{"as_of":"2026-08-14T17:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5be0d9df2cbb0841d40f2b6e133c00d5e05eda546d04c65ea59a5c0e4c671641","coverage":[{"denominator":77,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":77,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T14:30:39.144769Z","state":"measured"},{"denominator":77,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":77,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2508.21396/citation-record","integrity":"/paper/2508.21396/integrity","json":"/paper/2508.21396/citation-record.json","paper":"/paper/2508.21396"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:30:33.204164Z","title":"Sidiropoulos","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.204164Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:8070351b903fa0fd11f86cdefb2f3a80c6d4ec30156ee363ee4de3163a6c17da","observation_id":"87bfad03-cc59-47f2-af15-46265c69561f","resolution":{"observed_at":"2026-08-05T14:30:33.204164Z","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":"2022.31584","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:30:42.567158Z","title":"Sidiropoulos","venue":null,"work_id":"51c5ce35-a292-403c-bb1b-1d1e10315515","year":2022},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.254846Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:75fb589cad343fe8c3d1f590555c554ddabf2aa2b3f4acece5e8a20cb0e5455d","observation_id":"0bf99c31-987b-4d18-97b5-f0cd89360f02","resolution":{"observed_at":"2026-08-05T14:30:42.643776Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:50.152647Z","title":"Kakade, and Matus Telgarsky","venue":null,"work_id":"30489448-d514-4974-abbd-e185f68a1384","year":2014},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.332315Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:5879eec9d8ee7e3e984330a1909562a3afb4b83ccfe5b60e88cdc541599e7ce3","observation_id":"cdd26d92-5b82-4c68-8e93-89cbd0d652fb","resolution":{"observed_at":"2026-08-05T14:30:50.220228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:49.966081Z","title":"The more, the merrier: The blessing of dimensionality for learning large G aussian mixtures","venue":null,"work_id":"0a1ca1ee-663f-4d31-9f74-3ba4a1ffb5eb","year":2014},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.387661Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:fdb05791f351db47cc6b64eda2f49e7df6c2620fd067100e03d821936cabc6c2","observation_id":"bf8b3985-ae5f-4fe0-bb69-8b74bec86e9a","resolution":{"observed_at":"2026-08-05T14:30:50.038996Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.15150","last_updated":"2023-07-04T17:26:07Z","snapshot_observed_at":"2026-08-13T16:13:43.625034Z","submitted_at":"2022-03-28T23:53:48Z","title":"Tight Bounds on the Hardness of Learning Simple Nonparametric Mixtures","version":3},"cited_work":{"arxiv_id":"2203.15150","doi":"10.48550/arxiv.2203.15150","metadata_source":"pith","pith_arxiv_id":"2203.15150","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Tight Bounds on the Hardness of Learning Simple Nonparametric Mixtures","venue":"cs.LG","work_id":"ca01658b-6e70-4f9a-9c71-b34d7cbaaa78","year":2022},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.456566Z"},"links":{"cited_paper":"/paper/2203.15150","citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:1ddc1079b18ce8bfa44e1d95d4ebb6d50fa0acfe6e88c414b9832a9c02563ab6","observation_id":"19d090d1-2986-4309-b568-184ed83e3613","resolution":{"observed_at":"2026-08-05T14:30:41.017492Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/22-aos2255","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Uniform consistency in nonparametric mixture models","venue":"The Annals of Statistics","work_id":"2e1ceee4-2165-41cc-b36f-ead530cfafc1","year":2023},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.504643Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:0aa9402ac303297267058334697d73b41cb58e8e6bd4451550dd6de798cbb242","observation_id":"f1805639-95b4-4136-b76e-c7988ea2fe59","resolution":{"observed_at":"2026-08-05T14:30:40.875754Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:33.572920Z","title":"Xing, and Pradeep Ravikumar","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.572920Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:abec97acbdcb0a92dc459df969684f2b71d3c9196e2e60d022a32db5be600120","observation_id":"a324056d-a1b1-4185-948d-a2bb183778eb","resolution":{"observed_at":"2026-08-05T14:30:33.572920Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1802.04397","last_updated":"2020-02-18T03:52:29Z","snapshot_observed_at":"2026-08-09T00:19:36.900827Z","submitted_at":"2018-02-12T23:53:52Z","title":"Identifiability of Nonparametric Mixture Models and Bayes Optimal Clustering","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1802.04397","snapshot_observed_at":"2026-08-05T14:30:33.646269Z","title":"Xing, and Pradeep Ravikumar","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.646269Z"},"links":{"cited_paper":"/paper/1802.04397","citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:28536972e774faded02f4e63bb0400fa4f7a4c4814b93a2dff288d176949cbbf","observation_id":"8b0c6350-5b12-432a-a40e-6d3f5da05b65","resolution":{"observed_at":"2026-08-05T14:30:33.646269Z","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":"10.1109/focs.2012.49","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Learning