{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BWE24O4SOLX7RP4AVM3RA7SEGM","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":"5d9180e680c1243e3bca4a340f9f37b0dc2cfaec39eefa91d6ce0840464a77d2","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-04T19:51:57Z","title_canon_sha256":"49a3a5cf58dbe50336355a6faf803c8bfb711f0875673e36ee8fb60dfd2e14d2"},"schema_version":"1.0","source":{"id":"1408.0788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.0788","created_at":"2026-05-18T02:45:56Z"},{"alias_kind":"arxiv_version","alias_value":"1408.0788v1","created_at":"2026-05-18T02:45:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0788","created_at":"2026-05-18T02:45:56Z"},{"alias_kind":"pith_short_12","alias_value":"BWE24O4SOLX7","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BWE24O4SOLX7RP4A","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BWE24O4S","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:1a582516b76550ca76aaeb2730c6dfd33f9c4699fcb076c60d388cec10013969","target":"graph","created_at":"2026-05-18T02:45:56Z","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":"In recent years, a variety of useful extensions of the Wishart have been proposed in the literature for the purposes of studying Markov random fields/graphical models. In particular, generalizations of the Wishart, referred to as Type I and Type II Wishart distributions, have been introduced by Letac and Massam (\\emph{Annals of Statistics} 2006) and play important roles in both frequentist and Bayesian inference for Gaussian graphical models. These distributions have been especially useful in high-dimensional settings due to the flexibility offered by their multiple shape parameters. The domai","authors_text":"Bala Rajaratnam, Emanuel Ben-David","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-04T19:51:57Z","title":"The Letac-Massam conjecture and existence of high dimensional Bayes estimators for Graphical Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0788","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:e3f4b5d9bf781439a1af95c562db54069f507e22c19bdc68639e58ca44a1fdb7","target":"record","created_at":"2026-05-18T02:45:56Z","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":"5d9180e680c1243e3bca4a340f9f37b0dc2cfaec39eefa91d6ce0840464a77d2","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-04T19:51:57Z","title_canon_sha256":"49a3a5cf58dbe50336355a6faf803c8bfb711f0875673e36ee8fb60dfd2e14d2"},"schema_version":"1.0","source":{"id":"1408.0788","kind":"arxiv","version":1}},"canonical_sha256":"0d89ae3b9272eff8bf80ab37107e443321eb9fed994e94b78a2ebfd511e71dd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d89ae3b9272eff8bf80ab37107e443321eb9fed994e94b78a2ebfd511e71dd7","first_computed_at":"2026-05-18T02:45:56.233123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:56.233123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O+WdYeU4frmgIQB1iQz2+Tq0voEggxCU8k/RReehPNcNgwC8qVlbqDPeMk+Lq7pLtcd1TdEhJTp8kLTuZCrCDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:56.233645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.0788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3f4b5d9bf781439a1af95c562db54069f507e22c19bdc68639e58ca44a1fdb7","sha256:1a582516b76550ca76aaeb2730c6dfd33f9c4699fcb076c60d388cec10013969"],"state_sha256":"8c1898200eff4e057a3375179213373deea97287a80645985b72c98891a2f7d0"}