{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:K2VQAICWR36FYR4U6HA2KZ32N3","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":"fa7191d3d4fb7e7a91a10b8561ec86518e622047b1e93fc1e749a8f03b09458d","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-05-31T14:22:26Z","title_canon_sha256":"d8be68f45dd3b33bad07c2c030241d6904e9074ccbde895f03f173df11422ddf"},"schema_version":"1.0","source":{"id":"2305.19884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.19884","created_at":"2026-07-05T06:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"2305.19884v1","created_at":"2026-07-05T06:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.19884","created_at":"2026-07-05T06:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"K2VQAICWR36F","created_at":"2026-07-05T06:16:04Z"},{"alias_kind":"pith_short_16","alias_value":"K2VQAICWR36FYR4U","created_at":"2026-07-05T06:16:04Z"},{"alias_kind":"pith_short_8","alias_value":"K2VQAICW","created_at":"2026-07-05T06:16:04Z"}],"graph_snapshots":[{"event_id":"sha256:b09f8786508f14a533f3bfd8e0093930dd48265821714f22ca42dcf775e2b5b3","target":"graph","created_at":"2026-07-05T06:16:04Z","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/2305.19884/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a notion of positivity of Gaussian directed acyclic graphical models corresponding to a non-negativity constraint on the coefficients of the associated structural equation model. We prove that this constraint is equivalent to the distribution being conditionally increasing in sequence (CIS), a well-known subclass of positively associated random variables. These distributions require knowledge of a permutation, a CIS ordering, of the nodes for which the constraint of non-negativity holds. We provide an algorithm and prove in the noise-less setting that a CIS ordering can be recovered w","authors_text":"Asad Lodhia, Caroline Uhler, Jan-Christian H\\\"utter, Piotr Zwiernik","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-05-31T14:22:26Z","title":"Positivity in Linear Gaussian Structural Equation Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.19884","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":"sha256:1f0de70ba016f5ed73f20024d17268a190fdb9df503faa33a6335fad0fcf2716","target":"record","created_at":"2026-07-05T06:16:04Z","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":"fa7191d3d4fb7e7a91a10b8561ec86518e622047b1e93fc1e749a8f03b09458d","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-05-31T14:22:26Z","title_canon_sha256":"d8be68f45dd3b33bad07c2c030241d6904e9074ccbde895f03f173df11422ddf"},"schema_version":"1.0","source":{"id":"2305.19884","kind":"arxiv","version":1}},"canonical_sha256":"56ab0020568efc5c4794f1c1a5677a6ecb7d57a3dd928dd51a397e72447683f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56ab0020568efc5c4794f1c1a5677a6ecb7d57a3dd928dd51a397e72447683f2","first_computed_at":"2026-07-05T06:16:04.329045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:16:04.329045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ECT+/JIMPGubRFegKKA9A7PYXZ3ZxVXpi6J0eUDt9QNLdohJWHa2b59CbXyh5hEM7LtEM7nQcaeRPB1eUXhvCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:16:04.329458Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.19884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f0de70ba016f5ed73f20024d17268a190fdb9df503faa33a6335fad0fcf2716","sha256:b09f8786508f14a533f3bfd8e0093930dd48265821714f22ca42dcf775e2b5b3"],"state_sha256":"b3307042e56fcaca24ed04b8807e6408bb3286fa877f235c2549996165f6349c"}