topic models -- going beyond svd","venue":null,"work_id":"9a209918-3113-4a36-901a-9bd56f3f778c","year":2012},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.734842Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:d4a46ddbdfb7b675e198e0857890d1f44aab63b0d6033cffb309d52f6f74ee30","observation_id":"73f02c9e-215f-4ed7-8f7d-6692b7f56fcd","resolution":{"observed_at":"2026-08-05T14:30:40.690682Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:49.711182Z","title":"A practical algorithm for topic modeling with provable guarantees","venue":null,"work_id":"080e8f64-c172-4c25-adfc-7f65daa57c51","year":2013},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.800002Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:098e9d8ffbf9f2221eb4263c89b24d2d97776bae218ef18f0be559dd1de895eb","observation_id":"2a372fdf-0c5a-49b0-b996-cb2c231901eb","resolution":{"observed_at":"2026-08-05T14:30:49.873197Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:49.530594Z","title":"Nearly tight sample complexity bounds for learning mixtures of gaussians via sample compression schemes","venue":null,"work_id":"d59e5c37-b6ec-429e-8143-d988e0d1643f","year":2018},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.847848Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:fdef01fa5b28e2d6d78d28b02ca1a451b6ac7b371c066c178770e80ffd9553d7","observation_id":"a7eea2ce-69be-496a-a1c7-766ca6e424e3","resolution":{"observed_at":"2026-08-05T14:30:49.618270Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1609/aaai.v32i1.11627","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Sample-efficient learning of mixtures","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","work_id":"34d32cbb-baa7-44b7-9013-6a5c7ba3f8e3","year":2018},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.921195Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:f12c94ec79d00c431978a712d73522c677d9af56e40432411726d70695bab445","observation_id":"bca5d4c3-de6a-48d2-a770-ed62c7cd9a80","resolution":{"observed_at":"2026-08-05T14:30:40.541578Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.07175","last_updated":"2020-10-26T23:40:33Z","snapshot_observed_at":"2026-08-10T01:19:59.787806Z","submitted_at":"2020-09-15T15:25:51Z","title":"The Direct Radial Basis Function Partition of Unity (D-RBF-PU) Method for Solving PDEs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.07175","snapshot_observed_at":"2026-08-05T14:30:33.986088Z","title":"Hunter and","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:33.986088Z"},"links":{"cited_paper":"/paper/2009.07175","citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:013dd4e3cb903126c53f01216201c81664616cba4527f8310965adeb640104eb","observation_id":"8888a4e6-4bf2-41cb-8646-a90d1f0b7a90","resolution":{"observed_at":"2026-08-05T14:30:33.986088Z","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":"2026-08-05T14:30:49.377120Z","title":"Latent dirichlet allocation","venue":null,"work_id":"5967ba73-cf74-42e2-83d5-f5f5860c037d","year":2001},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.051859Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:cf5f0e39e11bd2316a14b10db066b11bebdb69e62da92b007a8137231a973e5e","observation_id":"54793f88-5a87-4e4d-8afb-8d155a7c9167","resolution":{"observed_at":"2026-08-05T14:30:49.435548Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/15-aos1376","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Estimating multivariate latent-structure models","venue":"The Annals of Statistics","work_id":"0479cf46-db23-4569-b8e1-f8790f2763d2","year":2016},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.128295Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:92a0eeda0681fd5560504a0822e55609a326397923f5cbdb7bac00913e33198b","observation_id":"9540566f-4853-49f7-b967-07f557afe287","resolution":{"observed_at":"2026-08-05T14:30:40.367735Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:49.136280Z","title":"The optimal approximation factor in density estimation","venue":null,"work_id":"d2515383-11ea-4643-886e-c489baa8e159","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.239044Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:676f5a44d36cd3acfd816ecf513ed39be29eb83e8da350c6eff06857a4e16f73","observation_id":"edf6c89f-c134-421a-a43f-18041e1bc2bc","resolution":{"observed_at":"2026-08-05T14:30:49.235436Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:34.301756Z","title":"Bruni and G","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.301756Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:e49850c85a8b6cd1500dbdde5d1d398763b7732d0432ccee6c31cb466fe5aeb4","observation_id":"8f6784de-b41e-4d25-97f5-d854c16aaec3","resolution":{"observed_at":"2026-08-05T14:30:34.301756Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.17209","last_updated":"2024-10-22T16:47:32Z","snapshot_observed_at":"2026-08-13T00:21:06.686964Z","submitted_at":"2024-04-26T07:34:39Z","title":"Generalized multi-view model: Adaptive density estimation under low-rank constraints","version":3},"cited_work":{"arxiv_id":"2404.17209","doi":"10.48550/arxiv.2404.17209","metadata_source":"pith","pith_arxiv_id":"2404.17209","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Generalized