{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:62WJTIFXNXLVEOUAS26R5W363U","short_pith_number":"pith:62WJTIFX","canonical_record":{"source":{"id":"1504.00828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-04-03T12:17:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f42e08933637d58c10762f90dd5d107be3dd2eceee47c2e9cd689d83b1700b66","abstract_canon_sha256":"eec9b523c55865e825b72fc92d3d2971838f284007812aae4ce477581b60b9b6"},"schema_version":"1.0"},"canonical_sha256":"f6ac99a0b76dd7523a8096bd1edb7edd19ac59a431643c4460d94d59aeef9b6b","source":{"kind":"arxiv","id":"1504.00828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00828","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00828v1","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00828","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"62WJTIFXNXLV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"62WJTIFXNXLVEOUA","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"62WJTIFX","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:62WJTIFXNXLVEOUAS26R5W363U","target":"record","payload":{"canonical_record":{"source":{"id":"1504.00828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-04-03T12:17:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f42e08933637d58c10762f90dd5d107be3dd2eceee47c2e9cd689d83b1700b66","abstract_canon_sha256":"eec9b523c55865e825b72fc92d3d2971838f284007812aae4ce477581b60b9b6"},"schema_version":"1.0"},"canonical_sha256":"f6ac99a0b76dd7523a8096bd1edb7edd19ac59a431643c4460d94d59aeef9b6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:36.956951Z","signature_b64":"bDbf35vCe4PxQdZuXV+iHcDv/oZVgh6ZkYRwScflhl1u/9bSDor5vfkWfKjF/Rnz7yATsM7OoHX3A3r17QwEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6ac99a0b76dd7523a8096bd1edb7edd19ac59a431643c4460d94d59aeef9b6b","last_reissued_at":"2026-05-18T02:19:36.956444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:36.956444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.00828","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":"2026-05-18T02:19:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QpBf9xhU4FwHxHtjGowZj51zwBL09JV4hVxPxaMiYkq+/CGF6JV+iLVKYTPyCKLeKhzQI0RgiAsnpNbdjgb0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:43:48.937239Z"},"content_sha256":"b1fd31875bae1b82ec5bf7b4f2142d026f20d2fb960e4b415cb9f5a06227c38a","schema_version":"1.0","event_id":"sha256:b1fd31875bae1b82ec5bf7b4f2142d026f20d2fb960e4b415cb9f5a06227c38a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:62WJTIFXNXLVEOUAS26R5W363U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Looking-backward probabilities for Gibbs-type exchangeable random partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Lorenzo Trippa, Sergio Bacallado, Stefano Favaro","submitted_at":"2015-04-03T12:17:06Z","abstract_excerpt":"Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems that are typically referred to as species sampling problems. In this paper, we consider the class of looking-backward species sampling problems introduced in Lijoi et al. (Ann. Appl. Probab. 18 (2008) 1519-1547) in Bayesian nonparametrics. Specifically, given some information on the random partition induced by an initial sample from a Gibbs-type random probabil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00828","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":"2026-05-18T02:19:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1R8V/dutEZqLKFyScwDQm6abyqW9T4mTFk/8f271tdqBeBDMAjO3t5yyp5ZbCAf9PJLsLrwp01IxoRiP+89DCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:43:48.937886Z"},"content_sha256":"17a6d8cccf800ee5328d01f05ad45b6e6ae837f433974815d57493debabf784e","schema_version":"1.0","event_id":"sha256:17a6d8cccf800ee5328d01f05ad45b6e6ae837f433974815d57493debabf784e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62WJTIFXNXLVEOUAS26R5W363U/bundle.json","state_url":"https://pith.science/pith/62WJTIFXNXLVEOUAS26R5W363U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62WJTIFXNXLVEOUAS26R5W363U/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":"2026-06-12T05:43:48Z","links":{"resolver":"https://pith.science/pith/62WJTIFXNXLVEOUAS26R5W363U","bundle":"https://pith.science/pith/62WJTIFXNXLVEOUAS26R5W363U/bundle.json","state":"https://pith.science/pith/62WJTIFXNXLVEOUAS26R5W363U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62WJTIFXNXLVEOUAS26R5W363U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:62WJTIFXNXLVEOUAS26R5W363U","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":"eec9b523c55865e825b72fc92d3d2971838f284007812aae4ce477581b60b9b6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-04-03T12:17:06Z","title_canon_sha256":"f42e08933637d58c10762f90dd5d107be3dd2eceee47c2e9cd689d83b1700b66"},"schema_version":"1.0","source":{"id":"1504.00828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00828","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00828v1","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00828","created_at":"2026-05-18T02:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"62WJTIFXNXLV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"62WJTIFXNXLVEOUA","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"62WJTIFX","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:17a6d8cccf800ee5328d01f05ad45b6e6ae837f433974815d57493debabf784e","target":"graph","created_at":"2026-05-18T02:19:36Z","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":"Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems that are typically referred to as species sampling problems. In this paper, we consider the class of looking-backward species sampling problems introduced in Lijoi et al. (Ann. Appl. Probab. 18 (2008) 1519-1547) in Bayesian nonparametrics. Specifically, given some information on the random partition induced by an initial sample from a Gibbs-type random probabil","authors_text":"Lorenzo Trippa, Sergio Bacallado, Stefano Favaro","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-04-03T12:17:06Z","title":"Looking-backward probabilities for Gibbs-type exchangeable random partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00828","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:b1fd31875bae1b82ec5bf7b4f2142d026f20d2fb960e4b415cb9f5a06227c38a","target":"record","created_at":"2026-05-18T02:19:36Z","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":"eec9b523c55865e825b72fc92d3d2971838f284007812aae4ce477581b60b9b6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-04-03T12:17:06Z","title_canon_sha256":"f42e08933637d58c10762f90dd5d107be3dd2eceee47c2e9cd689d83b1700b66"},"schema_version":"1.0","source":{"id":"1504.00828","kind":"arxiv","version":1}},"canonical_sha256":"f6ac99a0b76dd7523a8096bd1edb7edd19ac59a431643c4460d94d59aeef9b6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6ac99a0b76dd7523a8096bd1edb7edd19ac59a431643c4460d94d59aeef9b6b","first_computed_at":"2026-05-18T02:19:36.956444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:36.956444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bDbf35vCe4PxQdZuXV+iHcDv/oZVgh6ZkYRwScflhl1u/9bSDor5vfkWfKjF/Rnz7yATsM7OoHX3A3r17QwEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:36.956951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1fd31875bae1b82ec5bf7b4f2142d026f20d2fb960e4b415cb9f5a06227c38a","sha256:17a6d8cccf800ee5328d01f05ad45b6e6ae837f433974815d57493debabf784e"],"state_sha256":"7470bffe95a9360d186980ab077ce867e3c0180871db891255b57c62a58e15d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u7h8/sdFyi4SQ3xG56hyEm/eHUOC7vhqs9L+rikHUKfrkw6gzU5+jcnRaoa6GnslW/USKKbbAduiQGSzuwg+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:43:48.941001Z","bundle_sha256":"39cbee77b8e433c704cbdae0b1d697828525ec8969ebfb580ff13bd04211de58"}}