{"as_of":"2026-08-07T17:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:35e198c435419ffebc72d7e47411c2638f198e1c8fdb4f07e9c4dc3d2bac7c0c","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:01:12.262403Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.06888/citation-record","integrity":"/paper/2507.06888/integrity","json":"/paper/2507.06888/citation-record.json","paper":"/paper/2507.06888"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.851792Z","title":"Causal mechanisms in the social sciences.Annual review of sociology, 36(1):49–67, 2010","venue":null,"work_id":"78eabdf8-826a-4b64-9281-ef96688930f2","year":2010},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.090949Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:330847b7df411e32b3014637cc046df9b890d0f354b42b321ae561c56b20a033","observation_id":"01dcdbed-040d-47b1-8336-b4e0bcb393f5","resolution":{"observed_at":"2026-08-06T19:01:12.856945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.835750Z","title":"Academic Press, 2014","venue":null,"work_id":"3056b88f-0b90-415d-a309-ae26d4608ff7","year":2014},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.096609Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:1b6b896114894e1d605833250ae3a090bc1bad8c92a6a90f2fb9d6774fff3f6b","observation_id":"87db141d-5030-440e-8650-2fe95fc1a189","resolution":{"observed_at":"2026-08-06T19:01:12.840925Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.819318Z","title":"Prob- abilistic computational causal discovery for systems biology.Uncertainty in biology: a computa- tional modeling approach, pages 33–73, 2016","venue":null,"work_id":"6eb747a6-3d97-4fe3-8f73-18aa4fb516a5","year":2016},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.102018Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:41961809a68a4ac1cb3d61b73b060729511d7fe21d86fa8724220b473556c475","observation_id":"cae0f3fe-8a01-4199-bb6b-57b72409de7e","resolution":{"observed_at":"2026-08-06T19:01:12.825069Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.802704Z","title":"Causal discovery analysis: A promising tool in advancing precision medicine for eating disorders.International Journal of Eating Disorders, 56(11):2012–2021, 2023","venue":null,"work_id":"54450af7-5377-4124-b401-8d8fd3dc02dc","year":2012},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.106942Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:bc85b7640acec3cab9705731d3476ba0e448835b75a6fb25b19ad564b6d1fcb8","observation_id":"5ba2eaca-fdee-4117-847c-79cb1b317f83","resolution":{"observed_at":"2026-08-06T19:01:12.808443Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.03555","last_updated":"2023-01-17T04:25:30Z","snapshot_observed_at":"2026-07-06T12:16:05.364132Z","submitted_at":"2021-12-07T08:04:12Z","title":"FedDAG: Federated DAG Structure Learning","version":3},"cited_work":{"arxiv_id":"2112.03555","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.03555","snapshot_observed_at":"2026-08-06T19:01:12.348816Z","title":"FedDAG: Federated DAG Structure Learning","venue":"cs.LG","work_id":"abc1ac26-d0b1-4fa0-93cb-dff2bd2f2221","year":2021},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.112115Z"},"links":{"cited_paper":"/paper/2112.03555","citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:ebb7ab8b423a5a973475a46189e0624b4711dcc155ebf669e43b3be4108780c4","observation_id":"81a156d9-c642-4351-a096-8f52e61728a2","resolution":{"observed_at":"2026-08-06T19:01:12.353945Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.786599Z","title":"Federated causal discovery with missing data in a multicentric study on endometrial cancer.Available at SSRN 4998504, 2024","venue":null,"work_id":"ede9bd76-0e4c-469d-9beb-265920893e24","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.117513Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:5c383934cd1624bf1860cbe43a3cbce6ac60bd3df93a47b2bb66c3b5ef92650c","observation_id":"cbcadb8c-76d4-41d1-9393-1a4da36c2885","resolution":{"observed_at":"2026-08-06T19:01:12.791523Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.770976Z","title":"Towards practical federated causal structure learning","venue":null,"work_id":"541b0bea-9df4-488c-9445-21d670c88a66","year":2023},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.124132Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:e72c9dd186d4724365ab012f844ab7f269c9b3a835234c7b0e423ac3d33d4c76","observation_id":"a4be9717-6dc6-4065-b564-39a4150bc5ea","resolution":{"observed_at":"2026-08-06T19:01:12.776178Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.13241","last_updated":"2024-02-27T04:45:47Z","snapshot_observed_at":"2026-08-03T06:48:20.104234Z","submitted_at":"2024-02-20T18:53:53Z","title":"Federated Causal Discovery from Heterogeneous Data","version":2},"cited_work":{"arxiv_id":"2402.13241","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.13241","snapshot_observed_at":"2026-08-06T19:01:12.322430Z","title":"Federated