multi-view model: Adaptive density estimation under low-rank constraints","venue":"math.ST","work_id":"2f71ac67-c644-4b73-9a28-3838599647ef","year":2024},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.356612Z"},"links":{"cited_paper":"/paper/2404.17209","citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:cbed8b5d7f857334559055c0ae0a50ae9e56ef31e853079ee510c9d5d9dd48db","observation_id":"64906eee-98b2-42fd-8397-c8c28f23e848","resolution":{"observed_at":"2026-08-05T14:30:40.184443Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:48.928110Z","title":"The sample complexity of semi-supervised learning with nonparametric mixture models","venue":null,"work_id":"b6c5708d-fbff-4ba3-8deb-b12f3e1283e7","year":2018},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.432054Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:7cfc1c025e0fc3d13326911708e565d67d3e86af439eb93e13af776863d47a63","observation_id":"66472878-0203-4a0c-aec5-4a2d7163a81b","resolution":{"observed_at":"2026-08-05T14:30:49.028237Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:48.628500Z","title":"Image anomaly detection with generative adversarial networks","venue":null,"work_id":"294039bf-43a4-466d-bca5-8a81d028abc3","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.499958Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:a560be71f5f50f8f103440f38eba8c412df5995e684245af3590ea2d26f39b12","observation_id":"086220d8-fb95-4d5e-a99d-872314a003cf","resolution":{"observed_at":"2026-08-05T14:30:48.806814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:34.578573Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.578573Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:5dc588f86c28751d91677ec4567f42b9fbcddd85333f8ed44ca4533121b027da","observation_id":"7d27c13d-66b7-4106-ba78-dba09e97449b","resolution":{"observed_at":"2026-08-05T14:30:34.578573Z","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":"2026-08-05T14:30:48.401790Z","title":"Devroye and L","venue":null,"work_id":"cea49811-d629-4e57-84bf-53da56ea576d","year":1985},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.643768Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:8c7e57ad400574d3b2b2e0df9a500fbce4d45e754d59ed16f6570e9722c8f223","observation_id":"7e8d4e6e-c52f-4643-ae51-cc0349ff5c15","resolution":{"observed_at":"2026-08-05T14:30:48.496989Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:48.146442Z","title":"Devroye and G","venue":null,"work_id":"5f6d9009-8d3e-4fee-a5fb-4a90bf048a68","year":2001},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.715743Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:127a3849b1b16ff7791efec06a26a2cc958f7436ca20906ab6bb325dc86c4909","observation_id":"c01318e8-1ffb-433f-9261-9c07d20aa0ed","resolution":{"observed_at":"2026-08-05T14:30:48.289646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:47.953287Z","title":"An application of classical invariant theory to identifiability in nonparametric mixtures","venue":null,"work_id":"c83a2bdf-72fa-4957-b708-9f45bfe13290","year":2005},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.804305Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:88c4932500ba7c5e9f6273df3fa7522a9421e760ad6166c63e944bd8d468d198","observation_id":"a01cf1b4-7779-4f65-9c65-76e2fb3a7e7b","resolution":{"observed_at":"2026-08-05T14:30:48.012225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:47.812622Z","title":"Deep anomaly detection using geometric transformations","venue":null,"work_id":"c48fea46-2fc0-4bb2-b500-7e503645157b","year":2018},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:34.880507Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:b66e5f9cb63e11a51c0dfa36e1318382362672cba84c07c119346b2ffa54ad31","observation_id":"d98f8531-f29d-4bd2-8b4b-1597093d3d2b","resolution":{"observed_at":"2026-08-05T14:30:47.863814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.21437/interspeech.2005-624","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"A distance measure between gmms based on the unscented transform and its application to speaker recognition","venue":null,"work_id":"bbf216cb-d6f0-446c-9bae-0775e43a5651","year":2005},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.012015Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:8233ff248a8a539087ad787f1df4ed92d77a7010f056cd3424cab0ce63f43e0d","observation_id":"225055b1-e9da-4024-9020-a67057567e2a","resolution":{"observed_at":"2026-08-05T14:30:40.008962Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:47.671278Z","title":"Nonparametric estimation of component distributions in a multivariate mixture","venue":null,"work_id":"46083445-caad-421d-ad27-e91df1b162cc","year":2003},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.190713Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:0f815a618387823e020becff4b2a798cac61cac32bcc1f29c225f68ec021602b","observation_id":"4aeb30db-eda1-4152-a420-9eead34b08cf","resolution":{"observed_at":"2026-08-05T14:30:47.729317Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:47.535619Z","title":"Nonparametric inference in multivariate