{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AMG5I37JEXI7VMJGZG6NRTQ5HA","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":"5f6a6c203e826c2ca13d37fa2fd87a642cd8f37a32f522f273f60e1de3f2a7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T16:52:39Z","title_canon_sha256":"6989b19641bf0ef2a36964197fab9bc309a03eef424cf6623d9444c1c5958a87"},"schema_version":"1.0","source":{"id":"1301.1259","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1259","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1259v4","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1259","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"AMG5I37JEXI7","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AMG5I37JEXI7VMJG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AMG5I37J","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:85232c44aa41d595cd277545178506dbfda4576359e76bcdd64b7d8999214bc5","target":"graph","created_at":"2026-05-18T02:45:58Z","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 random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and prove that they satisfy an analogue of de Finetti's theorem. We also prove a more general result for arrays indexed by several trees, which includes a hierarchical version of the Aldous-Hoover representation.","authors_text":"Dmitry Panchenko, Tim Austin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T16:52:39Z","title":"A hierarchical version of the de Finetti and Aldous-Hoover representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1259","kind":"arxiv","version":4},"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":"sha256:1c207231da6d0834bf18ffe9da8d8c563f3a36599bda491656e719bd15cb4654","target":"record","created_at":"2026-05-18T02:45:58Z","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":"5f6a6c203e826c2ca13d37fa2fd87a642cd8f37a32f522f273f60e1de3f2a7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T16:52:39Z","title_canon_sha256":"6989b19641bf0ef2a36964197fab9bc309a03eef424cf6623d9444c1c5958a87"},"schema_version":"1.0","source":{"id":"1301.1259","kind":"arxiv","version":4}},"canonical_sha256":"030dd46fe925d1fab126c9bcd8ce1d3834500bac9e5233bd85ec21472bd281ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"030dd46fe925d1fab126c9bcd8ce1d3834500bac9e5233bd85ec21472bd281ae","first_computed_at":"2026-05-18T02:45:58.388896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:58.388896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YNxQ8D2UjvHE2WY2tIZbO9M5MSd3L/3LNQR6XzSPJCLRb0thOBIk3gqiZuy5Jrou17FvsiLJ3tw/YOx4d6sIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:58.389307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1259","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c207231da6d0834bf18ffe9da8d8c563f3a36599bda491656e719bd15cb4654","sha256:85232c44aa41d595cd277545178506dbfda4576359e76bcdd64b7d8999214bc5"],"state_sha256":"362e95f165a765382bc9c2af2a24417b3282f65d8457eb83187f19beb381b419"}