{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q2TGCTAI5VRLKV5BPSMTXINAWY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b6cb413bd26fbc25ac23d7f0dd6a13fd7e4a1b219a09d1782d8fdbc6e3267bb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-13T13:43:46Z","title_canon_sha256":"500fdd38b70dbe5b7e37567d03915208ba6e49ad8ed399f259ddf53d9fc17372"},"schema_version":"1.0","source":{"id":"1502.03983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03983","created_at":"2026-05-18T02:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03983v1","created_at":"2026-05-18T02:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03983","created_at":"2026-05-18T02:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"Q2TGCTAI5VRL","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q2TGCTAI5VRLKV5B","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q2TGCTAI","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:81d461cb3df4db89340a74ad9e1762d6f40ef4f1c6bbe0ce4dabefbc8b07b5c8","target":"graph","created_at":"2026-05-18T02:27:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Formulas are provided for the cumulants and the moments of the time $T$ back to the most recent common ancestor of the Kingman coalescent. It is shown that both the $j$th cumulant and the $j$th moment of $T$ are linear combinations of the values $\\zeta(2m)$, $m\\in\\{0,\\ldots,\\lfloor j/2\\rfloor\\}$, of the Riemann zeta function $\\zeta$ with integer coefficients. The proof is based on a solution of a two-dimensional recursion with countably many initial values. A closely related strong convergence result for the tree length $L_n$ of the Kingman coalescent restricted to a sample of size $n$ is deri","authors_text":"Helmut Pitters, Martin M\\\"ohle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-13T13:43:46Z","title":"Absorption time and tree length of the Kingman coalescent and the Gumbel distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03983","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a4598a6b6587df0ff9e28d85d5e179659214d7ad29b94f3ce29a3460292f2e9e","target":"record","created_at":"2026-05-18T02:27:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b6cb413bd26fbc25ac23d7f0dd6a13fd7e4a1b219a09d1782d8fdbc6e3267bb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-13T13:43:46Z","title_canon_sha256":"500fdd38b70dbe5b7e37567d03915208ba6e49ad8ed399f259ddf53d9fc17372"},"schema_version":"1.0","source":{"id":"1502.03983","kind":"arxiv","version":1}},"canonical_sha256":"86a6614c08ed62b557a17c993ba1a0b62399af7fa39b9876a27712f5a9a7a219","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86a6614c08ed62b557a17c993ba1a0b62399af7fa39b9876a27712f5a9a7a219","first_computed_at":"2026-05-18T02:27:06.787706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:06.787706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"elAInt/7KGy5mNBmzNC8/nmds+xkCqs5tcpMiqcBUlIzq17wSZuTwQvraJFjCY/9ou491ojSS6DDubhiFCp9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:06.788561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4598a6b6587df0ff9e28d85d5e179659214d7ad29b94f3ce29a3460292f2e9e","sha256:81d461cb3df4db89340a74ad9e1762d6f40ef4f1c6bbe0ce4dabefbc8b07b5c8"],"state_sha256":"550f819dbbf2bbb8480cb47e3560875ad10b07974a91b65f9af35198d8ad1c6a"}