mixtures","venue":null,"work_id":"fdc8bede-24de-4e49-be84-a77a7cf129f6","year":2005},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.369333Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:0a76a992b0086fb6f2daadb7e655189909e68a509467a2e2e0787ddc88335a72","observation_id":"a0871355-b96e-40e2-b49a-3d19bb699203","resolution":{"observed_at":"2026-08-05T14:30:47.607231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:35.486831Z","title":"Harris, K","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.486831Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:806f0843a3764b834411eea80b36ed9f78f08225162d2d2a05a3443734b85ef2","observation_id":"e0e0901c-a928-4995-9669-f0c6e607fd96","resolution":{"observed_at":"2026-08-05T14:30:35.486831Z","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":"2026-08-05T14:30:47.402852Z","title":"Deep anomaly detection with outlier exposure","venue":null,"work_id":"1f699374-6ab1-4b39-b4d3-624a7b80342c","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.554257Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:1402d3ee1b8ee38573289c898fde4513e25f2f445c095c236ade5168f123d7f7","observation_id":"e82780aa-efc1-4919-b5f0-50d4cd25aba1","resolution":{"observed_at":"2026-08-05T14:30:47.448445Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:47.279618Z","title":"Using self-supervised learning can improve model robustness and uncertainty","venue":null,"work_id":"c70bd345-42f1-4b85-940e-7abb0d09dc7c","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.620157Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:da753c9ab72b1946e3409d3fe52bf98c494a1d1dffd1d40a3ad1da665b2931c0","observation_id":"37f33da6-f4ed-4f0b-af55-16c76aed31e0","resolution":{"observed_at":"2026-08-05T14:30:47.314849Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/16-aos1444","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Convergence rates of parameter estimation for some weakly identifiable finite mixtures","venue":"The Annals of Statistics","work_id":"dd5ab426-5458-47ea-be5a-a0c8952bdf5a","year":2016},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.680848Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:b6762090fbac92dbbfbc2afb94c2cc87dd1f348acf0f8a5737cd0f8c640b127c","observation_id":"f0beaa7b-83c5-41ee-b836-1ba7a8f108cd","resolution":{"observed_at":"2026-08-05T14:30:39.807873Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:35.752479Z","title":"Dasvdd: Deep autoencoding support vector data descriptor for anomaly detection","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.752479Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:7a91ae853d4fc7c176a3b4b10a52fb1464526ec2933839fc2b186f2ac81a99d5","observation_id":"16881fba-d521-41fa-99d5-a9e2fd5f6fbd","resolution":{"observed_at":"2026-08-05T14:30:35.752479Z","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":"2026-08-05T14:30:47.149544Z","title":"Nonlinear ica using auxiliary variables and generalized contrastive learning","venue":null,"work_id":"c3d9050a-a2ea-47bf-8c44-138fe9a537a1","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.839017Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:87424837019b42a324d292802297c343be0444f9c3d7a5af3ab0c20746b48810","observation_id":"1eba6e8a-7c57-47ee-bcfb-c5ae40ae3041","resolution":{"observed_at":"2026-08-05T14:30:47.206168Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:47.001522Z","title":"Sidiropoulos","venue":null,"work_id":"6c12a371-0ebb-445c-aacc-e9a13ea8999d","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.919813Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:31214b404ea820e36fd776ee3b924de8cd4d1d20cd9a09b474a6d9acaf3e79c5","observation_id":"339375b9-ab79-4b3b-b78a-4a3652b0d1f1","resolution":{"observed_at":"2026-08-05T14:30:47.052341Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:46.857154Z","title":"Variational autoencoders and nonlinear ica: A unifying framework","venue":null,"work_id":"7bd125a5-e644-4862-9f99-fd76156b2e0f","year":2020},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:35.994993Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:05935fd4a12baf112dd6d26eb0524298b872862308933d3a7556a2356ef7d614","observation_id":"6f84800d-ff40-4fa5-a991-49312e0c3c5b","resolution":{"observed_at":"2026-08-05T14:30:46.926819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:46.695381Z","title":null,"venue":null,"work_id":"7aa85504-8dd4-45e6-92a4-3c304b0f4e8a","year":2012},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.088984Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:be2722797d9e90f385560a8efb723327b9ecc4407381a01d03b8efbf8557167a","observation_id":"8e230981-6b7c-41c4-b0bf-ec383da2b218","resolution":{"observed_at":"2026-08-05T14:30:46.772553Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:46.539770Z","title":"Identifiability of deep generative models without auxiliary information","venue":null,"work_id":"b0b0ab35-7860-4d9b-ad6e-720f9194ea71","year":2022},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.165215Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:62de4af187fa76995909e38947a07a2eb5d2eda3577694db2c1f6ed73d7c4585","observation_id":"804de05e-11a2-42a3-bcbb-3fc91725d936","resolution":{"observed_at":"2026-08-05T14:30:46.601393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/20-aos2032","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Estimation