{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:G5LZJ2FOMKKZW2XHIYBGX4RARK","short_pith_number":"pith:G5LZJ2FO","schema_version":"1.0","canonical_sha256":"375794e8ae62959b6ae746026bf2208a98fca6416ab4e2a5ac4382b42b40b7c4","source":{"kind":"arxiv","id":"1803.02133","version":2},"attestation_state":"computed","paper":{"title":"Trees within trees: Simple nested coalescents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Airam Blancas, Amaury Lambert, Arno Siri-J\\'egousse, Jean-Jil Duchamps","submitted_at":"2018-03-06T11:52:59Z","abstract_excerpt":"We consider the compact space of pairs of nested partitions of $\\mathbb N$, where by analogy with models used in molecular evolution, we call \"gene partition\" the finer partition and \"species partition\" the coarser one. We introduce the class of nondecreasing processes valued in nested partitions, assumed Markovian and with exchangeable semigroup. These processes are said simple when each partition only undergoes one coalescence event at a time (but possibly the same time). Simple nested exchangeable coalescent (SNEC) processes can be seen as the extension of $\\Lambda$-coalescents to nested pa"},"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":"1803.02133","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2018-03-06T11:52:59Z","cross_cats_sorted":[],"title_canon_sha256":"8248f904a233db7154310853b5279ac0554d8a62669998c417e0914f79864b40","abstract_canon_sha256":"d4604e1f0e904c0029566ba7910df5f2737308dc3bd0f4e663bda15cc47add05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:59.327488Z","signature_b64":"ysy24B4grxvT4K7dJDM9BHWqTKhfJBwhiTQTqt/InhV+e3QQ4Bk6LHcVKr3nFwiO0AnR9bjG/imM00KvublLAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"375794e8ae62959b6ae746026bf2208a98fca6416ab4e2a5ac4382b42b40b7c4","last_reissued_at":"2026-05-18T00:04:59.327082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:59.327082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trees within trees: Simple nested coalescents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Airam Blancas, Amaury Lambert, Arno Siri-J\\'egousse, Jean-Jil Duchamps","submitted_at":"2018-03-06T11:52:59Z","abstract_excerpt":"We consider the compact space of pairs of nested partitions of $\\mathbb N$, where by analogy with models used in molecular evolution, we call \"gene partition\" the finer partition and \"species partition\" the coarser one. We introduce the class of nondecreasing processes valued in nested partitions, assumed Markovian and with exchangeable semigroup. These processes are said simple when each partition only undergoes one coalescence event at a time (but possibly the same time). Simple nested exchangeable coalescent (SNEC) processes can be seen as the extension of $\\Lambda$-coalescents to nested pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02133","kind":"arxiv","version":2},"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":"1803.02133","created_at":"2026-05-18T00:04:59.327140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.02133v2","created_at":"2026-05-18T00:04:59.327140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02133","created_at":"2026-05-18T00:04:59.327140+00:00"},{"alias_kind":"pith_short_12","alias_value":"G5LZJ2FOMKKZ","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"G5LZJ2FOMKKZW2XH","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"G5LZJ2FO","created_at":"2026-05-18T12:32:25.280505+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/G5LZJ2FOMKKZW2XHIYBGX4RARK","json":"https://pith.science/pith/G5LZJ2FOMKKZW2XHIYBGX4RARK.json","graph_json":"https://pith.science/api/pith-number/G5LZJ2FOMKKZW2XHIYBGX4RARK/graph.json","events_json":"https://pith.science/api/pith-number/G5LZJ2FOMKKZW2XHIYBGX4RARK/events.json","paper":"https://pith.science/paper/G5LZJ2FO"},"agent_actions":{"view_html":"https://pith.science/pith/G5LZJ2FOMKKZW2XHIYBGX4RARK","download_json":"https://pith.science/pith/G5LZJ2FOMKKZW2XHIYBGX4RARK.json","view_paper":"https://pith.science/paper/G5LZJ2FO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.02133&json=true","fetch_graph":"https://pith.science/api/pith-number/G5LZJ2FOMKKZW2XHIYBGX4RARK/graph.json","fetch_events":"https://pith.science/api/pith-number/G5LZJ2FOMKKZW2XHIYBGX4RARK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G5LZJ2FOMKKZW2XHIYBGX4RARK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G5LZJ2FOMKKZW2XHIYBGX4RARK/action/storage_attestation","attest_author":"https://pith.science/pith/G5LZJ2FOMKKZW2XHIYBGX4RARK/action/author_attestation","sign_citation":"https://pith.science/pith/G5LZJ2FOMKKZW2XHIYBGX4RARK/action/citation_signature","submit_replication":"https://pith.science/pith/G5LZJ2FOMKKZW2XHIYBGX4RARK/action/replication_record"}},"created_at":"2026-05-18T00:04:59.327140+00:00","updated_at":"2026-05-18T00:04:59.327140+00:00"}