{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:SHY6GB5S6YZBMJO4DAPGWL6AUQ","short_pith_number":"pith:SHY6GB5S","canonical_record":{"source":{"id":"2004.05542","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-04-12T04:10:14Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"54e0904df07c881faaa2774863d786b055c3c7a5323e94f3e3d1baf1745b6c5d","abstract_canon_sha256":"b1dbd208daaec95da99cbf31e5746ded215bb16aae48f715108dce25a671794b"},"schema_version":"1.0"},"canonical_sha256":"91f1e307b2f6321625dc181e6b2fc0a42ee6c4249dc71455f35aed744ed081a6","source":{"kind":"arxiv","id":"2004.05542","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.05542","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"arxiv_version","alias_value":"2004.05542v3","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.05542","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"pith_short_12","alias_value":"SHY6GB5S6YZB","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"pith_short_16","alias_value":"SHY6GB5S6YZBMJO4","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"pith_short_8","alias_value":"SHY6GB5S","created_at":"2026-07-05T03:17:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:SHY6GB5S6YZBMJO4DAPGWL6AUQ","target":"record","payload":{"canonical_record":{"source":{"id":"2004.05542","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-04-12T04:10:14Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"54e0904df07c881faaa2774863d786b055c3c7a5323e94f3e3d1baf1745b6c5d","abstract_canon_sha256":"b1dbd208daaec95da99cbf31e5746ded215bb16aae48f715108dce25a671794b"},"schema_version":"1.0"},"canonical_sha256":"91f1e307b2f6321625dc181e6b2fc0a42ee6c4249dc71455f35aed744ed081a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:17:00.161684Z","signature_b64":"DgMNj7d26M+3t05jSne+MpVXXQiqQApMI0dHD9FMvzSR+AWYMUwgVZ95fqwSDVVaWpmC6Db4N+SGgnWRPmCeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91f1e307b2f6321625dc181e6b2fc0a42ee6c4249dc71455f35aed744ed081a6","last_reissued_at":"2026-07-05T03:17:00.161229Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:17:00.161229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.05542","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:17:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DZfHOCwWMF4U0phKfFF/SmcUBRP1+Tiy7LWgQRn7rvSVojARuVnQAXqwmOv/PazXrEgM1mMQ4oE4+6NH7bevBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:08.370932Z"},"content_sha256":"71e2ea92ee6f2a2c2f5b13750a67ac69d4a8238de7b8da51e1e8287a8332e0f3","schema_version":"1.0","event_id":"sha256:71e2ea92ee6f2a2c2f5b13750a67ac69d4a8238de7b8da51e1e8287a8332e0f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:SHY6GB5S6YZBMJO4DAPGWL6AUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of de Finetti's mixing measure in latent structure models for observed exchangeable sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"XuanLong Nguyen, Yun Wei","submitted_at":"2020-04-12T04:10:14Z","abstract_excerpt":"Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty about the latent parameters representing heterogeneity. In this paper posterior contraction theorems for de Finetti's mixing measure arising from finite mixtures of product distributions will be established, under the setting the number of exchangeable sequences of observed variables increases while sequence length(s) may be either fixed or varied. The role of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.05542","kind":"arxiv","version":3},"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/2004.05542/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:17:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SIkgAA7a2jQ5pKCVJnMqG04q7EU8cGD4RITnI2hIX8djIDL3hOCfYb/vgaK14G3V2SliNJ10zSXOFNGLb7i1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:08.371437Z"},"content_sha256":"79b21eb102c96c927cdc33ffa4b29d7db15b36fb618eb39d3e138f3a23594ac6","schema_version":"1.0","event_id":"sha256:79b21eb102c96c927cdc33ffa4b29d7db15b36fb618eb39d3e138f3a23594ac6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SHY6GB5S6YZBMJO4DAPGWL6AUQ/bundle.json","state_url":"https