Causal Discovery from Heterogeneous Data","venue":"cs.LG","work_id":"5d4c7764-b9c2-4f08-9d35-ebaf99ecd61d","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.129246Z"},"links":{"cited_paper":"/paper/2402.13241","citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:95ad5224995cb73a6f026182073ef6e180c62d59491c88994a7eb93f57b77464","observation_id":"766e9772-d878-4920-9073-09242093e1cf","resolution":{"observed_at":"2026-08-06T19:01:12.329979Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.753610Z","title":null,"venue":null,"work_id":"1627c91a-8c99-430f-8806-9134f96dde92","year":2021},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.135187Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:4543ea29cd3bf354a46556877ac3f4b00f3475d6433019d7e351df91f308a08b","observation_id":"d0e94359-1728-4164-974b-129a3ed5f3e5","resolution":{"observed_at":"2026-08-06T19:01:12.759171Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.738108Z","title":"Federated recommendation systems","venue":null,"work_id":"484887c1-8df8-4d5f-aebe-1d27465c2647","year":2020},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.140599Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:f600d4e2c47af716970da7453b3cbacacd8916bc97682bc23ff3268461a27161","observation_id":"8fd5465c-b436-4b31-a0f0-96b24d20ad0c","resolution":{"observed_at":"2026-08-06T19:01:12.743195Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2105.11099","last_updated":"2021-05-24T05:39:24Z","snapshot_observed_at":"2026-07-06T11:12:04.788175Z","submitted_at":"2021-05-24T05:39:24Z","title":"Federated Graph Learning -- A Position Paper","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.11099","snapshot_observed_at":"2026-08-06T19:01:12.146085Z","title":"Federated graph learning–a position paper.arXiv preprint arXiv:2105.11099, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.146085Z"},"links":{"cited_paper":"/paper/2105.11099","citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:02cb8c32cf526bc9710dca0dd11c5d230d000257a799b9bae1ffa472991649f4","observation_id":"c95252a9-445e-426b-ac68-e9247b9b1ed0","resolution":{"observed_at":"2026-08-06T19:01:12.146085Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.721751Z","title":"Hybrid federated learning for feature & sample heterogeneity: Algorithms and implementation.Transactions on Machine Learning Research, 2024","venue":null,"work_id":"e66f2771-cf6e-4699-a42d-a6048a4afce3","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.152466Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:514ef61c3093536cd17d90bdaf40c0af753a3f23b79116d72511ad726e57b2b6","observation_id":"6be603e5-5b99-43cd-ae42-902506d4bf44","resolution":{"observed_at":"2026-08-06T19:01:12.726865Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.157879Z","title":"A survey on homomorphic encryption schemes: Theory and implementation.ACM Computing Surveys (Csur), 51(4):1–35, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.157879Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:7ee31513cb05d027abb3e41f589590590473f6263f979e6e354973cc5f284d6b","observation_id":"b82dc9f2-2e34-42d3-9168-e93dd0a2acef","resolution":{"observed_at":"2026-08-06T19:01:12.157879Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.695570Z","title":"Causal discovery with latent confounders based on higher-order cumulants","venue":null,"work_id":"7b749619-7fc2-4e85-a6d9-2dfd632884db","year":2023},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.163126Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:41a6aa5a760bbfe4d7e83dbb6eaecf5c7b87a940f0e28836acaf785e68a187e9","observation_id":"848454ff-40cb-4eb2-b1bd-7ce9c12445ca","resolution":{"observed_at":"2026-08-06T19:01:12.700867Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.678973Z","title":"Identification of causal structure with latent variables based on higher order cumulants","venue":null,"work_id":"503f3ad2-a90d-4998-9e62-e3d9892c513c","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.167742Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:085c44c80e6e6deb9916bb48a45b0de6f6784b87833ca17c9317836999738c1f","observation_id":"80e3db36-1226-4990-8f00-7e71b3725e18","resolution":{"observed_at":"2026-08-06T19:01:12.684643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.658638Z","title":"Towards federated bayesian network structure learning with con- tinuous optimization","venue":null,"work_id":"185e47c5-15bf-4df4-bf93-8be323e469a7","year":2022},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.172822Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:6da73daa987e033bfb9ff259b8a0894e5fe401dd57c5cb28cf92863bcd6004da","observation_id":"ba3e1e88-a0de-483b-b895-96fd51104bb9","resolution":{"observed_at":"2026-08-06T19:01:12.666909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.642139Z","title":"Federated causality learning with explainable adaptive optimization","venue":null,"work_id":"a01e5cd1-0c48-4b2c-a241-740a53c418ed","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.177910Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:380d4f3bfcf1bbe02c029c3535db18e1e3090f01a0c0fc591966f8165d0d84b0","observation_id":"099df4c0-8995-4e4b-b814-bc97df6822b8","resolution":{"observed_at":"2026-08-06T19:01:12.647262Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.622572Z","title":"Federated learning of generalized linear causal networks.