{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DGUNZI33XKKRIFX4MJ2GGIBFFH","short_pith_number":"pith:DGUNZI33","canonical_record":{"source":{"id":"1509.04781","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2015-09-16T01:07:24Z","cross_cats_sorted":[],"title_canon_sha256":"ed995da977bde1699f057df74e0fbae470b5f15a77fde5eb8c34ee78737433db","abstract_canon_sha256":"e2b078e3f57ec912d8813bd4da44d78a70235e46a907ece35db3ed01ffac59d4"},"schema_version":"1.0"},"canonical_sha256":"19a8dca37bba951416fc627463202529dbbc3951b1511427013a1791f3d0d18f","source":{"kind":"arxiv","id":"1509.04781","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04781","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04781v1","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04781","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"DGUNZI33XKKR","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DGUNZI33XKKRIFX4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DGUNZI33","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DGUNZI33XKKRIFX4MJ2GGIBFFH","target":"record","payload":{"canonical_record":{"source":{"id":"1509.04781","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2015-09-16T01:07:24Z","cross_cats_sorted":[],"title_canon_sha256":"ed995da977bde1699f057df74e0fbae470b5f15a77fde5eb8c34ee78737433db","abstract_canon_sha256":"e2b078e3f57ec912d8813bd4da44d78a70235e46a907ece35db3ed01ffac59d4"},"schema_version":"1.0"},"canonical_sha256":"19a8dca37bba951416fc627463202529dbbc3951b1511427013a1791f3d0d18f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:51.719936Z","signature_b64":"ynsMFB8ODNMn1ewwS4pi+9ekXtKjX7vPd7CEotpJmY8/3Ll3s43ODuJi50DwWZBJaGIKTQv+Q9rDQI9AJtsECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19a8dca37bba951416fc627463202529dbbc3951b1511427013a1791f3d0d18f","last_reissued_at":"2026-05-18T01:32:51.719356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:51.719356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.04781","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":"2026-05-18T01:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ruex+QULPcNCcIZgAsZXbU8Lf+4B2S9wqPgq5o/TU0uNSJdVqakhuSZi4PisZG2E4DZsOKpHkyesOdTX3ZJtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:16:15.968623Z"},"content_sha256":"cdfe838f222460fd395b1b10758b740460e10ff9b1ab62c418bddd1ede9bcb97","schema_version":"1.0","event_id":"sha256:cdfe838f222460fd395b1b10758b740460e10ff9b1ab62c418bddd1ede9bcb97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DGUNZI33XKKRIFX4MJ2GGIBFFH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirichlet Fragmentation Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Hong Ge, Yarin Gal, Zoubin Ghahramani","submitted_at":"2015-09-16T01:07:24Z","abstract_excerpt":"Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese restaurant process (nCRP). Then we define a general class of probability distributions over trees: the Dirichlet fragmentation process (DFP) through a novel combination of the theory of Dirichlet processes and random fragmentation processes. This DFP presents a stick-breaking constru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04781","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":"2026-05-18T01:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KJx9jFJ+FQykINV6M690yyOrFXXNjtJLZTfAoeFXquO77P266yHwidmaBwkmyanySJgm/JOVeh7W/M7gQdenCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:16:15.969267Z"},"content_sha256":"e844ddc7972b1a1cf78623059915fa73ca01d629c854b984c45731019c5f3f31","schema_version":"1.0","event_id":"sha256:e844ddc7972b1a1cf78623059915fa73ca01d629c854b984c45731019c5f3f31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGUNZI33XKKRIFX4MJ2GGIBFFH/bundle.json","state_url":"https://pith.science/pith/DGUNZI33XKKRIFX4MJ2GGIBFFH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGUNZI33XKKRIFX4MJ2GGIBFFH/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":"2026-06-07T16:16:15Z","links":{"resolver":"https://pith.science/pith/DGUNZI33XKKRIFX4MJ2GGIBFFH","bundle":"https://pith.science/pith/DGUNZI33XKKRIFX4MJ2GGIBFFH/bundle.json","state":"https://pith.science/pith/DGUNZI33XKKRIFX4MJ2GGIBFFH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGUNZI33XKKRIFX4MJ2GGIBFFH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DGUNZI33XKKRIFX4MJ2GGIBFFH","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":"e2b078e3f57ec912d8813bd4da44d78a70235e46a907ece35db3ed01ffac59d4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2015-09-16T01:07:24Z","title_canon_sha256":"ed995da977bde1699f057df74e0fbae470b5f15a77fde5eb8c34ee78737433db"},"schema_version":"1.0","source":{"id":"1509.04781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04781","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04781v1","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04781","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"DGUNZI33XKKR","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DGUNZI33XKKRIFX4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DGUNZI33","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:e844ddc7972b1a1cf78623059915fa73ca01d629c854b984c45731019c5f3f31","target":"graph","created_at":"2026-05-18T01:32:51Z","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":"Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese restaurant process (nCRP). Then we define a general class of probability distributions over trees: the Dirichlet fragmentation process (DFP) through a novel combination of the theory of Dirichlet processes and random fragmentation processes. This DFP presents a stick-breaking constru","authors_text":"Hong Ge, Yarin Gal, Zoubin Ghahramani","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2015-09-16T01:07:24Z","title":"Dirichlet Fragmentation Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04781","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:cdfe838f222460fd395b1b10758b740460e10ff9b1ab62c418bddd1ede9bcb97","target":"record","created_at":"2026-05-18T01:32:51Z","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":"e2b078e3f57ec912d8813bd4da44d78a70235e46a907ece35db3ed01ffac59d4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2015-09-16T01:07:24Z","title_canon_sha256":"ed995da977bde1699f057df74e0fbae470b5f15a77fde5eb8c34ee78737433db"},"schema_version":"1.0","source":{"id":"1509.04781","kind":"arxiv","version":1}},"canonical_sha256":"19a8dca37bba951416fc627463202529dbbc3951b1511427013a1791f3d0d18f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19a8dca37bba951416fc627463202529dbbc3951b1511427013a1791f3d0d18f","first_computed_at":"2026-05-18T01:32:51.719356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:51.719356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ynsMFB8ODNMn1ewwS4pi+9ekXtKjX7vPd7CEotpJmY8/3Ll3s43ODuJi50DwWZBJaGIKTQv+Q9rDQI9AJtsECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:51.719936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdfe838f222460fd395b1b10758b740460e10ff9b1ab62c418bddd1ede9bcb97","sha256:e844ddc7972b1a1cf78623059915fa73ca01d629c854b984c45731019c5f3f31"],"state_sha256":"60c72406758d1d9228bdeb07714b5515b712cf2d330dcbcd2a9b191dc4ef6957"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OCT6RZcj3VeEz9nEJNF+DpDYAnZ4U16hExE62uA8A04oEqX0c3rBfEJCJS9dMDEYS4dPGGYBN/lESaoksyG6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:16:15.972703Z","bundle_sha256":"a795888f02f4a810c2fdbd2b9de63c544f5f74f466bfa5df297b5cadc4631859"}}