{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:ORBSPRPWBGKWJIVWMSWC2QDZT3","short_pith_number":"pith:ORBSPRPW","canonical_record":{"source":{"id":"math/0305313","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2003-05-22T14:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"b48501aebda9f53247e2ed283374d2dfbb95792d9415300a92f4823176806979","abstract_canon_sha256":"bc5bbbfae30f3420c1a2e6bfaf90666752a3a5ea1dfedae4cb50c4d305331d19"},"schema_version":"1.0"},"canonical_sha256":"744327c5f6099564a2b664ac2d40799ec0bcc42087758b9f50ba0543900b20e3","source":{"kind":"arxiv","id":"math/0305313","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305313","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305313v2","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305313","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"ORBSPRPWBGKW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ORBSPRPWBGKWJIVW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ORBSPRPW","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:ORBSPRPWBGKWJIVWMSWC2QDZT3","target":"record","payload":{"canonical_record":{"source":{"id":"math/0305313","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2003-05-22T14:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"b48501aebda9f53247e2ed283374d2dfbb95792d9415300a92f4823176806979","abstract_canon_sha256":"bc5bbbfae30f3420c1a2e6bfaf90666752a3a5ea1dfedae4cb50c4d305331d19"},"schema_version":"1.0"},"canonical_sha256":"744327c5f6099564a2b664ac2d40799ec0bcc42087758b9f50ba0543900b20e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:28.876716Z","signature_b64":"i+CDDIESPzNZjZTnVns+5KnOF/sDxdLbPwg4wP6vMzv3s5o4YEo7vdHUirD18NI3owLBbJK7EV6lICCiFAioDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"744327c5f6099564a2b664ac2d40799ec0bcc42087758b9f50ba0543900b20e3","last_reissued_at":"2026-05-18T01:05:28.876155Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:28.876155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0305313","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfk+JP814tM2/ZI1iQdY/xcnJnoAeuHVyJZR3ZRLL7naepZ3QFuZ/ca5YqicrMEbvPv//5F3dcA45i5jSos1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:44:49.150055Z"},"content_sha256":"c426bf97c04c0361f789eb822291f23f61f718c769270dada7d6ef38b4f68b34","schema_version":"1.0","event_id":"sha256:c426bf97c04c0361f789eb822291f23f61f718c769270dada7d6ef38b4f68b34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:ORBSPRPWBGKWJIVWMSWC2QDZT3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eddy Mayer-Wolf, Martin Zerner, Ofer Zeitouni, Persi Diaconis","submitted_at":"2003-05-22T14:13:51Z","abstract_excerpt":"We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirichlet law with parameter theta=1 is the unique invariant distribution for this Markov chain.\n Our proof uses a combination of probabilistic, combinatoric, and representation-theoretic arguments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305313","kind":"arxiv","version":2},"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":"2026-05-18T01:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c7wQlTjDmV1pKqjGIsrg6WuFFVIny++MJSdTu3B72kVisgBwGqVlt8wlwxCkcFnR96oBSl0QdVfJwstGG3UjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:44:49.150408Z"},"content_sha256":"c01f4a203cc38abd269056d481681ad97c3fffafddfa9feab09b039320ba509d","schema_version":"1.0","event_id":"sha256:c01f4a203cc38abd269056d481681ad97c3fffafddfa9feab09b039320ba509d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ORBSPRPWBGKWJIVWMSWC2QDZT3/bundle.json","state_url":"https://pith.science/pith/ORBSPRPWBGKWJIVWMSWC2QDZT3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ORBSPRPWBGKWJIVWMSWC2QDZT3/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":"2026-06-03T19:44:49Z","links":{"resolver":"https://pith.science/pith/ORBSPRPWBGKWJIVWMSWC2QDZT3","bundle":"https://pith.science/pith/ORBSPRPWBGKWJIVWMSWC2QDZT3/bundle.json","state":"https://pith.science/pith/ORBSPRPWBGKWJIVWMSWC2QDZT3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ORBSPRPWBGKWJIVWMSWC2QDZT3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:ORBSPRPWBGKWJIVWMSWC2QDZT3","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":"bc5bbbfae30f3420c1a2e6bfaf90666752a3a5ea1dfedae4cb50c4d305331d19","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2003-05-22T14:13:51Z","title_canon_sha256":"b48501aebda9f53247e2ed283374d2dfbb95792d9415300a92f4823176806979"},"schema_version":"1.0","source":{"id":"math/0305313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305313","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305313v2","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305313","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"ORBSPRPWBGKW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"ORBSPRPWBGKWJIVW","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"ORBSPRPW","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:c01f4a203cc38abd269056d481681ad97c3fffafddfa9feab09b039320ba509d","target":"graph","created_at":"2026-05-18T01:05:28Z","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":"We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirichlet law with parameter theta=1 is the unique invariant distribution for this Markov chain.\n Our proof uses a combination of probabilistic, combinatoric, and representation-theoretic arguments.","authors_text":"Eddy Mayer-Wolf, Martin Zerner, Ofer Zeitouni, Persi Diaconis","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2003-05-22T14:13:51Z","title":"The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305313","kind":"arxiv","version":2},"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:c426bf97c04c0361f789eb822291f23f61f718c769270dada7d6ef38b4f68b34","target":"record","created_at":"2026-05-18T01:05:28Z","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":"bc5bbbfae30f3420c1a2e6bfaf90666752a3a5ea1dfedae4cb50c4d305331d19","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2003-05-22T14:13:51Z","title_canon_sha256":"b48501aebda9f53247e2ed283374d2dfbb95792d9415300a92f4823176806979"},"schema_version":"1.0","source":{"id":"math/0305313","kind":"arxiv","version":2}},"canonical_sha256":"744327c5f6099564a2b664ac2d40799ec0bcc42087758b9f50ba0543900b20e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"744327c5f6099564a2b664ac2d40799ec0bcc42087758b9f50ba0543900b20e3","first_computed_at":"2026-05-18T01:05:28.876155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:28.876155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i+CDDIESPzNZjZTnVns+5KnOF/sDxdLbPwg4wP6vMzv3s5o4YEo7vdHUirD18NI3owLBbJK7EV6lICCiFAioDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:28.876716Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0305313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c426bf97c04c0361f789eb822291f23f61f718c769270dada7d6ef38b4f68b34","sha256:c01f4a203cc38abd269056d481681ad97c3fffafddfa9feab09b039320ba509d"],"state_sha256":"c85ca8cff974602777d8fb07364e08007ff08d7cac4fa937a97db205bab191ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZe0DkO2nseBKj1WxqdySmbWcpri6anwH1auR2aHVsahH5dE0AxDZQkCYrALLUZaLiFDrg6VxxGMMj+Xbju7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:44:49.152798Z","bundle_sha256":"9c1902a0247a1d9c0cc90d4128e614d666cfa2a5ffb26d9578115f781bc1500c"}}