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024","venue":null,"work_id":"a0612c33-a260-4724-926a-c1895e6623fe","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.183205Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:bf78be5546dd376f044eb01b9c07875a2a2730f83c2a3102f8ce7dae51d3a1f6","observation_id":"94051d4f-6233-4671-ab1c-752e271ce348","resolution":{"observed_at":"2026-08-06T19:01:12.629231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.604430Z","title":"Nothing but regrets—privacy-preserving federated causal discovery","venue":null,"work_id":"2c2da8b4-ba13-44e5-85c6-29a04f58f614","year":2023},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.187796Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:d756a88d251abcff1236ad1ad43a8a2b1866824ba0c599563b64ababc4276fe6","observation_id":"51011935-c530-45c9-b285-210288d9160a","resolution":{"observed_at":"2026-08-06T19:01:12.610123Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.587766Z","title":"Towards privacy-aware causal structure learning in federated setting.IEEE Transactions on Big Data, 9(6):1525–1535, 2023","venue":null,"work_id":"44edbf40-e1f0-424d-a11d-c0429deb586b","year":2023},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.192763Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:eec1c16fcacf2987be93cd623532eea72e80cde9bb67ef7ce6d134170a30cbb6","observation_id":"d13ae258-c735-4af6-b11d-21a4e4715ead","resolution":{"observed_at":"2026-08-06T19:01:12.593148Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.198038Z","title":"Enhancing causal discovery in federated settings with limited local samples","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.198038Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:0fca9f9c448436b0243a5fb9a75cfe938c0479e0653bc20921a85cfe65359193","observation_id":"64a4049d-ee28-478a-ab02-19b9fce18cb2","resolution":{"observed_at":"2026-08-06T19:01:12.198038Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.559020Z","title":"Fedcsl: A scalable and accurate approach to feder- ated causal structure learning","venue":null,"work_id":"ce6d44d4-4e56-4abd-9349-bd3746bc9d5f","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.202788Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:a7e29fc234601fd07d1ec76b9b92d043887ee224dcb0c02cade368034443e72c","observation_id":"54f70372-834f-4198-8001-b20b7a0831f4","resolution":{"observed_at":"2026-08-06T19:01:12.564795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.543444Z","title":"Sample quality heterogeneity-aware federated causal discovery through adaptive variable space selection","venue":null,"work_id":"24def88b-034c-4364-b00e-d245d2b3d1d9","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.208138Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:3f5924d94f51ba63b8e35af5882b6459d6dd5c936683eacdb74050154555d1f4","observation_id":"adc8dbef-5329-4bf8-bdf7-0c9290d961ef","resolution":{"observed_at":"2026-08-06T19:01:12.548478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.526713Z","title":"Integrating locally learned causal structures with overlapping variables.Advances in Neural Information Processing Systems, 21, 2008","venue":null,"work_id":"3eebc94a-1d8b-4955-9361-1c96913322eb","year":2008},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.212854Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:dabb95fe0313c7452e95e8244efae82912418a5448b438c7557cb7ba813203fb","observation_id":"f42f5b90-367b-4a06-9abf-adff1541eacf","resolution":{"observed_at":"2026-08-06T19:01:12.532357Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.509313Z","title":"Constraint-based causal discovery from multiple in- terventions over overlapping variable sets.The Journal of Machine Learning Research, 16(1):2147– 2205, 2015","venue":null,"work_id":"2ce86efb-c0b5-4b01-98c8-5f12618823bc","year":2015},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.217749Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:3bc22573cdb8f1075f17989c230a0dda11bf84b8560fca86f353af0152968558","observation_id":"4cfafe19-4b0f-4074-a3a8-fa4bbff94264","resolution":{"observed_at":"2026-08-06T19:01:12.514654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.492756Z","title":"Causal discovery from multiple data sets with non-identical variable