of the number of components of nonparametric multivariate finite mixture models","venue":"The Annals of Statistics","work_id":"1b78066e-9aee-41bf-bc51-f19d9eed8e6e","year":2021},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.221339Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:1fef3e1fc33cf5bbdc43b45ed0ff8107483c2fd97908be233747f648fad22e92","observation_id":"0aaeb3d6-f52a-4cac-997a-b9edaecd3e6a","resolution":{"observed_at":"2026-08-05T14:30:39.645129Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:46.418860Z","title":"The em algorithm gives sample-optimality for learning mixtures of well-separated gaussians","venue":null,"work_id":"79bc0ff3-c471-45ae-b424-3b9bd078f0f1","year":2020},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.308667Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:0a685f842309e2162b607889667db1e803b8eb4c096d1707ab3ecf4c7e20bfff","observation_id":"466fd542-2417-45f0-8bcd-6e49d37cda47","resolution":{"observed_at":"2026-08-05T14:30:46.451353Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:36.356987Z","title":"Numba: A llvm-based python jit compiler","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.356987Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:7c367f49f8801e5fa7c22ce74a89eee7c816c5787ebcabda7a82a8750352ccb3","observation_id":"53cd9986-26e6-460d-a42a-bd30a35e64ff","resolution":{"observed_at":"2026-08-05T14:30:36.356987Z","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":"2026-08-05T14:30:46.282971Z","title":"Vandermeulen, Billy Joe Franks, Klaus Robert Muller, and Marius Kloft","venue":null,"work_id":"5490092c-8d8c-4fe5-a67b-ac893b1a4f4d","year":2022},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.431887Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:1e0d9d5702219a0e37b6728c282d0fb745a0755aeccecf791a26bd879d55effc","observation_id":"7638f796-f40d-4d73-9635-4dde12958015","resolution":{"observed_at":"2026-08-05T14:30:46.330292Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0712.2869","last_updated":"2007-12-18T03:30:05Z","snapshot_observed_at":"2026-08-02T10:20:49.019377Z","submitted_at":"2007-12-18T03:30:05Z","title":"Density estimation in linear time","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0712.2869","snapshot_observed_at":"2026-08-05T14:30:36.492278Z","title":"Density estimation in linear time","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.492278Z"},"links":{"cited_paper":"/paper/0712.2869","citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:8fb445233142f24deff81ccebb4353eecde42f45d852d9123135b7596920c082","observation_id":"3b44f919-f86c-431c-9e96-0a9c59782fe7","resolution":{"observed_at":"2026-08-05T14:30:36.492278Z","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":"2026-08-05T14:30:46.185296Z","title":"Minimax Density Estimation for Growing Dimension","venue":null,"work_id":"52b6f26b-3ee5-4a80-b537-5fcecce86dd5","year":2017},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.558509Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:3f6e209da6b9999e283e1f9ea3dcdae589ad6589137ce0b59175e367425bb97d","observation_id":"e605df5d-f5eb-41ed-9ee8-aa9cf82bf49d","resolution":{"observed_at":"2026-08-05T14:30:46.221099Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:46.018832Z","title":"Do deep generative models know what they don't know? In International Conference on Learning Representations, 2019","venue":null,"work_id":"95bdba09-b9fe-4e00-a809-8079e07fcb34","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.626857Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:8774b4df3ceca9b440460aa311058b640299f9cc22416499c2c602b120918707","observation_id":"022e814f-9859-4de1-879a-111535e8095b","resolution":{"observed_at":"2026-08-05T14:30:46.095734Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1708.00568","last_updated":"2021-06-08T07:15:29Z","snapshot_observed_at":"2026-08-09T03:25:01.791290Z","submitted_at":"2017-08-02T01:05:19Z","title":"On $w$-mixtures: Finite convex combinations of prescribed component distributions","version":3},"cited_work":{"arxiv_id":"1708.00568","doi":"10.48550/arxiv.1708.00568","metadata_source":"pith","pith_arxiv_id":"1708.00568","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"On $w$-mixtures: Finite convex combinations of prescribed component distributions","venue":"cs.LG","work_id":"dac3ea13-3b83-4999-8ea2-b81bb92843e2","year":2017},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.720573Z"},"links":{"cited_paper":"/paper/1708.00568","citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:c1b2f65f775e6a1ac0b0e5cd2c72724b297b780c4bc452a7fe1827ab8532d521","observation_id":"54ff9c7a-e84d-4ce6-8a17-58b3319c7bdf","resolution":{"observed_at":"2026-08-05T14:30:39.518156Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:45.861823Z","title":"Pedregosa, G","venue":null,"work_id":"77910ad6-8182-43b1-87ee-753bba035c0e","year":2011},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.802251Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:a29db05395ae91bedd2d793b24261a51c4061ebe70a8abeb9721b5a68cb44a88","observation_id":"b05b3168-ad3a-40e1-81d6-908029a5caf9","resolution":{"observed_at":"2026-08