{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R7VVGN3C7ABKGHWK4T7YSNS3OF","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":"f091ee6db606c788645ca4ca5d90ff2f7e16f027cbaf7636a37f697db32156b0","cross_cats_sorted":["cs.AI","cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-10T08:38:37Z","title_canon_sha256":"5822ca797a593a55926ad2c6f3ce89febc6543a4c399c0c9e48f279965b11644"},"schema_version":"1.0","source":{"id":"1807.03527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03527","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03527v1","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03527","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"R7VVGN3C7ABK","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R7VVGN3C7ABKGHWK","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R7VVGN3C","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:3d45a3597219ca377619658c2c5c4e0c5f8e5522bc37c8c2d4fa5d60576d700c","target":"graph","created_at":"2026-05-18T00:11:10Z","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":"Despite their popularity, many questions about the algebraic constraints imposed by linear structural equation models remain open problems. For causal discovery, two of these problems are especially important: the enumeration of the constraints imposed by a model, and deciding whether two graphs define the same statistical model. We show how the half-trek criterion can be used to make progress in both of these problems. We apply our theoretical results to a small-scale model selection problem, and find that taking the additional algebraic constraints into account may lead to significant improv","authors_text":"Joris M. Mooij, Thijs van Ommen","cross_cats":["cs.AI","cs.LG","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-10T08:38:37Z","title":"Algebraic Equivalence of Linear Structural Equation Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03527","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:b609aaa4c1bf17c6a85dea5416ed1d4782fdb61d21540e996f2b6ca3f5c20d31","target":"record","created_at":"2026-05-18T00:11:10Z","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":"f091ee6db606c788645ca4ca5d90ff2f7e16f027cbaf7636a37f697db32156b0","cross_cats_sorted":["cs.AI","cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-10T08:38:37Z","title_canon_sha256":"5822ca797a593a55926ad2c6f3ce89febc6543a4c399c0c9e48f279965b11644"},"schema_version":"1.0","source":{"id":"1807.03527","kind":"arxiv","version":1}},"canonical_sha256":"8feb533762f802a31ecae4ff89365b71446361b3524a4921417cb40d0e30da9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8feb533762f802a31ecae4ff89365b71446361b3524a4921417cb40d0e30da9c","first_computed_at":"2026-05-18T00:11:10.179915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:10.179915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1y30o9Q9gtz0B+UqdkvAI1TX1+Bl3LW0b/sJOOh4K7FbaoHvZjikqKL+c7rnEy78u701U0pNtWH7eLSm3yN8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:10.180663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b609aaa4c1bf17c6a85dea5416ed1d4782fdb61d21540e996f2b6ca3f5c20d31","sha256:3d45a3597219ca377619658c2c5c4e0c5f8e5522bc37c8c2d4fa5d60576d700c"],"state_sha256":"836a272a487fca0f79194d5e9d08c5fb504da8762eb396b3527dff3a526bf36a"}