{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TSY5CBOJQPURC53YT5A2DN43ZW","short_pith_number":"pith:TSY5CBOJ","schema_version":"1.0","canonical_sha256":"9cb1d105c983e91177789f41a1b79bcd9f941d40e311c7473bf2431d37ade3cd","source":{"kind":"arxiv","id":"1807.07561","version":1},"attestation_state":"computed","paper":{"title":"Nested Covariance Determinants and Restricted Trek Separation in Gaussian Graphical Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Elina Robeva, Luca Weihs, Mathias Drton","submitted_at":"2018-07-19T17:59:10Z","abstract_excerpt":"Directed graphical models specify noisy functional relationships among a collection of random variables. In the Gaussian case, each such model corresponds to a semi-algebraic set of positive definite covariance matrices. The set is given via parametrization, and much work has gone into obtaining an implicit description in terms of polynomial (in-)equalities. Implicit descriptions shed light on problems such as parameter identification, model equivalence, and constraint-based statistical inference. For models given by directed acyclic graphs, which represent settings where all relevant variable"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.07561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-19T17:59:10Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c067f8d1e944808a624fba58a311f3cb5418b7f603ce9cc782c0b3014e69f2f2","abstract_canon_sha256":"45a16226bcf90ca900db469ef63655ebc5597cf28087f25999e5cbd7579206ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:19.893469Z","signature_b64":"PO6ZQKfJ29wg4P/0IiJAQ2Dsl9ybZ3ywAFPY+YFC0dqtof2EYe1k68lf3OqVjmk/7bdsGP+5muZexBHn6qi9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cb1d105c983e91177789f41a1b79bcd9f941d40e311c7473bf2431d37ade3cd","last_reissued_at":"2026-05-18T00:10:19.892932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:19.892932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nested Covariance Determinants and Restricted Trek Separation in Gaussian Graphical Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Elina Robeva, Luca Weihs, Mathias Drton","submitted_at":"2018-07-19T17:59:10Z","abstract_excerpt":"Directed graphical models specify noisy functional relationships among a collection of random variables. In the Gaussian case, each such model corresponds to a semi-algebraic set of positive definite covariance matrices. The set is given via parametrization, and much work has gone into obtaining an implicit description in terms of polynomial (in-)equalities. Implicit descriptions shed light on problems such as parameter identification, model equivalence, and constraint-based statistical inference. For models given by directed acyclic graphs, which represent settings where all relevant variable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07561","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.07561","created_at":"2026-05-18T00:10:19.893007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.07561v1","created_at":"2026-05-18T00:10:19.893007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07561","created_at":"2026-05-18T00:10:19.893007+00:00"},{"alias_kind":"pith_short_12","alias_value":"TSY5CBOJQPUR","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"TSY5CBOJQPURC53Y","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"TSY5CBOJ","created_at":"2026-05-18T12:32:56.356000+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.09537","citing_title":"Algebraic Statistics in Practice: Applications to Networks","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW","json":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW.json","graph_json":"https://pith.science/api/pith-number/TSY5CBOJQPURC53YT5A2DN43ZW/graph.json","events_json":"https://pith.science/api/pith-number/TSY5CBOJQPURC53YT5A2DN43ZW/events.json","paper":"https://pith.science/paper/TSY5CBOJ"},"agent_actions":{"view_html":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW","download_json":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW.json","view_paper":"https://pith.science/paper/TSY5CBOJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.07561&json=true","fetch_graph":"https://pith.science/api/pith-number/TSY5CBOJQPURC53YT5A2DN43ZW/graph.json","fetch_events":"https://pith.science/api/pith-number/TSY5CBOJQPURC53YT5A2DN43ZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW/action/storage_attestation","attest_author":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW/action/author_attestation","sign_citation":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW/action/citation_signature","submit_replication":"https://pith.science/pith/TSY5CBOJQPURC53YT5A2DN43ZW/action/replication_record"}},"created_at":"2026-05-18T00:10:19.893007+00:00","updated_at":"2026-05-18T00:10:19.893007+00:00"}