{"as_of":"2026-08-15T13:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cfd03e8e612bca449d3c9df5ab97cecb2131b4e5507f40865ec56a23ee3517c3","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T21:29:34.040415Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-08T17:24:52.674306Z","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":"2026-05-11T17:36:06.219654Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"cited_work":{"arxiv_id":"2501.04935","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.04935","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Geodesic variational Bayes for multiway covariances","venue":null,"work_id":"ddcd2f7c-1ae1-47e0-b591-af7bcab4431f","year":2025},"citing_paper":{"arxiv_id":"2605.03074","last_updated":"2026-05-04T18:43:50Z","snapshot_observed_at":"2026-07-06T23:16:05.372336Z","submitted_at":"2026-05-04T18:43:50Z","title":"Bures Geodesics and Restricted Barycenters for Kronecker Positive Definite Matrices","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-08T17:24:52.674306Z"},"links":{"cited_paper":"/paper/2501.04935","citing_paper":"/paper/2605.03074"},"observation_digest":"sha256:b6f60a02f4bafe29cb22c98f9eea22e1eaa56e4104aa586a7f4b9ec38e822054","observation_id":"36a2d098-dc82-45da-b2b9-183a75b00bfe","resolution":{"observed_at":"2026-05-11T17:36:06.221685Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2501.04935/citation-record","integrity":"/paper/2501.04935/integrity","json":"/paper/2501.04935/citation-record.json","paper":"/paper/2501.04935"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:29:34.341509Z","title":"On-line Kronecker product structured covariance estimation with Riemannian geometry for t-distributed data","venue":null,"work_id":"bed72a82-7d5d-496b-9152-a4595a62fc7e","year":2021},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.950991Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:bc106f81aa8b131b6791d29a68717e02838c53253b1510885dc8602bdea74b53","observation_id":"b1833658-3bc0-45a2-bdf7-7d535a88d785","resolution":{"observed_at":"2026-08-10T21:29:34.346078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.330317Z","title":"Variational inference for large-scale models of discrete choice","venue":null,"work_id":"1806a5b4-1563-48cc-9613-304df609a71d","year":2010},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.954962Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:d77fa73139f66b1d017a8b5a1df82b9ebfbce06910fbcb9baa9044e7fc048019","observation_id":"6873a03b-f985-4726-bcb1-131c7b251165","resolution":{"observed_at":"2026-08-10T21:29:34.334632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.320511Z","title":"Optimal Statistical Decisions","venue":null,"work_id":"413dbaad-21ed-448c-b944-9d3b8d746d42","year":2005},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.958522Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:f0ec7bf7d4b4b14c1653c302fa34bf60550281ebaab8075bb3df526ed4212277","observation_id":"9175ac3c-ba16-4853-a1c0-05633e74833b","resolution":{"observed_at":"2026-08-10T21:29:34.324066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.01050","last_updated":"2018-07-31T16:53:19Z","snapshot_observed_at":"2026-08-14T19:29:41.433503Z","submitted_at":"2018-04-03T16:04:22Z","title":"Training VAEs Under Structured Residuals","version":3},"cited_work":{"arxiv_id":"1804.01050","doi":null,"metadata_source":"pith","pith_arxiv_id":"1804.01050","snapshot_observed_at":"2026-08-10T21:29:34.083929Z","title":"Training VAEs Under Structured Residuals","venue":"stat.ML","work_id":"7f03c17f-b5c3-40a9-ab10-9f3c327593cc","year":2018},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.961648Z"},"links":{"cited_paper":"/paper/1804.01050","citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:b3f83e1f489e5e89e0661407468c06b389a6ff5c6ee45179e7195e8032900c93","observation_id":"5a62da30-0163-4ef6-91db-2eb25ca49ce3","resolution":{"observed_at":"2026-08-10T21:29:34.088389Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.310439Z","title":"The mle algorithm for the matrix normal