{"as_of":"2026-08-13T10:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:aa1bfff0a814212e734f966a402fcb4f2b89d89619a91fdce882ef0bfa6210d0","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T14:08:58.209121Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T19:02:27.699052Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-20T07:18:06.907497Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.15660","snapshot_observed_at":"2026-08-03T19:02:27.699052Z","title":"Federated pca and estimation for spiked covariance matrices: Optimal rates and efficient algorithm.arXiv preprint arXiv:2411.15660,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.02866","last_updated":"2026-07-31T09:41:16Z","snapshot_observed_at":"2026-08-08T09:37:44.294732Z","submitted_at":"2025-12-02T15:28:07Z","title":"Spectral Joint Subspace Estimation for Heterogeneous Multi-View Data: Geometry and Reweighting","version":2},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-03T19:02:27.699052Z"},"links":{"cited_paper":"/paper/2411.15660","citing_paper":"/paper/2512.02866"},"observation_digest":"sha256:c1809fc7cd972212f0b735a4e74a1a5d9ee1625b4520308fa824458786110401","observation_id":"43c6e754-da5f-4c6f-914b-bbc591a90e1e","resolution":{"observed_at":"2026-08-03T19:02:27.699052Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"cited_work":{"arxiv_id":"2411.15660","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.15660","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Tony Cai, Dong Xia, and Anru R","venue":null,"work_id":"4353bc12-774c-4b01-adb9-9f82a28f77f2","year":2024},"citing_paper":{"arxiv_id":"2605.19813","last_updated":"2026-07-08T09:10:31Z","snapshot_observed_at":"2026-07-12T16:29:27.707351Z","submitted_at":"2026-05-19T13:09:58Z","title":"A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-20T07:15:29.444050Z"},"links":{"cited_paper":"/paper/2411.15660","citing_paper":"/paper/2605.19813"},"observation_digest":"sha256:1d643a88e9bdc7db74406165bd8b9d80c948f88a869e00a376f51ebb5d968cdc","observation_id":"960e43da-43c9-41a8-bfee-3222d42f5020","resolution":{"observed_at":"2026-05-20T07:18:06.909041Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.15660","snapshot_observed_at":"2026-07-12T16:29:28.243675Z","title":"Tony Cai, Dong Xia, and Anru R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.19813","last_updated":"2026-07-08T09:10:31Z","snapshot_observed_at":"2026-07-12T16:29:27.707351Z","submitted_at":"2026-05-19T13:09:58Z","title":"A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-12T16:29:28.243675Z"},"links":{"cited_paper":"/paper/2411.15660","citing_paper":"/paper/2605.19813"},"observation_digest":"sha256:6c84395cbb572faacb1b7c422649e97f464c7f1fb146b3f1d50199a765c0c05d","observation_id":"edbdec41-56ca-4ba1-a1da-de4aeb2d8acd","resolution":{"observed_at":"2026-07-12T16:29:28.243675Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2411.15660/citation-record","integrity":"/paper/2411.15660/integrity","json":"/paper/2411.15660/citation-record.json","paper":"/paper/2411.15660"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:08:58.699471Z","title":"Upper bound forJ (p)","venue":null,"work_id":"18099ae9-0cc3-440a-8f76-6a1dc27f479a","year":1988},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:58.047632Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:1027ede237df060bcb48619d29880704d7f48021bc0ecd79252e5390f2d952dd","observation_id":"54b14cae-3ed0-4707-9639-2bd2788b8639","resolution":{"observed_at":"2026-08-12T14:08:58.730004Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:58.750393Z","title":"(40) Meanwhile (see Appendix C.2), ∇ψ(Θ)∗ : Rp×p → Rp×r is given by ∇ψ(Θ)∗(M ) = ¯Θ⊥ ¯Θ⊤ ⊥(M + M ⊤) ¯ΘW −1/2","venue":null,"work_id":"9705f6ab-0eac-4dd7-b078-a3dba6cf0c5e","year":1988},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.999813Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:17472431eb5b0438db3713aaa2dcc36940ca831b2596553e2cb95cec7893bf69","observation_id":"e628546f-d664-48b6-a831-bae84a42f917","resolution":{"observed_at":"2026-08-12T14:08:58.753860Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:58.829442Z","title":"Local privacy and statistical minimax rates","venue":null,"work_id":"78cef7b3-d356-4a0d-9a1b-8592f2ebb9e9","year":2013},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.825898Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:df727b5bfc718ce495504b209ffd4d4b2d46cc7c851594e1998ffc849d1fff14","observation_id":"36e6d8de-0526-4be7-9557-ebc4f79fa6b7","resolution":{"observed_at":"2026-08-12T14:08:58.833075Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:58.818273Z","title":"Calibrating