{"as_of":"2026-08-15T23:59:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:26644e0763f67b04d5626306f5696ce3297858d00ee74874b97b55ee5054ddca","coverage":[{"denominator":113,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T15:22:26.631108Z","state":"measured"},{"denominator":100,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":100,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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/2608.01182/citation-record","integrity":"/paper/2608.01182/integrity","json":"/paper/2608.01182/citation-record.json","paper":"/paper/2608.01182"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.276971Z","title":"2026 , eprint=","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.276971Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:773389f3a5bd22b6408cb4b4f00122590c031617b585c085b1f9718158b1099e","observation_id":"d1314f5e-50cf-4fe2-b433-210bff9b025e","resolution":{"observed_at":"2026-08-15T15:22:26.276971Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.02260","last_updated":"2025-05-04T21:31:53Z","snapshot_observed_at":"2026-08-07T15:56:34.644843Z","submitted_at":"2025-05-04T21:31:53Z","title":"Weighted minimum $\\alpha$-Green energy problems","version":1},"cited_work":{"arxiv_id":"2505.02260","doi":"10.48550/arxiv.2505.02260","metadata_source":"pith","pith_arxiv_id":"2505.02260","snapshot_observed_at":"2026-08-15T18:16:14.067578Z","title":"Weighted minimum $\\alpha$-Green energy problems","venue":"math.CA","work_id":"0a682b2b-7e3d-4122-a530-b64bf0a315cf","year":2025},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.282800Z"},"links":{"cited_paper":"/paper/2505.02260","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:1e34d07709f1fd00806b3e6f32d1d56b77e2c1494f99bc6790ad535c8e98ed02","observation_id":"4796bbcd-a0e5-413f-bd6d-1bc75e2c0c69","resolution":{"observed_at":"2026-08-15T15:22:26.755319Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.12418","last_updated":"2023-03-13T08:19:03Z","snapshot_observed_at":"2026-08-13T16:34:29.645008Z","submitted_at":"2022-02-24T23:29:42Z","title":"On the role of the point at infinity in Deny's principle of positivity of mass for Riesz potentials","version":2},"cited_work":{"arxiv_id":"2202.12418","doi":null,"metadata_source":"pith","pith_arxiv_id":"2202.12418","snapshot_observed_at":"2026-08-15T15:22:26.973519Z","title":"On the role of the point at infinity in Deny's principle of positivity of mass for Riesz potentials","venue":"math.CA","work_id":"c0700c64-526a-4b2f-ac26-4e716eed9228","year":2022},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.287078Z"},"links":{"cited_paper":"/paper/2202.12418","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:7baa50bd774d832fa7216859db7d58c1253cd701088225cb9e6e989c77eaebce","observation_id":"e19835c6-f123-4d42-adcb-f7c8ec5361fa","resolution":{"observed_at":"2026-08-15T15:22:26.978137Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.03733","last_updated":"2022-05-18T12:22:01Z","snapshot_observed_at":"2026-08-13T19:43:38.644990Z","submitted_at":"2021-04-08T12:35:14Z","title":"Riesz energy problems with external fields and related theory","version":3},"cited_work":{"arxiv_id":"2104.03733","doi":null,"metadata_source":"pith","pith_arxiv_id":"2104.03733","snapshot_observed_at":"2026-08-15T15:22:26.957588Z","title":"Riesz energy problems with external fields and related theory","venue":"math.CA","work_id":"374e0613-d9d5-4a1c-96d0-77891c9b3620","year":2021},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.291047Z"},"links":{"cited_paper":"/paper/2104.03733","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:dfda11d7cf76e4948844a27eddebe4370a568dc83c5cdd424795a436e5cb9519","observation_id":"773bf7d3-066e-445b-8a55-adebf6002568","resolution":{"observed_at":"2026-08-15T15:22:26.961619Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1507.07356","last_updated":"2015-09-14T19:09:40Z","snapshot_observed_at":"2026-08-15T21:41:04.327770Z","submitted_at":"2015-07-27T10:38:20Z","title":"Ten equivalent definitions of the fractional Laplace operator","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1507.07356","snapshot_observed_at":"2026-08-15T15:22:26.295314Z","title":"Fractional Calculus and Applied Analysis , volume =","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.295314Z"},"links":{"cited_paper":"/paper/1507.07356","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:d747f882bfe1b62c1f88b913d140400e19968e5e8336042ee0ae5313e58671f6","observation_id":"ffd6c9b1-012f-4c03-a099-170352036091","resolution":{"observed_at":"2026-08-15T15:22:26.295314Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.12579","last_updated":"2026-07-29T17:47:30Z","snapshot_observed_at":"2026-08-15T13:24:12.326640Z","submitted_at":"2026-07-14T09:49:46Z","title":"Wasserstein gradient flows for Coulomb discrepancies","version":2},"cited_work":{"arxiv_id":"2607.12579","doi":"10.48550/arxiv.2607.12579","metadata_source":"pith","pith_arxiv_id":"2607.12579","snapshot_observed_at":"2026-08-15T18:16:14.067578Z","title":"Wasserstein gradient flows for Coulomb