{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:KI6G3J22V7DG3WL63SICXQDBVE","short_pith_number":"pith:KI6G3J22","canonical_record":{"source":{"id":"0803.4112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-03-28T13:32:37Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7916047542a6107ffdaeee98aa37a2e4e471c12308a8b5df54f4a82bc1c6875b","abstract_canon_sha256":"3af3d6790a67c74ebfff9e6a0e5c2eb7923c900716589cb91e3c5ff7911f427e"},"schema_version":"1.0"},"canonical_sha256":"523c6da75aafc66dd97edc902bc061a90c407f12fe53c842d560b555b4f4632c","source":{"kind":"arxiv","id":"0803.4112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.4112","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"0803.4112v1","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.4112","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"KI6G3J22V7DG","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"pith_short_16","alias_value":"KI6G3J22V7DG3WL6","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"pith_short_8","alias_value":"KI6G3J22","created_at":"2026-07-04T15:34:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:KI6G3J22V7DG3WL63SICXQDBVE","target":"record","payload":{"canonical_record":{"source":{"id":"0803.4112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-03-28T13:32:37Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7916047542a6107ffdaeee98aa37a2e4e471c12308a8b5df54f4a82bc1c6875b","abstract_canon_sha256":"3af3d6790a67c74ebfff9e6a0e5c2eb7923c900716589cb91e3c5ff7911f427e"},"schema_version":"1.0"},"canonical_sha256":"523c6da75aafc66dd97edc902bc061a90c407f12fe53c842d560b555b4f4632c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:34:39.140426Z","signature_b64":"R/rp4KZjiban5ekXQPPDWMLhvIWwzFd+HQgT2jHgxk8vMnmmKwDbfZJPTGGmB34VQRcvkZqbd1v4lMzCcqbSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"523c6da75aafc66dd97edc902bc061a90c407f12fe53c842d560b555b4f4632c","last_reissued_at":"2026-07-04T15:34:39.140049Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:34:39.140049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0803.4112","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:34:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ic1koyzlHh7P//y6F4gd2kEl+/hTvzmc6D5YIGA6HZpb4mXuE/4nxZ23DWH/ZcM1ZxOJXKz2VY9j/yyd4cJbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:49:03.491808Z"},"content_sha256":"574a0fa528b07d99ca53687627cfd5367077b82e8c1fa182e9b04ad138d631b3","schema_version":"1.0","event_id":"sha256:574a0fa528b07d99ca53687627cfd5367077b82e8c1fa182e9b04ad138d631b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:KI6G3J22V7DG3WL63SICXQDBVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimation of the covariance matrix of random effects in longitudinal studies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Howell Tong, Wenyang Zhang, Yan Sun","submitted_at":"2008-03-28T13:32:37Z","abstract_excerpt":"Longitudinal studies are often conducted to explore the cohort and age effects in many scientific areas. The within cluster correlation structure plays a very important role in longitudinal data analysis. This is because not only can an estimator be improved by incorporating the within cluster correlation structure into the estimation procedure, but also the within cluster correlation structure can sometimes provide valuable insights in practical problems. For example, it can reveal the correlation strengths among the impacts of various factors. Motivated by data typified by a set from Banglad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.4112","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0803.4112/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:34:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fg9KkcjtZWsYCEm1+oCFcUZYPxFcM8tTZZs5xGyT9ILNrL4H5oBl1yfu2YES7cpX0pvHh6xh1HOUz/zHEIkMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:49:03.492428Z"},"content_sha256":"a117d92517259bb7a053a8dfacb984bac501efc29d0f5fec22b5599f373122bf","schema_version":"1.0","event_id":"sha256:a117d92517259bb7a053a8dfacb984bac501efc29d0f5fec22b5599f373122bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KI6G3J22V7DG3WL63SICXQDBVE/bundle.json","state_url":"https://pith.science/pith/KI6G3J22V7DG3WL63SICXQDBVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KI6G3J22V7DG3WL63SICXQDBVE/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":"2026-08-03T14:49:03Z","links":{"resolver":"https://pith.science/pith/KI6G3J22V7DG3WL63SICXQDBVE","bundle":"https://pith.science/pith/KI6G3J22V7DG3WL63SICXQDBVE/bundle.json","state":"https://pith.science/pith/KI6G3J22V7DG3WL63SICXQDBVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KI6G3J22V7DG3WL63SICXQDBVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:KI6G3J22V7DG3WL63SICXQDBVE","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":"3af3d6790a67c74ebfff9e6a0e5c2eb7923c900716589cb91e3c5ff7911f427e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-03-28T13:32:37Z","title_canon_sha256":"7916047542a6107ffdaeee98aa37a2e4e471c12308a8b5df54f4a82bc1c6875b"},"schema_version":"1.0","source":{"id":"0803.4112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.4112","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"0803.4112v1","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.4112","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"KI6G3J22V7DG","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"pith_short_16","alias_value":"KI6G3J22V7DG3WL6","created_at":"2026-07-04T15:34:39Z"},{"alias_kind":"pith_short_8","alias_value":"KI6G3J22","created_at":"2026-07-04T15:34:39Z"}],"graph_snapshots":[{"event_id":"sha256:a117d92517259bb7a053a8dfacb984bac501efc29d0f5fec22b5599f373122bf","target":"graph","created_at":"2026-07-04T15:34:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0803.4112/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Longitudinal studies are often conducted to explore the cohort and age effects in many scientific areas. The within cluster correlation structure plays a very important role in longitudinal data analysis. This is because not only can an estimator be improved by incorporating the within cluster correlation structure into the estimation procedure, but also the within cluster correlation structure can sometimes provide valuable insights in practical problems. For example, it can reveal the correlation strengths among the impacts of various factors. Motivated by data typified by a set from Banglad","authors_text":"Howell Tong, Wenyang Zhang, Yan Sun","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-03-28T13:32:37Z","title":"Estimation of the covariance matrix of random effects in longitudinal studies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.4112","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":"sha256:574a0fa528b07d99ca53687627cfd5367077b82e8c1fa182e9b04ad138d631b3","target":"record","created_at":"2026-07-04T15:34:39Z","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":"3af3d6790a67c74ebfff9e6a0e5c2eb7923c900716589cb91e3c5ff7911f427e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-03-28T13:32:37Z","title_canon_sha256":"7916047542a6107ffdaeee98aa37a2e4e471c12308a8b5df54f4a82bc1c6875b"},"schema_version":"1.0","source":{"id":"0803.4112","kind":"arxiv","version":1}},"canonical_sha256":"523c6da75aafc66dd97edc902bc061a90c407f12fe53c842d560b555b4f4632c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"523c6da75aafc66dd97edc902bc061a90c407f12fe53c842d560b555b4f4632c","first_computed_at":"2026-07-04T15:34:39.140049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:34:39.140049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R/rp4KZjiban5ekXQPPDWMLhvIWwzFd+HQgT2jHgxk8vMnmmKwDbfZJPTGGmB34VQRcvkZqbd1v4lMzCcqbSCg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:34:39.140426Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.4112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:574a0fa528b07d99ca53687627cfd5367077b82e8c1fa182e9b04ad138d631b3","sha256:a117d92517259bb7a053a8dfacb984bac501efc29d0f5fec22b5599f373122bf"],"state_sha256":"b6221055e537f77190e0f41f043db9118e72f1617496b41ce6da8956c7609b45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a4aSXPLTETqCwirgQiKUXmcI1aIn9FNZ3WyW7U3FXAchnhkVQxgHAm6cjZDx5dNlHInU5CubaQl8bck5EUyKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T14:49:03.497034Z","bundle_sha256":"ecedeb8f793576c1784b001baeeb2219fa2ea83cee635c34bfafadc25e0559c4"}}