noise to sensitivity in private data analysis","venue":null,"work_id":"5663a1f0-abbf-4fc1-a6ee-14a7add44335","year":2006},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.864948Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:08bb5e74c880e133920a7a9c94e27cfc7a4330eab98f3ad3fd1f1722cdcbfd2c","observation_id":"b08046b7-10b3-4ee6-9475-b636601bb866","resolution":{"observed_at":"2026-08-12T14:08:58.821873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:58.786321Z","title":"Asymptotics and concentration bounds for bilinear forms of spectral projectors of sample covariance","venue":null,"work_id":"112555d3-eec9-4184-be95-7bc133662e91","year":1976},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.883144Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:fea3119e7fb6155da77080af4f679498b3e4a69f1531b89b24d0ced701f298b3","observation_id":"9828e6b4-689d-478d-acb3-bfed0405b914","resolution":{"observed_at":"2026-08-12T14:08:58.791077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:57.887222Z","title":"URL https://doi.org/10","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.887222Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:6b67f36460afb0f8fccdef72c4d86d70cdc0554759262407fc2ea46f96169549","observation_id":"78f04332-de90-430e-aa4d-37a555fd9b98","resolution":{"observed_at":"2026-08-12T14:08:57.887222Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:08:57.903106Z","title":"John Novembre and Matthew Stephens","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.903106Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:efd8cc1d15274cb75995bb370a023a6034f6aad0eed83b224e27a7653c03fd4e","observation_id":"0be0d1c5-ecdb-40fb-96f9-c669f9f6fa51","resolution":{"observed_at":"2026-08-12T14:08:57.903106Z","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":"2026-08-12T14:08:58.762306Z","title":"Using these facts, we have E X j1,··· ,jl∈[m] wj1 · · ·wjltr(U ⊤M (s1)M (s1)⊤∆j1M (s2) · · ·M (sl)⊤∆jlM (sl+1)M (sl+1)⊤U ) · 1(E) ≤ r · X j∈I2(s) uj1 · · ·ujl","venue":null,"work_id":"f876798c-0489-40ff-aef1-0ad57c627b76","year":2012},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.955102Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:3e22e74622b36bd644ce6b40b33e98a8fa23981f3cb1d597f71a68324503b741","observation_id":"a489bf57-c58f-47a2-9041-9dd05476fb19","resolution":{"observed_at":"2026-08-12T14:08:58.766061Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:58.636699Z","title":"Recall G(j) 1 = E⟨∇ψ(Θ)(∇ log p(Dj; Θ| bUj)), ∇ψ(Θ)(∇ log p(X (j) 1 ; Θ| bUj))⟩","venue":null,"work_id":"417fd4f3-44e4-479b-97c5-e75ff5a65424","year":2017},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:58.084143Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:ec509921dbe2530aafcd7db986d716d46c7f669ba67229afe93010977ee8175a","observation_id":"7c06f8a3-f9f2-4b50-b98a-bdd5561340cb","resolution":{"observed_at":"2026-08-12T14:08:58.670536Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:58.520404Z","title":"The term Etr(W −4) can be computed using the Theorem 4.1 of Von Rosen (1988), which implies Etr(W −4) · e−c1p/2 ≤ p−2","venue":null,"work_id":"9b24748e-104f-4706-97dd-f9ea2a1206c1","year":1988},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:58.141738Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:2509ad19e2d5f62c373dd2845588649da24e21d8b1e3e36d203caee32011f9d9","observation_id":"26c4d52c-652b-4a2f-b215-d5d3257ae60f","resolution":{"observed_at":"2026-08-12T14:08:58.556106Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:58.445279Z","title":"Lemma 5 (Koltchinskii and Lounici (2017))","venue":null,"work_id":"5c78320a-8000-484a-aa98-f3ce99600ff2","year":2017},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:58.209121Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:3c1b08f7377d219b3c9fc58ccc515c6d33ed01b6f554d97a060f1f5058ee2250","observation_id":"6e41e1cb-a1c3-41b3-9966-afd584cb06ec","resolution":{"observed_at":"2026-08-12T14:08:58.469200Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:57.878684Z","title":"Principal component analysis: a review and recent developments","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2001,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.878684Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:93ada94503d34d6e45eb6ac645b46b42b11e8a007870fcec5168a1a340c02936","observation_id":"df397a00-a683-4cf2-8c19-81e126354f07","resolution":{"observed_at":"2026-08-12T14:08:57.878684Z","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":"2026-08-12T14:08:58.807369Z","title":"The