{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:UZMR6KYR46HJPO7F5PD6U66FT5","short_pith_number":"pith:UZMR6KYR","canonical_record":{"source":{"id":"2303.05561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-09T19:58:13Z","cross_cats_sorted":["cs.LG","q-bio.NC","stat.ME"],"title_canon_sha256":"a512566d6d26cdb5a6cb87ccfaffeade22b7194b7348b662f85c6265049c39c3","abstract_canon_sha256":"e19667f6ff324ce9ef5dfdbe6c6d4cdbb855eb2ab4016dfdfa3e5c9dc318b7fc"},"schema_version":"1.0"},"canonical_sha256":"a6591f2b11e78e97bbe5ebc7ea7bc59f4cdb34aca9f66543fde109b81182e7b7","source":{"kind":"arxiv","id":"2303.05561","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.05561","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"2303.05561v2","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.05561","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"UZMR6KYR46HJ","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"pith_short_16","alias_value":"UZMR6KYR46HJPO7F","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"pith_short_8","alias_value":"UZMR6KYR","created_at":"2026-07-05T08:07:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:UZMR6KYR46HJPO7F5PD6U66FT5","target":"record","payload":{"canonical_record":{"source":{"id":"2303.05561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-09T19:58:13Z","cross_cats_sorted":["cs.LG","q-bio.NC","stat.ME"],"title_canon_sha256":"a512566d6d26cdb5a6cb87ccfaffeade22b7194b7348b662f85c6265049c39c3","abstract_canon_sha256":"e19667f6ff324ce9ef5dfdbe6c6d4cdbb855eb2ab4016dfdfa3e5c9dc318b7fc"},"schema_version":"1.0"},"canonical_sha256":"a6591f2b11e78e97bbe5ebc7ea7bc59f4cdb34aca9f66543fde109b81182e7b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:07:55.776955Z","signature_b64":"TPTBb09OYxsFD7+f8p6QkE7O0Z4rO1I3oXK/Lty9EolIhcNYgDcXXOaskfiPtjHCUXFfAYrET7shw31gGOCBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6591f2b11e78e97bbe5ebc7ea7bc59f4cdb34aca9f66543fde109b81182e7b7","last_reissued_at":"2026-07-05T08:07:55.776425Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:07:55.776425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.05561","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tAiCk5KdkLy9xz9cSezMmvILm5zzSRWCfNEiliBeHAsZi5RnJdTyYQ7r7RyrWFCmwHE2D1+e5AEgoMX8fDu0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:22:47.943923Z"},"content_sha256":"3fbb231f8a08b42af94da2aa0dbff0353cfabce5e33ad0f8f55368deb6ff79ff","schema_version":"1.0","event_id":"sha256:3fbb231f8a08b42af94da2aa0dbff0353cfabce5e33ad0f8f55368deb6ff79ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:UZMR6KYR46HJPO7F5PD6U66FT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploration of the search space of Gaussian graphical models for paired data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","q-bio.NC","stat.ME"],"primary_cat":"stat.ML","authors_text":"Alberto Roverato, Dung Ngoc Nguyen","submitted_at":"2023-03-09T19:58:13Z","abstract_excerpt":"We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for the paired data problem. Commonly, graphical models are ordered by the submodel relationship so that the search space is a lattice, called the model inclusion lattice. We introduce a novel order between models, named the twin order. We show that, embedded with this order, the model space is a lattice that, unlike the model inclusion lattice, is distributive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.05561","kind":"arxiv","version":2},"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/2303.05561/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":"2026-07-05T08:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6Tghp1p4x8HKotZR9qgxW0DGmTEQyqCAI2EOVvi0Znac2kmy42A9oEhOu5gKljzsMjcnz4J807dmo2ABKctCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:22:47.944315Z"},"content_sha256":"0ebcc8113fb48a489a3d08e5986c5b78484260b1954860bf1e655c4d55aaf68e","schema_version":"1.0","event_id":"sha256:0ebcc8113fb48a489a3d08e5986c5b78484260b1954860bf1e655c4d55aaf68e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZMR6KYR46HJPO7F5PD6U66FT5/bundle.json","state_url":"https://pith.science/pith/UZMR6KYR46HJPO7F5PD6U66FT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZMR6KYR46HJPO7F5PD6U66FT5/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":"2026-08-04T05:22:47Z","links":{"resolver":"https://pith.science/pith/UZMR6KYR46HJPO7F5PD6U66FT5","bundle":"https://pith.science/pith/UZMR6KYR46HJPO7F5PD6U66FT5/bundle.json","state":"https://pith.science/pith/UZMR6KYR46HJPO7F5PD6U66FT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZMR6KYR46HJPO7F5PD6U66FT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:UZMR6KYR46HJPO7F5PD6U66FT5","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":"e19667f6ff324ce9ef5dfdbe6c6d4cdbb855eb2ab4016dfdfa3e5c9dc318b7fc","cross_cats_sorted":["cs.LG","q-bio.NC","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-09T19:58:13Z","title_canon_sha256":"a512566d6d26cdb5a6cb87ccfaffeade22b7194b7348b662f85c6265049c39c3"},"schema_version":"1.0","source":{"id":"2303.05561","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.05561","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"2303.05561v2","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.05561","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"UZMR6KYR46HJ","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"pith_short_16","alias_value":"UZMR6KYR46HJPO7F","created_at":"2026-07-05T08:07:55Z"},{"alias_kind":"pith_short_8","alias_value":"UZMR6KYR","created_at":"2026-07-05T08:07:55Z"}],"graph_snapshots":[{"event_id":"sha256:0ebcc8113fb48a489a3d08e5986c5b78484260b1954860bf1e655c4d55aaf68e","target":"graph","created_at":"2026-07-05T08:07:55Z","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/2303.05561/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for the paired data problem. Commonly, graphical models are ordered by the submodel relationship so that the search space is a lattice, called the model inclusion lattice. We introduce a novel order between models, named the twin order. We show that, embedded with this order, the model space is a lattice that, unlike the model inclusion lattice, is distributive.","authors_text":"Alberto Roverato, Dung Ngoc Nguyen","cross_cats":["cs.LG","q-bio.NC","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-09T19:58:13Z","title":"Exploration of the search space of Gaussian graphical models for paired data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.05561","kind":"arxiv","version":2},"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":"sha256:3fbb231f8a08b42af94da2aa0dbff0353cfabce5e33ad0f8f55368deb6ff79ff","target":"record","created_at":"2026-07-05T08:07:55Z","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":"e19667f6ff324ce9ef5dfdbe6c6d4cdbb855eb2ab4016dfdfa3e5c9dc318b7fc","cross_cats_sorted":["cs.LG","q-bio.NC","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-03-09T19:58:13Z","title_canon_sha256":"a512566d6d26cdb5a6cb87ccfaffeade22b7194b7348b662f85c6265049c39c3"},"schema_version":"1.0","source":{"id":"2303.05561","kind":"arxiv","version":2}},"canonical_sha256":"a6591f2b11e78e97bbe5ebc7ea7bc59f4cdb34aca9f66543fde109b81182e7b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6591f2b11e78e97bbe5ebc7ea7bc59f4cdb34aca9f66543fde109b81182e7b7","first_computed_at":"2026-07-05T08:07:55.776425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:07:55.776425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPTBb09OYxsFD7+f8p6QkE7O0Z4rO1I3oXK/Lty9EolIhcNYgDcXXOaskfiPtjHCUXFfAYrET7shw31gGOCBAA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:07:55.776955Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.05561","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fbb231f8a08b42af94da2aa0dbff0353cfabce5e33ad0f8f55368deb6ff79ff","sha256:0ebcc8113fb48a489a3d08e5986c5b78484260b1954860bf1e655c4d55aaf68e"],"state_sha256":"e8c531877c79733d977dda88057888fe4988a2a8c31ac9b136513bab64abff4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t3q/SOR1BaLTpxwL5sy91Oc09qCUzNb4IxxXB5Saf/dneWKGq7Kvs4/nIV+Zs3CfWsEzcIVRf3WXanxRF3JHAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:22:47.947475Z","bundle_sha256":"f099579d61d84edf3ad17f98dcaefaad74e912cdfee231962d89655f755bbfa1"}}