{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LVAHBD7DJE3SIEBT2KXWAD7E4I","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":"3c4b4e2a69d6b36afcf2e38876e1bf3adc3248e2f76c2a89a6a020f7197e5275","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-01-19T15:42:33Z","title_canon_sha256":"f027feade06d77d48a3edb69b31bb505b6e4ab0b1c812639eb7b029e29d99d09"},"schema_version":"1.0","source":{"id":"1101.3709","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3709","created_at":"2026-05-18T03:50:25Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3709v3","created_at":"2026-05-18T03:50:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3709","created_at":"2026-05-18T03:50:25Z"},{"alias_kind":"pith_short_12","alias_value":"LVAHBD7DJE3S","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LVAHBD7DJE3SIEBT","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LVAHBD7D","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:9b7dc09745a490894d84528e18b9d3dc4260099ade9e31fc375d1886b3bd7c26","target":"graph","created_at":"2026-05-18T03:50:25Z","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 study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose corresponding means are restricted to being identical. We find a necessary and sufficient condition on the partition to ensure equality between the maximum likelihood and least-squares estimators of the mean.","authors_text":"Helene Gehrmann, Steffen L. Lauritzen","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-01-19T15:42:33Z","title":"Estimation of means in graphical Gaussian models with symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3709","kind":"arxiv","version":3},"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":"sha256:091e9c5e098ff32e3e2302651f20f9a50eb43e396609a233eee7726465b3d36d","target":"record","created_at":"2026-05-18T03:50:25Z","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":"3c4b4e2a69d6b36afcf2e38876e1bf3adc3248e2f76c2a89a6a020f7197e5275","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-01-19T15:42:33Z","title_canon_sha256":"f027feade06d77d48a3edb69b31bb505b6e4ab0b1c812639eb7b029e29d99d09"},"schema_version":"1.0","source":{"id":"1101.3709","kind":"arxiv","version":3}},"canonical_sha256":"5d40708fe34937241033d2af600fe4e2047b3da51fd193f4d971601e53bf42be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d40708fe34937241033d2af600fe4e2047b3da51fd193f4d971601e53bf42be","first_computed_at":"2026-05-18T03:50:25.944897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:25.944897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j2izeZz2i7dyeuZC72trgR/wB8+QHWkdBpiq9d3kIMO6AazfHV6LUGkcvT6nwq7kuC0T8PCtR4kIi8hKka03Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:25.945694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3709","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:091e9c5e098ff32e3e2302651f20f9a50eb43e396609a233eee7726465b3d36d","sha256:9b7dc09745a490894d84528e18b9d3dc4260099ade9e31fc375d1886b3bd7c26"],"state_sha256":"4856c31681ab9f1de3ff0d3b6c8925868d441bb394a2eae634f677fec5e5ae68"}