algorithmic foundations of differential privacy.Foundations and Trends® in Theoretical Computer Science , 9(3–4):211–407, 2014a","venue":null,"work_id":"0edc49a1-d1e9-4ad1-bfab-6aff8307b033","year":2014},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2006,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.868578Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:5979f509b6d1c49c1df27c9bc43a878e080da52057a6e03ab7ba9dc297eb13a6","observation_id":"4142b718-0141-4a8d-8f90-b90c7e2bb3fd","resolution":{"observed_at":"2026-08-12T14:08:58.810770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:57.592724Z","title":"URL https://doi.org/10.1214/ 08-AOS600","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2008,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.592724Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:208a35d82a075b52a052e1c16fb4e63302b8a1a9984261fd3f38b003200e8424","observation_id":"b4b0a4a8-7702-4f70-90b8-b48f4750274b","resolution":{"observed_at":"2026-08-12T14:08:57.592724Z","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":"10.1214/09-aos752","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:08:58.291136Z","title":"URL https://doi.org/10.1214/09-AOS752","venue":null,"work_id":"31c4de54-ccbb-45ab-bf0a-20911f1c6314","year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.676574Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:6c6b5d0f530c24fb117cca76b41d62032c592f2b0f7d6d4afb8151f272e8e54f","observation_id":"6d8f54a9-194d-492a-b301-10ce84e4205c","resolution":{"observed_at":"2026-08-12T14:08:58.297225Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T14:08:57.745799Z","title":"URL https: //doi.org/10.1214/13-AOS1178","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.745799Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:f93c7c4c4838798c6e95a84b31ffe6544761ec078cf4c64b919490f7498a1ce2","observation_id":"5b387a57-34c8-4098-9e46-93eaf5455c87","resolution":{"observed_at":"2026-08-12T14:08:57.745799Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:08:57.874868Z","title":"ISBN 9781450329576","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.874868Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:da934cfcc350ee2e6e97324be464985320b53486340f5509bb9a4fb7823f41f4","observation_id":"703904cc-aff5-475a-ade3-4630d36bdcee","resolution":{"observed_at":"2026-08-12T14:08:57.874868Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.06755","last_updated":"2024-06-10T19:34:07Z","snapshot_observed_at":"2026-08-12T23:46:06.432267Z","submitted_at":"2024-06-10T19:34:07Z","title":"Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.06755","snapshot_observed_at":"2026-08-12T14:08:57.795048Z","title":"URL https://doi.org/10.1214/15-EJS1081","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.795048Z"},"links":{"cited_paper":"/paper/2406.06755","citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:adc761ea11ef09656e09445267d28da53a34b1ba064d967578d87e60b20f909b","observation_id":"1ef41d7c-c9a1-45da-b7b4-50e92d59a7f3","resolution":{"observed_at":"2026-08-12T14:08:57.795048Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:08:57.634351Z","title":"URL https://doi.org/10.1214/17-AOS1541","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.634351Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:187552b9d68f2ca1a2f208c45816ee7eb9b8e4e539cdd5f98159ed8afa24664d","observation_id":"ccf6a1d2-4d03-4520-a3df-02a475bef6e0","resolution":{"observed_at":"2026-08-12T14:08:57.634351Z","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":"2026-08-12T14:08:58.772900Z","title":"In the proof, we set λmax = λ1 and λmin = λr","venue":null,"work_id":"ffdde3d9-1332-4cbe-a849-65972897475e","year":2021},"citing_paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-12T14:08:57.931771Z"},"links":{"citing_paper":"/paper/2411.15660"},"observation_digest":"sha256:0b19699a5efd67524ad26b7df1fb9285181fdad55771c3a0e32014574ca70652","observation_id":"d98ff82c-6562-4419-9d3b-14c1bdc8efe3","resolution":{"observed_at":"2026-08-12T14:08:58.777425Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.15660","last_updated":"2024-11-23T21:57:50Z","latest_version":1,"primary_category":"math.ST","snapshot_observed_at":"2026-08-12T14:01:14.289136Z","submitted_at":"2024-11-23T21:57:50Z","title":"Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":1,"verified_fuzzy":11},"total_outbound_references":20},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 3 inbound Pith citation observations for arXiv:2411.15660."}