{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:FLCQVNGRKK26ALGKHSIS6HH6M7","short_pith_number":"pith:FLCQVNGR","schema_version":"1.0","canonical_sha256":"2ac50ab4d152b5e02cca3c912f1cfe67c8cc3d10d30552c0a9c43d33e1bb97c5","source":{"kind":"arxiv","id":"2106.07523","version":1},"attestation_state":"computed","paper":{"title":"Dependency in DAG models with Hidden Variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Robin J. Evans","submitted_at":"2021-06-14T15:47:07Z","abstract_excerpt":"Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for two variables to be identically equal, while all other observed variables stay jointly independent of them and mutually of each other. We find that this is possible if and only if the two variables are `densely connected'; in other words, if applications of identifiable causal interventions on the graph cannot (non-trivially) separate them. As a consequence"},"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":"2106.07523","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2021-06-14T15:47:07Z","cross_cats_sorted":["stat.CO","stat.TH"],"title_canon_sha256":"7f593eab216415c7378f038254356a615fc84333c7d8d6a003467f40a4754f92","abstract_canon_sha256":"4ae8299889497d05732285ce324e408a1edc77355a5758e6f9a301a6d59476a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:49:05.886519Z","signature_b64":"VqjHuFkala33PjzxYHcQGzdvuEYYGcRNNlQESjp5jmy5xCyULlFVAf5zrqeaxGuAf2nVYTnM0RaEyxzv6HxsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ac50ab4d152b5e02cca3c912f1cfe67c8cc3d10d30552c0a9c43d33e1bb97c5","last_reissued_at":"2026-07-05T02:49:05.886036Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:49:05.886036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dependency in DAG models with Hidden Variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Robin J. Evans","submitted_at":"2021-06-14T15:47:07Z","abstract_excerpt":"Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for two variables to be identically equal, while all other observed variables stay jointly independent of them and mutually of each other. We find that this is possible if and only if the two variables are `densely connected'; in other words, if applications of identifiable causal interventions on the graph cannot (non-trivially) separate them. As a consequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.07523","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/2106.07523/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2106.07523","created_at":"2026-07-05T02:49:05.886094+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.07523v1","created_at":"2026-07-05T02:49:05.886094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.07523","created_at":"2026-07-05T02:49:05.886094+00:00"},{"alias_kind":"pith_short_12","alias_value":"FLCQVNGRKK26","created_at":"2026-07-05T02:49:05.886094+00:00"},{"alias_kind":"pith_short_16","alias_value":"FLCQVNGRKK26ALGK","created_at":"2026-07-05T02:49:05.886094+00:00"},{"alias_kind":"pith_short_8","alias_value":"FLCQVNGR","created_at":"2026-07-05T02:49:05.886094+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.07891","citing_title":"The Observational Partial Order of Causal Structures with Latent Variables","ref_index":36,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7","json":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7.json","graph_json":"https://pith.science/api/pith-number/FLCQVNGRKK26ALGKHSIS6HH6M7/graph.json","events_json":"https://pith.science/api/pith-number/FLCQVNGRKK26ALGKHSIS6HH6M7/events.json","paper":"https://pith.science/paper/FLCQVNGR"},"agent_actions":{"view_html":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7","download_json":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7.json","view_paper":"https://pith.science/paper/FLCQVNGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.07523&json=true","fetch_graph":"https://pith.science/api/pith-number/FLCQVNGRKK26ALGKHSIS6HH6M7/graph.json","fetch_events":"https://pith.science/api/pith-number/FLCQVNGRKK26ALGKHSIS6HH6M7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7/action/storage_attestation","attest_author":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7/action/author_attestation","sign_citation":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7/action/citation_signature","submit_replication":"https://pith.science/pith/FLCQVNGRKK26ALGKHSIS6HH6M7/action/replication_record"}},"created_at":"2026-07-05T02:49:05.886094+00:00","updated_at":"2026-07-05T02:49:05.886094+00:00"}