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We show that for each fixed $m$ the distribution of $\\Pi_{n,m}$ converges to the distribution of the restriction to $[m]$ of the exchangeable random partition of $\\mathbb{N}$ with the same ranked frequencies as $\\Pi_\\infty$. As a consequence, the partially exchangeable random partition $\\Pi_\\infty$ is exchangeable if and only if $\\Pi_\\i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.00313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-02T16:19:52Z","cross_cats_sorted":[],"title_canon_sha256":"498bfbe3e23b600e12e2049f8f8381208aad5fb9e2e143bfc99fee9954c81bc7","abstract_canon_sha256":"b087df436ec41825db80d0249fc2896ccd85f4f45e5c9099a205fd3065eaaf31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:03.767014Z","signature_b64":"MzaUxehhaXIsAqoJUub2Q/Xuh1GmQZrFC2SBp51v3dWK4DJtd6CL1jPj+ovmvL2gYtWXX12J0Qh6Icc1hi0xDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d4440241d9cf310e8436dc8b5c0bc240ebdc1546be16fc69b6e8bc61725a00a","last_reissued_at":"2026-05-18T00:41:03.766355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:03.766355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An ergodic theorem for partially exchangeable random partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jim Pitman, Yuri Yakubovich","submitted_at":"2017-07-02T16:19:52Z","abstract_excerpt":"We consider shifts $\\Pi_{n,m}$ of a partially exchangeable random partition $\\Pi_\\infty$ of $\\mathbb{N}$ obtained by restricting $\\Pi_\\infty$ to $\\{n+1,n+2,\\dots, n+m\\}$ and then subtracting $n$ from each element to get a partition of $[m]:= \\{1, \\ldots, m \\}$. We show that for each fixed $m$ the distribution of $\\Pi_{n,m}$ converges to the distribution of the restriction to $[m]$ of the exchangeable random partition of $\\mathbb{N}$ with the same ranked frequencies as $\\Pi_\\infty$. As a consequence, the partially exchangeable random partition $\\Pi_\\infty$ is exchangeable if and only if $\\Pi_\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00313","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.00313","created_at":"2026-05-18T00:41:03.766458+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.00313v1","created_at":"2026-05-18T00:41:03.766458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00313","created_at":"2026-05-18T00:41:03.766458+00:00"},{"alias_kind":"pith_short_12","alias_value":"PVCEAJA5TTZR","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PVCEAJA5TTZRB2CD","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PVCEAJA5","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ","json":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ.json","graph_json":"https://pith.science/api/pith-number/PVCEAJA5TTZRB2CDNXELLQF4EQ/graph.json","events_json":"https://pith.science/api/pith-number/PVCEAJA5TTZRB2CDNXELLQF4EQ/events.json","paper":"https://pith.science/paper/PVCEAJA5"},"agent_actions":{"view_html":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ","download_json":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ.json","view_paper":"https://pith.science/paper/PVCEAJA5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.00313&json=true","fetch_graph":"https://pith.science/api/pith-number/PVCEAJA5TTZRB2CDNXELLQF4EQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PVCEAJA5TTZRB2CDNXELLQF4EQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ/action/storage_attestation","attest_author":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ/action/author_attestation","sign_citation":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ/action/citation_signature","submit_replication":"https://pith.science/pith/PVCEAJA5TTZRB2CDNXELLQF4EQ/action/replication_record"}},"created_at":"2026-05-18T00:41:03.766458+00:00","updated_at":"2026-05-18T00:41:03.766458+00:00"}