sets","venue":null,"work_id":"8af2dd4a-c47a-40a5-8999-b606e65ff776","year":2020},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.223122Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:2175ced97d80c04851d6c0394df7228eb272ac68dbbd3ef8f80810b0546128e0","observation_id":"06005892-d025-4a32-8cf7-b5d74f5f6679","resolution":{"observed_at":"2026-08-06T19:01:12.497850Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.475135Z","title":"Causal discovery from unknown interventional datasets over overlapping variable sets.IEEE Transactions on Knowledge and Data Engineering, 2024","venue":null,"work_id":"408fe22b-9b77-49df-ab4a-8b239921269c","year":2024},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.227845Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:2aff84e9765bcb2e5c8512b08a00561ac79d30634e2c09daf6dedf3ace1a728d","observation_id":"ff6fdcbd-13ce-448b-b2d4-be20991c61a7","resolution":{"observed_at":"2026-08-06T19:01:12.481026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.457982Z","title":"A novel data enhancement approach to dag learning with small data samples.Applied Intelligence, 53(22):27589–27607, 2023","venue":null,"work_id":"62eb6dfd-7237-4083-9452-0b2004d0718b","year":2023},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.232940Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:91a896811deb74b56106ef804970292fafafb60a84c98e292166c30e27a73c2b","observation_id":"01a99b1d-9458-43ed-8637-d4421cd42e99","resolution":{"observed_at":"2026-08-06T19:01:12.463195Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.441208Z","title":"Multi-target markov boundary discovery: Theory, algorithm, and application.IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(4):4964–4980, 2022","venue":null,"work_id":"f27e594c-5439-4269-bd05-57602a08d4dd","year":2022},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.237895Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:93e95ba83afb9c3ea8560389ea1fdb8931728cb10ff44c02057691de07a45a15","observation_id":"044670bb-f79c-4f5a-a800-5892611f946e","resolution":{"observed_at":"2026-08-06T19:01:12.446681Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.242566Z","title":"SIAM, 2001","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.242566Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:b35549b3c857ef1148a50b18d5a1fcf060f1b448447850ce9779bb5cd817b651","observation_id":"253e560b-6d47-403e-bef5-7d6fb5d11a82","resolution":{"observed_at":"2026-08-06T19:01:12.242566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.411083Z","title":"Independent component analysis, adaptive and learning systems for signal processing, communications, and control.vol, 1:11–14, 2002","venue":null,"work_id":"84d7609c-3e31-4387-8a82-24b4156f5696","year":2002},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.247468Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:71fbb1ce2aa3a9b3462aa88aa08615ea2d950caecb509ba567d3aa67758e144a","observation_id":"f67914f1-2549-412f-adb4-320d0f21c2d1","resolution":{"observed_at":"2026-08-06T19:01:12.417546Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.394665Z","title":"A linear non-gaussian acyclic model for causal discovery.Journal of Machine Learning Research, 7(10), 2006","venue":null,"work_id":"8a0d0538-1db9-4021-a52a-bdea845cc91d","year":2006},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.252148Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:eb65dbc0481012bcd5adbd1347ccc356ce0a8ecbfc2fdd42d30a3643820b2c6c","observation_id":"2acaf9d0-83fb-4ee9-a3d3-366e3b30975d","resolution":{"observed_at":"2026-08-06T19:01:12.399898Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.257304Z","title":"Directlingam: A direct method for learning a linear non-gaussian structural equation model.Journal of Machine Learning Research-JMLR, 12(Apr):1225–1248, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.257304Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:b82bf2c083e18b13f150520a34e575a9f04b6afdacdf92667561f268dabc2407","observation_id":"252b8fdd-2c49-455e-9143-a82e6f91471c","resolution":{"observed_at":"2026-08-06T19:01:12.257304Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:01:12.366897Z","title":"Secure multiparty computation.Communications of the ACM, 64(1):86–96, 2020","venue":null,"work_id":"66447f12-a803-4cd8-9f59-0dee6d5db44f","year":2020},"citing_paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T19:01:12.262403Z"},"links":{"citing_paper":"/paper/2507.06888"},"observation_digest":"sha256:f3b3fa8aafe734a2a605f76c3c7baba487b2c420d76e41578f9d5dea89ab40d2","observation_id":"005fc214-d7f2-4e28-ad7e-e950364d364f","resolution":{"observed_at":"2026-08-06T19:01:12.372756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.06888","last_updated":"2025-07-09T14:25:51Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-06T18:49:44.476061Z","submitted_at":"2025-07-09T14:25:51Z","title":"Horizontal and Vertical Federated Causal Structure Learning via Higher-order Cumulants"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":2,"verified_fuzzy":26},"total_outbound_references":34},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2507.06888."}