://pith.science/pith/SHY6GB5S6YZBMJO4DAPGWL6AUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SHY6GB5S6YZBMJO4DAPGWL6AUQ/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":"2026-08-22T11:07:08Z","links":{"resolver":"https://pith.science/pith/SHY6GB5S6YZBMJO4DAPGWL6AUQ","bundle":"https://pith.science/pith/SHY6GB5S6YZBMJO4DAPGWL6AUQ/bundle.json","state":"https://pith.science/pith/SHY6GB5S6YZBMJO4DAPGWL6AUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SHY6GB5S6YZBMJO4DAPGWL6AUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:SHY6GB5S6YZBMJO4DAPGWL6AUQ","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":"b1dbd208daaec95da99cbf31e5746ded215bb16aae48f715108dce25a671794b","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-04-12T04:10:14Z","title_canon_sha256":"54e0904df07c881faaa2774863d786b055c3c7a5323e94f3e3d1baf1745b6c5d"},"schema_version":"1.0","source":{"id":"2004.05542","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.05542","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"arxiv_version","alias_value":"2004.05542v3","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.05542","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"pith_short_12","alias_value":"SHY6GB5S6YZB","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"pith_short_16","alias_value":"SHY6GB5S6YZBMJO4","created_at":"2026-07-05T03:17:00Z"},{"alias_kind":"pith_short_8","alias_value":"SHY6GB5S","created_at":"2026-07-05T03:17:00Z"}],"graph_snapshots":[{"event_id":"sha256:79b21eb102c96c927cdc33ffa4b29d7db15b36fb618eb39d3e138f3a23594ac6","target":"graph","created_at":"2026-07-05T03:17:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.05542/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty about the latent parameters representing heterogeneity. In this paper posterior contraction theorems for de Finetti's mixing measure arising from finite mixtures of product distributions will be established, under the setting the number of exchangeable sequences of observed variables increases while sequence length(s) may be either fixed or varied. The role of","authors_text":"XuanLong Nguyen, Yun Wei","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-04-12T04:10:14Z","title":"Convergence of de Finetti's mixing measure in latent structure models for observed exchangeable sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.05542","kind":"arxiv","version":3},"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":"sha256:71e2ea92ee6f2a2c2f5b13750a67ac69d4a8238de7b8da51e1e8287a8332e0f3","target":"record","created_at":"2026-07-05T03:17:00Z","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":"b1dbd208daaec95da99cbf31e5746ded215bb16aae48f715108dce25a671794b","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-04-12T04:10:14Z","title_canon_sha256":"54e0904df07c881faaa2774863d786b055c3c7a5323e94f3e3d1baf1745b6c5d"},"schema_version":"1.0","source":{"id":"2004.05542","kind":"arxiv","version":3}},"canonical_sha256":"91f1e307b2f6321625dc181e6b2fc0a42ee6c4249dc71455f35aed744ed081a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91f1e307b2f6321625dc181e6b2fc0a42ee6c4249dc71455f35aed744ed081a6","first_computed_at":"2026-07-05T03:17:00.161229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:17:00.161229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DgMNj7d26M+3t05jSne+MpVXXQiqQApMI0dHD9FMvzSR+AWYMUwgVZ95fqwSDVVaWpmC6Db4N+SGgnWRPmCeBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:17:00.161684Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.05542","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71e2ea92ee6f2a2c2f5b13750a67ac69d4a8238de7b8da51e1e8287a8332e0f3","sha256:79b21eb102c96c927cdc33ffa4b29d7db15b36fb618eb39d3e138f3a23594ac6"],"state_sha256":"be178a049238ebea516a7c55443d768a7fbc266fd4e9cc90e43922f04c03d3c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"66sWZ1ISl1wDP5iOTmrLFtgCOwxm3VsoYaOqYS6LqiTwiZlFJSWe0bRIn6rqdS3m7jfvuQKHABcYPaRds1R4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T11:07:08.376153Z","bundle_sha256":"9405250c4e86718a360328b01428a817ba0381192b33e3f990c83051f77b7544"}}