{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ASV7NZ63DUWNE5Z7PNONKMY6F2","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":"b9336713fa96690353484f1e0f4d1cbcf71eccd3e4be6d33a1742be49a341694","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-28T19:58:18Z","title_canon_sha256":"10194366099ffa274f9b1af1f860c6b770c132ad7cb89cace5e86ea18843b004"},"schema_version":"1.0","source":{"id":"1206.6812","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6812","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6812v1","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6812","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"ASV7NZ63DUWN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ASV7NZ63DUWNE5Z7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ASV7NZ63","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:2851ed14620bce8e60ce2fbd4e044f36c93b94c7a70d01fbbfb0623a0d8427d2","target":"graph","created_at":"2026-05-18T03:52:15Z","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":"We obtain some approximation results for the weights appearing in the exchangeable partition probability function identifying Gibbs partition models of parameter $\\alpha \\in (0,1)$, as introduced in Gnedin and Pitman (2006). We rely on approximation results for central and non-central generalized Stirling numbers and on known results for conditional and unconditional $\\alpha$ diversity. We provide an application to an approximate Bayesian nonparametric estimation of discovery probability in species sampling problems under normalized inverse Gaussian priors.","authors_text":"Annalisa Cerquetti","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-28T19:58:18Z","title":"Stirling's approximations for exchangeable Gibbs weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6812","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:be5eb46068c47bfd76e9c18a080c8a25bbe776a513fdff5f1807495a1f3aa08a","target":"record","created_at":"2026-05-18T03:52:15Z","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":"b9336713fa96690353484f1e0f4d1cbcf71eccd3e4be6d33a1742be49a341694","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-28T19:58:18Z","title_canon_sha256":"10194366099ffa274f9b1af1f860c6b770c132ad7cb89cace5e86ea18843b004"},"schema_version":"1.0","source":{"id":"1206.6812","kind":"arxiv","version":1}},"canonical_sha256":"04abf6e7db1d2cd2773f7b5cd5331e2eb9a369daf1048944b9a9608075c56c6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04abf6e7db1d2cd2773f7b5cd5331e2eb9a369daf1048944b9a9608075c56c6d","first_computed_at":"2026-05-18T03:52:15.953041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:15.953041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r2CTUxzBqS7GciiUXCDVFicI1Uj4FTFQqQti9tMpviSGKOkI/GFE4BkCMxOhmjuPb2Qyu+jgL+yPgLQA+dTAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:15.953740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6812","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5eb46068c47bfd76e9c18a080c8a25bbe776a513fdff5f1807495a1f3aa08a","sha256:2851ed14620bce8e60ce2fbd4e044f36c93b94c7a70d01fbbfb0623a0d8427d2"],"state_sha256":"808a75a4c0b3b26d057498732c169be6130309e1e5fa7bd29f4e9408b77ab084"}