{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KPTEBNUIOXMXROI5UMNBO6KLE6","short_pith_number":"pith:KPTEBNUI","canonical_record":{"source":{"id":"1610.03328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T13:36:49Z","cross_cats_sorted":[],"title_canon_sha256":"c1b944a1c97fa4d26317f48d55bb119c6b15e266c84bc00ae6a7883b8e022258","abstract_canon_sha256":"fc017abcbf7787be2c3f695a3dca510093b87aae036928e074ca2f943fb7f458"},"schema_version":"1.0"},"canonical_sha256":"53e640b68875d978b91da31a17794b27a2425a7375abcde3b232df44ddda8817","source":{"kind":"arxiv","id":"1610.03328","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03328","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03328v1","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03328","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"pith_short_12","alias_value":"KPTEBNUIOXMX","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KPTEBNUIOXMXROI5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KPTEBNUI","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KPTEBNUIOXMXROI5UMNBO6KLE6","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T13:36:49Z","cross_cats_sorted":[],"title_canon_sha256":"c1b944a1c97fa4d26317f48d55bb119c6b15e266c84bc00ae6a7883b8e022258","abstract_canon_sha256":"fc017abcbf7787be2c3f695a3dca510093b87aae036928e074ca2f943fb7f458"},"schema_version":"1.0"},"canonical_sha256":"53e640b68875d978b91da31a17794b27a2425a7375abcde3b232df44ddda8817","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:31.776130Z","signature_b64":"1BER2eZaLg2PltkXrSQ7eKxdnI2PnBoDHjwf5OCIkCbBA82hntpPyfJU+AsoY0LtkTCQcVKaMowoJQIUQDrgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53e640b68875d978b91da31a17794b27a2425a7375abcde3b232df44ddda8817","last_reissued_at":"2026-05-18T01:02:31.775496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:31.775496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03328","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HOTQlgAodzKpb4RNBkW9cn7KAfMccSSunk4jHCW+AoC0qlcB5++8BYOcmDm+mRkKYA30z+63KIPHWfmVTHN7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:26:23.392764Z"},"content_sha256":"1a254395f3e0a05e0d2e575eb142e85b4c4d98c7c152386dbf9d1493a106ae0a","schema_version":"1.0","event_id":"sha256:1a254395f3e0a05e0d2e575eb142e85b4c4d98c7c152386dbf9d1493a106ae0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KPTEBNUIOXMXROI5UMNBO6KLE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moderate deviations for Ewens-Pitman exchangeable random partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fuqing Gao, Shui Feng, Stefano Favaro","submitted_at":"2016-10-11T13:36:49Z","abstract_excerpt":"Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of different types and the number of types appearing in the sample with a fixed frequency are important statistics. In this paper we establish the moderate deviation principles for these quantities. The corresponding rate functions are explicitly identified, which help revealing a critical scale and understanding the exact role of the parameters. Conditional, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03328","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQuayCPffldldP7r5cv7iLWsQp5rFXuOmt73lQK7UN5IWK9fKbuVp/hWxzU7wjfdTcIl+x1QB/jZngzmV8BqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:26:23.393413Z"},"content_sha256":"74675b30285c356fb1d6662fc42fabb7bc6190f041e08299ca25791532f64345","schema_version":"1.0","event_id":"sha256:74675b30285c356fb1d6662fc42fabb7bc6190f041e08299ca25791532f64345"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KPTEBNUIOXMXROI5UMNBO6KLE6/bundle.json","state_url":"https://pith.science/pith/KPTEBNUIOXMXROI5UMNBO6KLE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KPTEBNUIOXMXROI5UMNBO6KLE6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T19:26:23Z","links":{"resolver":"https://pith.science/pith/KPTEBNUIOXMXROI5UMNBO6KLE6","bundle":"https://pith.science/pith/KPTEBNUIOXMXROI5UMNBO6KLE6/bundle.json","state":"https://pith.science/pith/KPTEBNUIOXMXROI5UMNBO6KLE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KPTEBNUIOXMXROI5UMNBO6KLE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KPTEBNUIOXMXROI5UMNBO6KLE6","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":"fc017abcbf7787be2c3f695a3dca510093b87aae036928e074ca2f943fb7f458","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T13:36:49Z","title_canon_sha256":"c1b944a1c97fa4d26317f48d55bb119c6b15e266c84bc00ae6a7883b8e022258"},"schema_version":"1.0","source":{"id":"1610.03328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03328","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03328v1","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03328","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"pith_short_12","alias_value":"KPTEBNUIOXMX","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KPTEBNUIOXMXROI5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KPTEBNUI","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:74675b30285c356fb1d6662fc42fabb7bc6190f041e08299ca25791532f64345","target":"graph","created_at":"2026-05-18T01:02:31Z","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":"Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of different types and the number of types appearing in the sample with a fixed frequency are important statistics. In this paper we establish the moderate deviation principles for these quantities. The corresponding rate functions are explicitly identified, which help revealing a critical scale and understanding the exact role of the parameters. Conditional, ","authors_text":"Fuqing Gao, Shui Feng, Stefano Favaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T13:36:49Z","title":"Moderate deviations for Ewens-Pitman exchangeable random partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03328","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":"sha256:1a254395f3e0a05e0d2e575eb142e85b4c4d98c7c152386dbf9d1493a106ae0a","target":"record","created_at":"2026-05-18T01:02:31Z","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":"fc017abcbf7787be2c3f695a3dca510093b87aae036928e074ca2f943fb7f458","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-11T13:36:49Z","title_canon_sha256":"c1b944a1c97fa4d26317f48d55bb119c6b15e266c84bc00ae6a7883b8e022258"},"schema_version":"1.0","source":{"id":"1610.03328","kind":"arxiv","version":1}},"canonical_sha256":"53e640b68875d978b91da31a17794b27a2425a7375abcde3b232df44ddda8817","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53e640b68875d978b91da31a17794b27a2425a7375abcde3b232df44ddda8817","first_computed_at":"2026-05-18T01:02:31.775496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:31.775496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1BER2eZaLg2PltkXrSQ7eKxdnI2PnBoDHjwf5OCIkCbBA82hntpPyfJU+AsoY0LtkTCQcVKaMowoJQIUQDrgAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:31.776130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a254395f3e0a05e0d2e575eb142e85b4c4d98c7c152386dbf9d1493a106ae0a","sha256:74675b30285c356fb1d6662fc42fabb7bc6190f041e08299ca25791532f64345"],"state_sha256":"f603c52b9f2938ec4e4fa012406d4b726b79faebbb51d2bc4c743985065d4f33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PntWtfMDAWmSjqLPfO2HhAgp+zxvb3nFvQvcdfBR0RmADn0C+8Gq0nM7L+snLzaROvlmCD9LW5tz940XVpbuBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:26:23.396964Z","bundle_sha256":"27269aadfde2b7000130f353dfbf4a117a9e2b6207d7c7abe15942406478494f"}}