distribution","venue":null,"work_id":"eaa9592b-2e3c-4c21-8167-353be494e802","year":1999},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.966856Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:4a823ce6359a7cd5c227af2ae619f1bcf79434d1cf05160f8c08996e7bfb3603","observation_id":"f5fe4338-5c2d-4ff1-9511-0fb4828e0dfb","resolution":{"observed_at":"2026-08-10T21:29:34.313896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.300977Z","title":"Separable factor analysis with applications to mortality data","venue":null,"work_id":"2c872f07-49b9-4197-92e4-e76962439243","year":2014},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.970508Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:5d05bf9f69025cbebf811f0a67867880bdbbb3e409f6e892450af86f404663a0","observation_id":"5dafefed-c01c-4304-8cbf-fe4a1a722acf","resolution":{"observed_at":"2026-08-10T21:29:34.304441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.291339Z","title":"A tutorial on variational Bayesian inference","venue":null,"work_id":"a4b1b4bd-f40d-4fb7-9ad0-13ee12b88d70","year":2012},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.974142Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:47521f6c935c1cbd4436faef3b08a920ab2fd1b538824cf765ec232614c5fb14","observation_id":"5fb9fe05-197e-4c1d-99ef-6d5f998f3312","resolution":{"observed_at":"2026-08-10T21:29:34.295161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.281611Z","title":"Kronecker Products and Matrix Calculus with Applications","venue":null,"work_id":"127943cd-68ab-437c-bea2-45e56c6d3cf9","year":2018},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.977026Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:b5f6ea8785cb0c1b402fc4a3754de3e9fdfed07f8eb9051749139db9aa8da874","observation_id":"d02eb17b-cd2a-4253-b659-f6c8031e52d4","resolution":{"observed_at":"2026-08-10T21:29:34.285291Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.272036Z","title":"Bayesian tensor regression","venue":null,"work_id":"0696b039-f4bf-46e4-b5c3-81492859ec60","year":2017},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.980399Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:ff8af130c7a2094545791eb0da8ca8513cd6b3b3940752a834ca7718a58e4a30","observation_id":"ef8a4fce-2928-47c5-afda-1e441988a200","resolution":{"observed_at":"2026-08-10T21:29:34.275007Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.262465Z","title":"On Riemannian optimization over positive definite matrices with the Bures-Wasserstein geometry","venue":null,"work_id":"4b4ddef5-8c0d-4d4e-beba-ab57e7a1fcd2","year":2021},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.983437Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:1f0357f3f4cc207abca87a2d29fdb72e39c20731a382a8310b5db9ca2df47431","observation_id":"41eb528f-6af8-4d61-af12-5e4c8d901471","resolution":{"observed_at":"2026-08-10T21:29:34.266267Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.252251Z","title":"Hierarchical multilinear models for multiway data","venue":null,"work_id":"c8c79908-a937-4120-95d3-60cbbbfdc487","year":2011},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.986573Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:ea247f9dde345c4614ebc550189e5599efa21fca7ca6cadc1eb251b0a031736b","observation_id":"ac42f827-7623-4c42-adb5-2786cf4d80a7","resolution":{"observed_at":"2026-08-10T21:29:34.256399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.242527Z","title":"Separable covariance arrays via the Tucker product, with applications to mul- tivariate relational data","venue":null,"work_id":"e9a85080-4fe5-4826-aa98-6d0b4e140fb0","year":2011},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.989886Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:b498c1c458051a31144e782af4e22049a72d71793ee721d986a228717c34a4cd","observation_id":"382c5724-f7af-41a8-a8be-382fa0dc8a58","resolution":{"observed_at":"2026-08-10T21:29:34.246739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.231239Z","title":"Log-euclidean metric learning on symmetric positive definite manifold with application to image set