-05T14:30:45.938471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:45.730920Z","title":"Pedregosa, G","venue":null,"work_id":"2d8218de-d865-4de1-967f-4fbe946f5896","year":2011},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.868289Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:b0fbaf03b9765f7f36c03d84f8b7e0cbcc8eb9844c47617dc346d80f4b78df15","observation_id":"21a1bb30-32ff-4d89-92aa-5125079694fe","resolution":{"observed_at":"2026-08-05T14:30:45.778630Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:45.547456Z","title":null,"venue":null,"work_id":"de71a4d1-4545-4b10-9525-e12ca3a10087","year":1989},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.902235Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:deac6577c7d5c983bbdd8485fbee5588e09607250c820128a992a64310b12417","observation_id":"63433db6-0647-451e-a40a-4ed852d67cc9","resolution":{"observed_at":"2026-08-05T14:30:45.625980Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:45.385075Z","title":"Consistent estimation of identifiable nonparametric mixture models from grouped observations","venue":null,"work_id":"2775f454-e019-416e-99b6-ccd754e87b96","year":2020},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:36.960080Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:82769d0dada438c7196446007f154705390431044488ce5c45e5977d91f88978","observation_id":"b6b968d2-18f8-45d6-a686-f369aa1f3419","resolution":{"observed_at":"2026-08-05T14:30:45.452852Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:37.023239Z","title":"Deep one-class classification","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.023239Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:84ed3a6835fe0bd4faf5860a3f92b87d38868660a96b8667026f68b39344abe5","observation_id":"aed94132-03b1-4d5a-bf10-ab9f02adb2fd","resolution":{"observed_at":"2026-08-05T14:30:37.023239Z","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":"2026-08-05T14:30:37.079708Z","title":"Kauffmann, Robert A","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.079708Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:de3e61104625f300878c18faf1c52e8c733fab924d7b61aea39dc5a7c4a218c5","observation_id":"35f71b17-edd5-41a5-86c4-57371959b09c","resolution":{"observed_at":"2026-08-05T14:30:37.079708Z","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":"2026-08-05T14:30:37.155037Z","title":"A Useful Convergence Theorem for Probability Distributions","venue":null,"work_id":null,"year":1947},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.155037Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:bfe26504745ea2c72595bd1db2e93ef194fe381495b7988719d5fc2021d87c6d","observation_id":"727a1f79-6b76-43b7-9400-d27680abc18f","resolution":{"observed_at":"2026-08-05T14:30:37.155037Z","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":"2026-08-05T14:30:45.197237Z","title":"Waldstein, Ursula Schmidt-Erfurth, and Georg Langs","venue":null,"work_id":"4de3ab6b-191a-455f-a086-ce33fe2f2b59","year":2017},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.219325Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:ed5da4c47dc39964dacaf49286ffa413c04a662642d57db3f3c8cc7261651394","observation_id":"b6c470d6-3281-486e-9305-c015304909e2","resolution":{"observed_at":"2026-08-05T14:30:45.269413Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:37.291338Z","title":"Waldstein, Georg Langs, and Ursula Schmidt-Erfurth","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.291338Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:09d8631f9e4602f57ad98dfa4bd2a1b5c8d0566c2537a819cdef1f738a961abc","observation_id":"f84fc68e-059d-401d-8764-1f9d63bd4ad8","resolution":{"observed_at":"2026-08-05T14:30:37.291338Z","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":"2026-08-05T14:30:45.066579Z","title":null,"venue":null,"work_id":"356c1cb2-f806-4640-a265-131c7c025211","year":1986},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.355667Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:394b50291df231f29924caa16938c457907df80f928d03bdff04ca3bdb36450d","observation_id":"48736039-e96d-42fd-92b3-97942d7addb8","resolution":{"observed_at":"2026-08-05T14:30:45.126993Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:44.880970Z","title":"Robust low rank kernel embeddings of multivariate distributions","venue":null,"work_id":"24b7f74f-aaa5-40a9-bd14-45e5b350b588","year":2013},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.435298Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:a9a62d5ac38b011061199f32822d40559759d86d68cb2e35000465a98e36ebc8","observation_id":"51aa109d-1c98-459d-9d3f-e441d170a998","resolution":{"observed_at":"2026-08-05T14:30:44.955366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:44.722646Z","title":"Nonparametric estimation of multi-view latent variable models","venue":null,"work_id":"9da26558-fb25-442d-a9be-dff58db6ef67","year":2014},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.505628Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:9f86110a35b38df01be958429cf5463d9e287f7f0c62b1e3d87331ec3d88595d","observation_id":"68c01b0c-6a70-4424-bbb7-59bb2c7caa6a","resolution":{"observed_at":"2026-08-05T14:30:44.807020Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:37.681446Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.681446Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:75ee0c3bb95bd58d86518bc403355435bcedb58d62d322271ff8d6b654c8a647","observation_id":"ccb3eb93-09bb-4030-94f5-36a059073d4c","resolution":{"observed_at":"2026-08-05T14:30:37.681446Z","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":"2026-08-05T14:30:44.527052Z","title":"Csi: