{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:L64JE2NU4F4HFHM4AMGNHPEVFV","short_pith_number":"pith:L64JE2NU","canonical_record":{"source":{"id":"1008.2420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-14T08:39:44Z","cross_cats_sorted":[],"title_canon_sha256":"9ef52a7449487330b6d0f2758a1383b2d7c223c4e5733a253e03dc8cd87e13a3","abstract_canon_sha256":"20c375748b300fd125cb202753a74337e5316dd050a424fd251934ee956b199f"},"schema_version":"1.0"},"canonical_sha256":"5fb89269b4e178729d9c030cd3bc952d7aa6756a394f1b186ae8d244501967ed","source":{"kind":"arxiv","id":"1008.2420","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2420","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2420v1","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2420","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"L64JE2NU4F4H","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"L64JE2NU4F4HFHM4","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"L64JE2NU","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:L64JE2NU4F4HFHM4AMGNHPEVFV","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-14T08:39:44Z","cross_cats_sorted":[],"title_canon_sha256":"9ef52a7449487330b6d0f2758a1383b2d7c223c4e5733a253e03dc8cd87e13a3","abstract_canon_sha256":"20c375748b300fd125cb202753a74337e5316dd050a424fd251934ee956b199f"},"schema_version":"1.0"},"canonical_sha256":"5fb89269b4e178729d9c030cd3bc952d7aa6756a394f1b186ae8d244501967ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:13.355863Z","signature_b64":"HTejg869KNwSgb22vh4+eeoIkDDY/ZP2ifTzLBm/cQ2qpZFeaViF2xFmU/2Cjb2T2gcpEWCg72NhtQ4OnwPDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fb89269b4e178729d9c030cd3bc952d7aa6756a394f1b186ae8d244501967ed","last_reissued_at":"2026-05-18T04:42:13.355348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:13.355348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2420","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":"2026-05-18T04:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2kZpPsmnPXkO5zX6KAQm+7qlcrGFPclk+v1WgliyoksOLIrP1nr3yz8sOmtTfS6rEsuI019mG2bS/WSUAJXPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:37:43.401970Z"},"content_sha256":"ff8f048a2bfe1edda9ae145770b56c7aed0a77a68b5a6b9aa7173a2d7cf091b4","schema_version":"1.0","event_id":"sha256:ff8f048a2bfe1edda9ae145770b56c7aed0a77a68b5a6b9aa7173a2d7cf091b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:L64JE2NU4F4HFHM4AMGNHPEVFV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coag-Frag duality for a class of stable Poisson-Kingman mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lancelot F. James","submitted_at":"2010-08-14T08:39:44Z","abstract_excerpt":"Exchangeable sequences of random probability measures (partitions of mass) and their corresponding exchangeable bridges play an important role in a variety of areas in probability, statistics and related areas, including Bayesian statistics, physics, finance and machine learning. An area of theoretical as well as practical interest, is the study of coagulation and fragmentation operators on partitions of mass. In this regard, an interesting but formidable question is the identification of operators and distributional families on mass partitions that exhibit interesting duality relations. In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2420","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":"2026-05-18T04:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qvgOm/c+BW7FI186AiXcmkM9rIcavYr6zeNwIPAZZ68pcsSMmm2pHNhttD9+GTjwFPS/z8X9VjeJ3mnN6YOEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:37:43.402734Z"},"content_sha256":"cd49d50032d96ad09c7d7e27c1eaf56b25d703bb8f0f00606de2575ef18c604f","schema_version":"1.0","event_id":"sha256:cd49d50032d96ad09c7d7e27c1eaf56b25d703bb8f0f00606de2575ef18c604f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L64JE2NU4F4HFHM4AMGNHPEVFV/bundle.json","state_url":"https://pith.science/pith/L64JE2NU4F4HFHM4AMGNHPEVFV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L64JE2NU4F4HFHM4AMGNHPEVFV/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":"2026-06-09T07:37:43Z","links":{"resolver":"https://pith.science/pith/L64JE2NU4F4HFHM4AMGNHPEVFV","bundle":"https://pith.science/pith/L64JE2NU4F4HFHM4AMGNHPEVFV/bundle.json","state":"https://pith.science/pith/L64JE2NU4F4HFHM4AMGNHPEVFV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L64JE2NU4F4HFHM4AMGNHPEVFV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:L64JE2NU4F4HFHM4AMGNHPEVFV","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":"20c375748b300fd125cb202753a74337e5316dd050a424fd251934ee956b199f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-14T08:39:44Z","title_canon_sha256":"9ef52a7449487330b6d0f2758a1383b2d7c223c4e5733a253e03dc8cd87e13a3"},"schema_version":"1.0","source":{"id":"1008.2420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2420","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2420v1","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2420","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"L64JE2NU4F4H","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"L64JE2NU4F4HFHM4","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"L64JE2NU","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:cd49d50032d96ad09c7d7e27c1eaf56b25d703bb8f0f00606de2575ef18c604f","target":"graph","created_at":"2026-05-18T04:42:13Z","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":"Exchangeable sequences of random probability measures (partitions of mass) and their corresponding exchangeable bridges play an important role in a variety of areas in probability, statistics and related areas, including Bayesian statistics, physics, finance and machine learning. An area of theoretical as well as practical interest, is the study of coagulation and fragmentation operators on partitions of mass. In this regard, an interesting but formidable question is the identification of operators and distributional families on mass partitions that exhibit interesting duality relations. In th","authors_text":"Lancelot F. James","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-14T08:39:44Z","title":"Coag-Frag duality for a class of stable Poisson-Kingman mixtures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2420","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:ff8f048a2bfe1edda9ae145770b56c7aed0a77a68b5a6b9aa7173a2d7cf091b4","target":"record","created_at":"2026-05-18T04:42:13Z","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":"20c375748b300fd125cb202753a74337e5316dd050a424fd251934ee956b199f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-14T08:39:44Z","title_canon_sha256":"9ef52a7449487330b6d0f2758a1383b2d7c223c4e5733a253e03dc8cd87e13a3"},"schema_version":"1.0","source":{"id":"1008.2420","kind":"arxiv","version":1}},"canonical_sha256":"5fb89269b4e178729d9c030cd3bc952d7aa6756a394f1b186ae8d244501967ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fb89269b4e178729d9c030cd3bc952d7aa6756a394f1b186ae8d244501967ed","first_computed_at":"2026-05-18T04:42:13.355348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:13.355348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HTejg869KNwSgb22vh4+eeoIkDDY/ZP2ifTzLBm/cQ2qpZFeaViF2xFmU/2Cjb2T2gcpEWCg72NhtQ4OnwPDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:13.355863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff8f048a2bfe1edda9ae145770b56c7aed0a77a68b5a6b9aa7173a2d7cf091b4","sha256:cd49d50032d96ad09c7d7e27c1eaf56b25d703bb8f0f00606de2575ef18c604f"],"state_sha256":"ab65a68eaf7b80d86f202e816218832841230e47977e18d317d7e8d6db681f54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OJ2ROcPCmHuQbOD+6Uo/ywVO3p/TOe6ktUDb4iVGQoxrsqwZAQb8vfdYJ6LoX9S7xCEOtdf1ZXt/Svy4RHQzCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:37:43.406894Z","bundle_sha256":"91a43a46ab1a1bdad0fa83037569e4f5e0d2f07f57413d090f50006d0a956199"}}