{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OTC45XL5BIX2QU6RGOPICANU4T","short_pith_number":"pith:OTC45XL5","schema_version":"1.0","canonical_sha256":"74c5cedd7d0a2fa853d1339e8101b4e4f2354b6bb15967f44c43dc0549e9a04c","source":{"kind":"arxiv","id":"1809.00882","version":1},"attestation_state":"computed","paper":{"title":"An elementary proof of de Finetti's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Werner Kirsch","submitted_at":"2018-09-04T10:41:48Z","abstract_excerpt":"A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finetti's theorem characterizes all $\\{0,1\\}$-valued exchangeable sequences as a \"mixture\" of sequences of independent random variables. We present an new, elementary proof of de Finetti's Theorem. The purpose of this paper is to make this theorem accessible to a broader community through an essentially self-contained proof."},"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":"1809.00882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-04T10:41:48Z","cross_cats_sorted":[],"title_canon_sha256":"02d6f989fb68d8f568229943e5b783058819caab1fd7e8ca62e24e6e75207a70","abstract_canon_sha256":"a62b067385b3767de008623bed4494c35f90096cfd7e957976123612c5cedd87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:32.249060Z","signature_b64":"0v+ycsWGw9oG7Cyy9PJFABkVEcUNrCSIa9JvsC6L5AoRbPqlOx0Aw7hm2bISWlzB3MDl5I9sNRubr8nq8ls/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74c5cedd7d0a2fa853d1339e8101b4e4f2354b6bb15967f44c43dc0549e9a04c","last_reissued_at":"2026-05-18T00:06:32.248601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:32.248601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An elementary proof of de Finetti's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Werner Kirsch","submitted_at":"2018-09-04T10:41:48Z","abstract_excerpt":"A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finetti's theorem characterizes all $\\{0,1\\}$-valued exchangeable sequences as a \"mixture\" of sequences of independent random variables. We present an new, elementary proof of de Finetti's Theorem. The purpose of this paper is to make this theorem accessible to a broader community through an essentially self-contained proof."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00882","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":"1809.00882","created_at":"2026-05-18T00:06:32.248672+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.00882v1","created_at":"2026-05-18T00:06:32.248672+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00882","created_at":"2026-05-18T00:06:32.248672+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTC45XL5BIX2","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTC45XL5BIX2QU6R","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTC45XL5","created_at":"2026-05-18T12:32:43.782077+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/OTC45XL5BIX2QU6RGOPICANU4T","json":"https://pith.science/pith/OTC45XL5BIX2QU6RGOPICANU4T.json","graph_json":"https://pith.science/api/pith-number/OTC45XL5BIX2QU6RGOPICANU4T/graph.json","events_json":"https://pith.science/api/pith-number/OTC45XL5BIX2QU6RGOPICANU4T/events.json","paper":"https://pith.science/paper/OTC45XL5"},"agent_actions":{"view_html":"https://pith.science/pith/OTC45XL5BIX2QU6RGOPICANU4T","download_json":"https://pith.science/pith/OTC45XL5BIX2QU6RGOPICANU4T.json","view_paper":"https://pith.science/paper/OTC45XL5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.00882&json=true","fetch_graph":"https://pith.science/api/pith-number/OTC45XL5BIX2QU6RGOPICANU4T/graph.json","fetch_events":"https://pith.science/api/pith-number/OTC45XL5BIX2QU6RGOPICANU4T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTC45XL5BIX2QU6RGOPICANU4T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTC45XL5BIX2QU6RGOPICANU4T/action/storage_attestation","attest_author":"https://pith.science/pith/OTC45XL5BIX2QU6RGOPICANU4T/action/author_attestation","sign_citation":"https://pith.science/pith/OTC45XL5BIX2QU6RGOPICANU4T/action/citation_signature","submit_replication":"https://pith.science/pith/OTC45XL5BIX2QU6RGOPICANU4T/action/replication_record"}},"created_at":"2026-05-18T00:06:32.248672+00:00","updated_at":"2026-05-18T00:06:32.248672+00:00"}