Novelty detection via contrastive learning on distributionally shifted instances","venue":null,"work_id":"7d5c4228-def9-4bf8-94a7-867f4f554c4e","year":2020},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.691027Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:0dc96e271e01c11e5eba3d548e3b8231e608bd4396093ba1f38fcd118a618f3f","observation_id":"cc756292-0479-43ee-974e-d215740b9520","resolution":{"observed_at":"2026-08-05T14:30:44.615446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:37.766341Z","title":"Identifiability of Finite Mixtures","venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.766341Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:277ecbdd81f01cece984ec2325a2a091d265014abfe5cf1ecfd4288b194a00a9","observation_id":"c52bbf52-9492-4efe-bf35-972dea63aa04","resolution":{"observed_at":"2026-08-05T14:30:37.766341Z","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":"2026-08-05T14:30:44.342672Z","title":"Identifiability of mixtures of product measures","venue":null,"work_id":"00907cb7-738b-429b-85d8-0692709d4372","year":1967},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:37.897282Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:b3eeb86b4cd9697962fb281603974e095981d9d4780c5bcbd0357f349a0d0b02","observation_id":"ed08f22f-d581-4821-bb26-be0398497a6e","resolution":{"observed_at":"2026-08-05T14:30:44.429163Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:44.108544Z","title":"Tsybakov","venue":null,"work_id":"80978e82-6a7b-4ec7-9085-a5aef312ff75","year":2009},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.018364Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:4171634c29da51abd8796d3654f1d0a7a0a3ee744b4b7ffaebbe6ca84cafbd3b","observation_id":"2d16598d-eb66-44ef-b34d-010dca95ac30","resolution":{"observed_at":"2026-08-05T14:30:44.213782Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.04292","last_updated":"2023-02-08T19:11:53Z","snapshot_observed_at":"2026-08-13T12:48:31.578274Z","submitted_at":"2023-02-08T19:11:53Z","title":"Sample Complexity Using Infinite Multiview Models","version":1},"cited_work":{"arxiv_id":"2302.04292","doi":null,"metadata_source":"pith","pith_arxiv_id":"2302.04292","snapshot_observed_at":"2026-08-05T14:30:41.543740Z","title":"Sample Complexity Using Infinite Multiview Models","venue":"math.ST","work_id":"fcf21672-3fc8-4116-81cd-62f75084e295","year":2023},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.123989Z"},"links":{"cited_paper":"/paper/2302.04292","citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:f74332ce22f93328f214a45445387d59f143b9fbd2115dce87e57d6c2e87ccca","observation_id":"4c1c9fa0-132a-4d23-8cf1-c1a420e08e1d","resolution":{"observed_at":"2026-08-05T14:30:41.618347Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:43.954256Z","title":"Beyond smoothness: Incorporating low-rank analysis into nonparametric density estimation","venue":null,"work_id":"d075a160-cbdf-46a2-b552-0b651d59623b","year":2021},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.202513Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:0b208627de2c9ee5087887247211b813828be7ff340f057dc5294dd5a2aebb57","observation_id":"5c019f84-f13a-4b42-aea5-847b0e9b4063","resolution":{"observed_at":"2026-08-05T14:30:44.022845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2024.33674","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T14:30:41.350548Z","title":"Vandermeulen and René Saitenmacher","venue":null,"work_id":"1067f0d6-1412-4c7c-8232-5f746733a458","year":2024},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.325305Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:1fa7aacc86ccb0b88e885d360aa1443bdebe18df169de7e3fb4cb633b4b04ced","observation_id":"5e81d633-d01f-44c9-b265-0a1b4c09bab2","resolution":{"observed_at":"2026-08-05T14:30:41.449156Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:43.751745Z","title":"An operator theoretic approach to nonparametric mixture models","venue":null,"work_id":"e34cdeb0-a6ae-4abf-9882-286cfdcd1446","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.401957Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:29da98187fc9994bc03f45902ae6406aefe97ac8bf6ca511a4f2d1fab1aa6d97","observation_id":"2175560c-58d0-4a58-bb83-c3fce96fabb8","resolution":{"observed_at":"2026-08-05T14:30:43.848057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:43.560409Z","title":"Vandermeulen, Wai Ming Tai, and Bryon Aragam","venue":null,"work_id":"7f291311-f2f8-46c8-a460-22aaf8c12dd3","year":2024},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.489063Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:9594e78d4f2f14319fc8aee52d8a1db9684c648d9ab7aec8992b2a28bea54db6","observation_id":"9df9e313-09ab-412b-a3c2-03f3c7f37f82","resolution":{"observed_at":"2026-08-05T14:30:43.649311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:43.368160Z","title":"Dimension-independent