{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:JF6SKZA6LH55UJXKBWAKUIAB5P","short_pith_number":"pith:JF6SKZA6","schema_version":"1.0","canonical_sha256":"497d25641e59fbda26ea0d80aa2001ebed88b72ae5c75eaaa0dc4730b42d4d26","source":{"kind":"arxiv","id":"2412.12319","version":1},"attestation_state":"computed","paper":{"title":"The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"David Aldous, Svante Janson","submitted_at":"2024-12-16T19:37:04Z","abstract_excerpt":"In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\\propto 1/(i(m-i))$. The height of a uniform random leaf can be represented as the absorption time of a certain {\\em harmonic descent} Markov chain. Recent work on these heights $D_n$ and $L_n$ (corresponding to discrete or continuous versions of the tree) has led to quite sharp expressions for their asymptotic distributions, based on their Markov chain description. This articl"},"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":"2412.12319","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-16T19:37:04Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"9627dbba4f16db4eb9c6d95cd6ce46e365f4a7039c80b1f29b33f1d39313d276","abstract_canon_sha256":"4dbc841fbafdace4bfa5a7ec84adbc3f007324ebe7a59d4ee2f0b7a6934f2ea5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:50:13.240340Z","signature_b64":"vWrfA3dXu6yEdz31SKDrGhEfxHrS0XbXfQWElXdRnk1fdFCFj+9GXQdCs9sG/e+CgTbnAeAWxw5x1All1vygDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"497d25641e59fbda26ea0d80aa2001ebed88b72ae5c75eaaa0dc4730b42d4d26","last_reissued_at":"2026-07-05T09:50:13.239861Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:50:13.239861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Critical Beta-splitting Random Tree IV: Mellin analysis of Leaf Height","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"David Aldous, Svante Janson","submitted_at":"2024-12-16T19:37:04Z","abstract_excerpt":"In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\\propto 1/(i(m-i))$. The height of a uniform random leaf can be represented as the absorption time of a certain {\\em harmonic descent} Markov chain. Recent work on these heights $D_n$ and $L_n$ (corresponding to discrete or continuous versions of the tree) has led to quite sharp expressions for their asymptotic distributions, based on their Markov chain description. This articl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.12319","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/2412.12319/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":"2412.12319","created_at":"2026-07-05T09:50:13.239918+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.12319v1","created_at":"2026-07-05T09:50:13.239918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.12319","created_at":"2026-07-05T09:50:13.239918+00:00"},{"alias_kind":"pith_short_12","alias_value":"JF6SKZA6LH55","created_at":"2026-07-05T09:50:13.239918+00:00"},{"alias_kind":"pith_short_16","alias_value":"JF6SKZA6LH55UJXK","created_at":"2026-07-05T09:50:13.239918+00:00"},{"alias_kind":"pith_short_8","alias_value":"JF6SKZA6","created_at":"2026-07-05T09:50:13.239918+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/JF6SKZA6LH55UJXKBWAKUIAB5P","json":"https://pith.science/pith/JF6SKZA6LH55UJXKBWAKUIAB5P.json","graph_json":"https://pith.science/api/pith-number/JF6SKZA6LH55UJXKBWAKUIAB5P/graph.json","events_json":"https://pith.science/api/pith-number/JF6SKZA6LH55UJXKBWAKUIAB5P/events.json","paper":"https://pith.science/paper/JF6SKZA6"},"agent_actions":{"view_html":"https://pith.science/pith/JF6SKZA6LH55UJXKBWAKUIAB5P","download_json":"https://pith.science/pith/JF6SKZA6LH55UJXKBWAKUIAB5P.json","view_paper":"https://pith.science/paper/JF6SKZA6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.12319&json=true","fetch_graph":"https://pith.science/api/pith-number/JF6SKZA6LH55UJXKBWAKUIAB5P/graph.json","fetch_events":"https://pith.science/api/pith-number/JF6SKZA6LH55UJXKBWAKUIAB5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JF6SKZA6LH55UJXKBWAKUIAB5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JF6SKZA6LH55UJXKBWAKUIAB5P/action/storage_attestation","attest_author":"https://pith.science/pith/JF6SKZA6LH55UJXKBWAKUIAB5P/action/author_attestation","sign_citation":"https://pith.science/pith/JF6SKZA6LH55UJXKBWAKUIAB5P/action/citation_signature","submit_replication":"https://pith.science/pith/JF6SKZA6LH55UJXKBWAKUIAB5P/action/replication_record"}},"created_at":"2026-07-05T09:50:13.239918+00:00","updated_at":"2026-07-05T09:50:13.239918+00:00"}