clas- sification","venue":null,"work_id":"7480be3f-d846-4b04-be00-b9561e198e44","year":2015},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.993275Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:7a559b0b7130689c9dde459f0d2585afac4fb6f4f49d3948ec6a67c2db4cedd4","observation_id":"2117cfcb-3069-4385-988a-4b69e8e8e731","resolution":{"observed_at":"2026-08-10T21:29:34.235084Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.220664Z","title":"Tensor decompositions and applications","venue":null,"work_id":"408b1015-2127-41f8-a0be-892e5db66f20","year":2009},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.996378Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:c1b4565602a0bcc6e2f8f6238b6f1cb2c83b0564a0d92c76fea93f7ddaa746fc","observation_id":"7c392c1c-f5b5-4013-ac8a-21be670fcc7b","resolution":{"observed_at":"2026-08-10T21:29:34.224047Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.210065Z","title":"Bartlett decomposition and Wishart distribution","venue":null,"work_id":"3005cea4-afe1-4939-93aa-d910ec99a22f","year":1959},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:33.999653Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:d2183327467218b7f9e176731f9f26259893a6c27f9795ea30dee3b9c4108331","observation_id":"3b886fc0-04b2-4342-af3b-0f13bde84855","resolution":{"observed_at":"2026-08-10T21:29:34.214380Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.200317Z","title":"Riemannian geometry of symmetric positive definite matrices via cholesky de- composition","venue":null,"work_id":"937c5a44-1099-4197-9630-791ad0fc8771","year":2019},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.002755Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:6364c93181c1b1675b0b30399a2ae1be1d47ea89ae13464c5688f6ff6e7c0efb","observation_id":"edaab560-8583-494c-96ab-28324333fd2c","resolution":{"observed_at":"2026-08-10T21:29:34.203712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2308.02260","last_updated":"2023-08-04T11:35:19Z","snapshot_observed_at":"2026-08-13T10:40:42.457091Z","submitted_at":"2023-08-04T11:35:19Z","title":"Information Geometry and Asymptotics for Kronecker Covariances","version":1},"cited_work":{"arxiv_id":"2308.02260","doi":null,"metadata_source":"pith","pith_arxiv_id":"2308.02260","snapshot_observed_at":"2026-08-10T21:29:34.068502Z","title":"Information Geometry and Asymptotics for Kronecker Covariances","venue":"math.ST","work_id":"310ff251-b1a0-4cb4-b7be-6165e6e86334","year":2023},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.006146Z"},"links":{"cited_paper":"/paper/2308.02260","citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:9d962dce628725fb1903d95876a00f7e0c1ca878e4cdc3f75fd93f359fc55dce","observation_id":"a237c519-6830-411c-988e-f2af54b0f6fa","resolution":{"observed_at":"2026-08-10T21:29:34.074442Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.189723Z","title":"Symmetric positive-definite matrices: From geome- try to applications and visualization","venue":null,"work_id":"e58dc9a7-a37f-49d3-adcd-c3f755cd54de","year":2006},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.009746Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:1a1f23c1b5c9e53ba8c4a5dab97fe7683cf7f3dc2dcaafbcf3406af958a1ba5d","observation_id":"c2b82b01-d0c7-4bb1-955d-6807b505166d","resolution":{"observed_at":"2026-08-10T21:29:34.194426Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.178311Z","title":"The Riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data","venue":null,"work_id":"4b0f2752-7626-4156-a404-61b0b1be578f","year":2011},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.013048Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:0d6dfd5741f614b27222757328e6936ebe8b6513d2edf9a10396b570a1211279","observation_id":"8e91cbdc-6f1c-4561-9be8-f53a15e65a0b","resolution":{"observed_at":"2026-08-10T21:29:34.182899Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.168617Z","title":"Tensor-train decomposition","venue":null,"work_id":"f20a91d5-8242-4744-81f7-77c3f483d762","year":2011},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.016186Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:52e3c9a1556e8808dafaed9ef7fbad70d2c5fc3c1914d31dab51dbe1324ff974","observation_id":"d3a4c9f7-b8e0-45e0-bde0-e0e69bfed0f7","resolution":{"observed_at":"2026-08-10T21:29:34.171952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.158695Z","title":"Structured