{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:S3RWSJ6BB6KE3C2BTFVZIIBCNY","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":"96d11e8bfe38abdec3c99f5d56ff07fa792b37720447ff1e4f7d4606f3a600c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-11T01:44:02Z","title_canon_sha256":"aead3a549aa2102a8b4afe796c7cb3eff6846f572111309cb6cc8815e1f18044"},"schema_version":"1.0","source":{"id":"0905.1524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.1524","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"arxiv_version","alias_value":"0905.1524v1","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.1524","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"pith_short_12","alias_value":"S3RWSJ6BB6KE","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"S3RWSJ6BB6KE3C2B","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"S3RWSJ6B","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:00766cdf52d2d40f6ad679dc61305c750f6410c2021c5cbd7cfc33965f4f3f4e","target":"graph","created_at":"2026-05-18T04:42:03Z","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 present a detailed proof of the Dovbysh-Sudakov representation for symmetric positive definite weakly exchangeable infinite random arrays, called Gram-de Finetti matrices, which is based on the representation result of Aldous and Hoover for arbitrary (not necessarily positive definite) symmetric weakly exchangeable arrays.","authors_text":"Dmitry Panchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-11T01:44:02Z","title":"On the Dovbysh-Sudakov representation result"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1524","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:aaf8f2e7f5e0afe103146a85ee64d562fd78bbf8d670fa5d928b628e2c8c1394","target":"record","created_at":"2026-05-18T04:42:03Z","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":"96d11e8bfe38abdec3c99f5d56ff07fa792b37720447ff1e4f7d4606f3a600c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-11T01:44:02Z","title_canon_sha256":"aead3a549aa2102a8b4afe796c7cb3eff6846f572111309cb6cc8815e1f18044"},"schema_version":"1.0","source":{"id":"0905.1524","kind":"arxiv","version":1}},"canonical_sha256":"96e36927c10f944d8b41996b9420226e29bc81fad711fcd30075a872005f54f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96e36927c10f944d8b41996b9420226e29bc81fad711fcd30075a872005f54f6","first_computed_at":"2026-05-18T04:42:03.462794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:03.462794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"45JjAHWZW1LnMGMblgQj1oelv9/vSxVX2moLEZ4pgg0gvskqkcV+UHYEBzeQmq0vQHazc07pKik76tEoyrw9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:03.463247Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.1524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaf8f2e7f5e0afe103146a85ee64d562fd78bbf8d670fa5d928b628e2c8c1394","sha256:00766cdf52d2d40f6ad679dc61305c750f6410c2021c5cbd7cfc33965f4f3f4e"],"state_sha256":"2e2cb89bb9fea88b2bdceb0f65a1063521f33957d9e7bb609134711cacd624bf"}