rates for structured neural density estimation","venue":null,"work_id":"3333cf2b-324f-4826-abfc-acf2e1ae4cda","year":2025},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.576550Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:4de2fab652a3ebabcf281269a9dde956d7e03814a6b6d0e049fb1a126d895021","observation_id":"4175354f-1498-4855-934a-ecb86bcd705f","resolution":{"observed_at":"2026-08-05T14:30:43.425491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:43.195225Z","title":"Vankadara, Sebastian Bordt, Ulrike von Luxburg, and Debarghya Ghoshdastidar","venue":null,"work_id":"cf0a5658-287a-4260-b736-c12dd3b2a4b6","year":2021},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.623634Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:0d47a9daab711d64c3d15ada0052a6414daecf9f97f6589af2cbb9f13c9cf19d","observation_id":"4d586f08-55d2-41ee-9a50-f162a344df82","resolution":{"observed_at":"2026-08-05T14:30:43.300443Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11222-017-9793-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Mclachlan","venue":"Statistics and Computing","work_id":"1f51bc69-1208-4667-9e9c-0b79c2a2312b","year":2019},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.670087Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:240a0f50f8019b3bc4b96db795cb60df8da5c862edd7c7b17f19e78e66cf8843","observation_id":"41635b51-8cf0-4325-9bcb-299059fc4a81","resolution":{"observed_at":"2026-08-05T14:30:39.374175Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:38.774947Z","title":"Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St \\'e fan J","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.774947Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:9902fd32d86b32bf7e271131a65032194f03408bed6413fb1e28fbaad3c1a5a1","observation_id":"c855bc12-751c-4c06-88d7-79758b96e5ee","resolution":{"observed_at":"2026-08-05T14:30:38.774947Z","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":"2026-08-05T14:30:43.052843Z","title":"An equal-size hard EM algorithm for diverse dialogue generation","venue":null,"work_id":"97bb34e9-cb46-4f99-950f-c08600ccd14d","year":2023},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.839209Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:f26b9bd1d6bb738ff447deca3fec8713300dfe2ebcbad677339691ee9402e8f0","observation_id":"78b52611-fbb2-4f75-b3e6-88a9d8c372f9","resolution":{"observed_at":"2026-08-05T14:30:43.094923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:42.902972Z","title":"On the identifiability of finite mixtures","venue":null,"work_id":"b669a7fe-5529-4199-a508-dad7eccb320c","year":1968},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.913755Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:18d54e29fd0bba59f7d1f5fc025b8d8746ef55caeaf27b2b48a48f5bb0f4393f","observation_id":"7f34b840-c0b8-4b1a-bfd6-0a01d577e5b5","resolution":{"observed_at":"2026-08-05T14:30:42.972059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-05T14:30:38.977435Z","title":"Yatracos","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:38.977435Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:605fb074b8529a1bb6a12b99a66fd0baae2b8782f6100283209833502dbbfd00","observation_id":"fd9b2603-3cbc-453e-882f-7b3c228c3868","resolution":{"observed_at":"2026-08-05T14:30:38.977435Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2111.07677","last_updated":"2021-11-16T06:33:39Z","snapshot_observed_at":"2026-08-13T17:34:01.767269Z","submitted_at":"2021-11-15T11:15:02Z","title":"FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.07677","snapshot_observed_at":"2026-08-05T14:30:39.055706Z","title":"FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:39.055706Z"},"links":{"cited_paper":"/paper/2111.07677","citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:a32434b396d65f5aa8db7ee5ee24a2247e98c1942bf98daaab0460ec60516c32","observation_id":"94f00d52-8328-41bd-a9d6-1bb6aebd604e","resolution":{"observed_at":"2026-08-05T14:30:39.055706Z","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":"2026-08-05T14:30:42.813970Z","title":"P-kdgan: progressive knowledge distillation with gans for one-class novelty detection","venue":null,"work_id":"06d2df75-3432-4efc-abe5-cec24af3e4e2","year":2021},"citing_paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-08-05T14:30:39.144769Z"},"links":{"citing_paper":"/paper/2508.21396"},"observation_digest":"sha256:502e7c2166f32aacbe959920ac2e0d45a00621151c3d3416b0395693b45cfbec","observation_id":"271f31f8-045d-4d1f-9bd2-bc3ad11396f7","resolution":{"observed_at":"2026-08-05T14:30:42.837737Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.21396","last_updated":"2025-08-29T08:14:53Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-10T14:32:21.955112Z","submitted_at":"2025-08-29T08:14:53Z","title":"PMODE: Theoretically Grounded and Modular Mixture Modeling"},"reference_resolution":{"displayed":77,"state_counts":{"malformed_identifier":0,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":22,"verified_exact":12,"verified_fuzzy":41},"total_outbound_references":77},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 77 of 77 outbound references and 0 inbound Pith citation observations for arXiv:2508.21396."}