variational Bayesian infer- ence for gaussian state-space models with regime switching","venue":null,"work_id":"995184ed-564f-4868-b35b-9f5bdbf2257d","year":1953},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.019887Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:97537eb7944bed29c47838815b3d7c0a29a076672ff87fdbe900b4caeaa09eb9","observation_id":"9284be51-376a-430b-b443-1384cf6ce9e6","resolution":{"observed_at":"2026-08-10T21:29:34.162407Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.147206Z","title":null,"venue":null,"work_id":"aa4dc607-71b8-4f20-accd-757d3d752fcc","year":1997},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.023473Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:452c4ac497b483c7b53b65aa1e3a28f60cf50660c639ba0622d86ae6e8f17d18","observation_id":"65fd755e-21be-4f90-9747-67ea3c04728b","resolution":{"observed_at":"2026-08-10T21:29:34.151772Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.135455Z","title":"Scalable Bayesian low-rank decomposition of incomplete multiway tensors","venue":null,"work_id":"460e8286-35ef-433b-a026-9eb7d22eb3b3","year":2014},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.026817Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:91609e5470c764061e4735d0635632df850769e82fee6115fad4c49cb6255f78","observation_id":"fdeeff19-df24-4f2f-9ed2-dbf9a76f2c97","resolution":{"observed_at":"2026-08-10T21:29:34.140201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.125310Z","title":"Variational Bayes on manifolds.Statistics and Computing , 31:1–17, 2021","venue":null,"work_id":"0f87bf81-1e5f-4920-9b82-ff46e48dae05","year":2021},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.030392Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:950a5aaa1bdf52fb5e02e492ffc0825965a1ea2255b1854e0ca93822a7cd4194","observation_id":"a6616b12-8ec0-4e84-b9c2-176501bfbd85","resolution":{"observed_at":"2026-08-10T21:29:34.129062Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.114985Z","title":"Structured variational inference in Bayesian state-space models","venue":null,"work_id":"2c43c2b4-2854-4476-8623-cbd4c0d040d5","year":2022},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.033851Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:ce5dd33c70c42c232b238de167ff708da6a481480c61965987227cc0c2aa9662","observation_id":"18073504-27ee-4dd8-8a52-91e58a38ef22","resolution":{"observed_at":"2026-08-10T21:29:34.118951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.105106Z","title":"Geodesic convexity and covariance estimation","venue":null,"work_id":"efdb708c-0a5e-41b4-a859-3f103c3cb2e2","year":2012},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.037105Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:80097a276b7fc61c8ced655c5add0eaa78f5cb7a8921c65dc2f08507faaea0f9","observation_id":"f4a7fa8d-f6da-45ad-8970-d47a7359ba72","resolution":{"observed_at":"2026-08-10T21:29:34.108627Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-10T21:29:34.095388Z","title":"Bayesian nonparametric models for multiway data analysis","venue":null,"work_id":"d24477f3-3627-46fa-b2eb-37fa9a6398c6","year":null},"citing_paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T21:29:34.040415Z"},"links":{"citing_paper":"/paper/2501.04935"},"observation_digest":"sha256:d330f4867251307e048bc97072e95ca6419555808e4fd01d9c2d8a66f8fe9997","observation_id":"f9a8bff5-7e31-40ea-981b-276e8a97c547","resolution":{"observed_at":"2026-08-10T21:29:34.098838Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.04935","last_updated":"2025-01-09T02:54:06Z","latest_version":1,"primary_category":"stat.CO","snapshot_observed_at":"2026-08-11T07:40:35.362458Z","submitted_at":"2025-01-09T02:54:06Z","title":"Geodesic Variational Bayes for Multiway Covariances"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":2,"verified_fuzzy":24},"total_outbound_references":27},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2501.04935."}