{o}s-R\\'enyi process.\n  We show tightness of the fixation time in the \"Brownian\" regime, explicitly determining the median value of the fixation time to within an optimal $O(1)$ window. This generalizes {\\L}uczak's result [31] for the Erd\\H{o}s-R\\'enyi random graph using complet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09908","kind":"arxiv","version":4},"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/1703.09908/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":"1703.09908","created_at":"2026-07-05T01:06:05.942036+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.09908v4","created_at":"2026-07-05T01:06:05.942036+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09908","created_at":"2026-07-05T01:06:05.942036+00:00"},{"alias_kind":"pith_short_12","alias_value":"D6BKTNIJ34GD","created_at":"2026-07-05T01:06:05.942036+00:00"},{"alias_kind":"pith_short_16","alias_value":"D6BKTNIJ34GDZITX","created_at":"2026-07-05T01:06:05.942036+00:00"},{"alias_kind":"pith_short_8","alias_value":"D6BKTNIJ","created_at":"2026-07-05T01:06:05.942036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.23049","citing_title":"Generalized Multiple Operator Integrals and Perturbation Theory for Operators with Continuous Spectra","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL","json":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL.json","graph_json":"https://pith.science/api/pith-number/D6BKTNIJ34GDZITXZDIPG6ZQUL/graph.json","events_json":"https://pith.science/api/pith-number/D6BKTNIJ34GDZITXZDIPG6ZQUL/events.json","paper":"https://pith.science/paper/D6BKTNIJ"},"agent_actions":{"view_html":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL","download_json":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL.json","view_paper":"https://pith.science/paper/D6BKTNIJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.09908&json=true","fetch_graph":"https://pith.science/api/pith-number/D6BKTNIJ34GDZITXZDIPG6ZQUL/graph.json","fetch_events":"https://pith.science/api/pith-number/D6BKTNIJ34GDZITXZDIPG6ZQUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL/action/storage_attestation","attest_author":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL/action/author_attestation","sign_citation":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL/action/citation_signature","submit_replication":"https://pith.science/pith/D6BKTNIJ34GDZITXZDIPG6ZQUL/action/replication_record"}},"created_at":"2026-07-05T01:06:05.942036+00:00","updated_at":"2026-07-05T01:06:05.942036+00:00"}