discrepancies","venue":"math.AP","work_id":"37ea1f3c-a1dd-49cc-9595-ec733ab6c0d6","year":2026},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.299958Z"},"links":{"cited_paper":"/paper/2607.12579","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:841d889c0c574fa29663843aaa237587ba18cfe331e78985c6f3112386ffcd8a","observation_id":"b3dd6b24-e079-45fd-874f-b53bea07f964","resolution":{"observed_at":"2026-08-15T15:22:26.740110Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.303736Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.303736Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:3b13aaacf3470220de1f03d564fa3925337a787e5ccb7a783340e230df7c079d","observation_id":"4efe2211-0cba-44e9-99ff-a5290df737df","resolution":{"observed_at":"2026-08-15T15:22:26.303736Z","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":"2026-08-15T15:22:26.307250Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.307250Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:43e617cb01c70e1989685eb4d07954774928b94bc3da36f69aa9b3d9cdbfb95b","observation_id":"0dce49a2-a4f5-4be4-8b02-827b099e0859","resolution":{"observed_at":"2026-08-15T15:22:26.307250Z","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":"2026-08-15T15:22:26.310668Z","title":"doi:10.1007/BFb0103945 , isbn =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.310668Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:2a0d8d3df70969a153f67d77d449a8a6da5448a03aef0b35e2c54a7d22abb1af","observation_id":"5495fcef-22cb-407c-b696-b958b65e074b","resolution":{"observed_at":"2026-08-15T15:22:26.310668Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.18497","last_updated":"2026-06-09T11:42:00Z","snapshot_observed_at":"2026-08-14T21:33:54.994410Z","submitted_at":"2026-05-18T14:49:52Z","title":"Sharp Rates of MMD Empirical Estimation with Power Kernels","version":2},"cited_work":{"arxiv_id":"2605.18497","doi":null,"metadata_source":"pith","pith_arxiv_id":"2605.18497","snapshot_observed_at":"2026-08-15T15:22:26.929661Z","title":"Sharp Rates of MMD Empirical Estimation with Power Kernels","venue":"math.PR","work_id":"54705fc0-128a-44d8-b9f9-6d3bbad0957e","year":2026},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.314274Z"},"links":{"cited_paper":"/paper/2605.18497","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:df676f39160910a17ae7e5ce9969208ec88727ded4980208c926fdd364e2cab1","observation_id":"1a27e4f9-59eb-4f56-b05f-5c15d048fb77","resolution":{"observed_at":"2026-08-15T15:22:26.933811Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.318121Z","title":"International Conference on Learning Representations , volume=","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.318121Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:b4b007ffb6c34f8bb751cefe93fe1a04aa23ad86b2edfe88757626a8a044be5a","observation_id":"aa943fa4-64cd-414b-ba16-677e7c6b4bfd","resolution":{"observed_at":"2026-08-15T15:22:26.318121Z","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":"2026-08-15T15:22:26.321590Z","title":"2015 , eprint=","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.321590Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:c3f9ad844b9e0df41fa718c959d5e388f60cca1f8dbd5ef6a444dc1ed3f3bf42","observation_id":"da6c2e11-7e18-40c8-ba98-7aceb3d82610","resolution":{"observed_at":"2026-08-15T15:22:26.321590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1609.01780","last_updated":"2018-02-18T13:05:27Z","snapshot_observed_at":"2026-08-14T21:41:03.694293Z","submitted_at":"2016-09-06T22:38:49Z","title":"On Kato-Ponce and fractional Leibniz","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.01780","snapshot_observed_at":"2026-08-15T15:22:26.325370Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.325370Z"},"links":{"cited_paper":"/paper/1609.01780","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:33d6866ff97c234c4e1bf18f808a418af375c2df238b14561d6690b578f9efaa","observation_id":"c1d5a585-714f-4188-94b4-ad83adf891c0","resolution":{"observed_at":"2026-08-15T15:22:26.325370Z","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":"2026-08-15T15:22:26.329048Z","title":"ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pages=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.329048Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:55d4b2a6d991fe2c04e3b934508d691418fcc0f83ad85a3d60edc300ea03768f","observation_id":"cf229926-7b57-4a1f-8404-9d26e5ce9b95","resolution":{"observed_at":"2026-08-15T15:22:26.329048Z","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":"2026-08-15T15:22:26.332144Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.332144Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:aed054610fce76eacc9f378a71037394860381d97f1806902802ac53f666fcb7","observation_id":"926c803f-844e-4fac-9bb0-950aeda1a50a","resolution":{"observed_at":"2026-08-15T15:22:26.332144Z","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":"2026-08-15T15:22:26.335511Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.335511Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:454fbef6660f7919570831adce93acd8bb47e3bc97f31e67f8a309978a405133","observation_id":"3cb9f28f-31b9-4225-9845-c8dbd857e97a","resolution":{"observed_at":"2026-08-15T15:22:26.335511Z","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":"cocv/2025097","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.899630Z","title":"ESAIM Control Optim","venue":null,"work_id":"def15e23-516f-4203-8f7b-a6e8d139664d","year":2026},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.338696Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:be5d85a2a7c7b5c290abe54334f8011e4691bf31f79049e7b3a3f0ffdb703984","observation_id":"6f230926-dd8e-40e3-b28b-9fa5a8c68371","resolution":{"observed_at":"2026-08-15T15:22:26.905898Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.342264Z","title":"Conference on learning theory , pages=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.342264Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:5d1f77fcab376b663a3254d4d9196d509bb8a62379eabca9df5f0dbc0ceb62f0","observation_id":"a6bf08a8-48b2-414d-95e6-d4fd95461fb0","resolution":{"observed_at":"2026-08-15T15:22:26.342264Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1805.00915","last_updated":"2019-07-30T14:20:51Z","snapshot_observed_at":"2026-08-14T19:19:34.850219Z","submitted_at":"2018-05-02T17:23:42Z","title":"Trainability and Accuracy of Neural Networks: An Interacting Particle System Approach","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1805.00915","snapshot_observed_at":"2026-08-15T15:22:26.345392Z","title":"Communications on Pure and Applied Mathematics , volume=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.345392Z"},"links":{"cited_paper":"/paper/1805.00915","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:9f5058c0c07e71c71d5c288313fa1aa36062319b7289910663741528e97acc67","observation_id":"6b85957a-ed9f-42dc-8789-c698e79858fe","resolution":{"observed_at":"2026-08-15T15:22:26.345392Z","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":"2026-08-15T15:22:26.348997Z","title":"Stochastic Processes and their Applications , volume=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.348997Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:131528aac7396c7e9b28c558aa122178b92c0eecb335d9a665d28e720b59d7af","observation_id":"e7b0bf1d-bda3-4069-9984-4d67772df816","resolution":{"observed_at":"2026-08-15T15:22:26.348997Z","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":"2026-08-15T15:22:26.352152Z","title":"NeurIPS , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.352152Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:ebf5ed8d0555fdde2cd7894d81701c8934b24684d7669a99415acd5aba624a42","observation_id":"3db29058-49a8-4330-8c46-2a83898675b5","resolution":{"observed_at":"2026-08-15T15:22:26.352152Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.14917","last_updated":"2024-04-07T09:08:29Z","snapshot_observed_at":"2026-08-13T00:48:12.954746Z","submitted_at":"2024-03-22T02:41:57Z","title":"Mean-field Analysis on Two-layer Neural Networks from a Kernel Perspective","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.14917","snapshot_observed_at":"2026-08-15T15:22:26.355447Z","title":"Proceedings of the 41st International Conference on Machine Learning , series=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.355447Z"},"links":{"cited_paper":"/paper/2403.14917","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:970347125e06350b076d4d0cb06e4f1c172c996943c292f97791b72635212289","observation_id":"239a683d-0cf6-46f6-be74-67ea18af1074","resolution":{"observed_at":"2026-08-15T15:22:26.355447Z","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":"2026-08-15T15:22:26.358938Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.358938Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:87562b65e2b3809276c0c3c311d71eebc44151f49f02410a72ff683effecbe25","observation_id":"0c9f3484-734e-42b5-99a6-036e731f944f","resolution":{"observed_at":"2026-08-15T15:22:26.358938Z","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":"2026-08-15T15:22:26.361658Z","title":"4: applications of harmonic analysis , author=","venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.361658Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:1f112eb4196f3bcb3c2ceb7070ef73b761ab750182a46fa7cd2aae5fadb47df5","observation_id":"2ff3f17c-584c-40ac-bf99-3505146772c2","resolution":{"observed_at":"2026-08-15T15:22:26.361658Z","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":"2026-08-15T15:22:26.364382Z","title":"2019 , publisher=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.364382Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:eae6ee21e4f34b6ba9acde5500eb0013b581b1b64a3d095c626589f145821612","observation_id":"ebf24835-196e-4779-add8-31882a942b95","resolution":{"observed_at":"2026-08-15T15:22:26.364382Z","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":"2026-08-15T15:22:26.367351Z","title":"Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.367351Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:5518e7cc86a7a9bcd9b16cceb75ef734273e0a9ddcaf23e93a27066532dd923d","observation_id":"f72ef185-a5ce-4dc6-a700-57c826c895ff","resolution":{"observed_at":"2026-08-15T15:22:26.367351Z","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":"2026-08-15T15:22:26.370180Z","title":"Wasserstein steepest descent flows of discrepancies with","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.370180Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:1e49e20ad8fc187f91cc6052eb7330bbf98ada67e19ef702e0144dea20664526","observation_id":"ad993a12-01aa-4bb6-b381-c39c89af080b","resolution":{"observed_at":"2026-08-15T15:22:26.370180Z","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":"2026-08-15T15:22:26.373113Z","title":"Generalization of an inequality by","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.373113Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:532eebf8a8864b6fc5276c0080b34c7988582192f96fc8f68fa7c2307d586343","observation_id":"ca5993b7-9917-4d97-a693-d4e2499130e2","resolution":{"observed_at":"2026-08-15T15:22:26.373113Z","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":"2026-08-15T15:22:26.375995Z","title":"2008 , publisher=","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.375995Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:889ae2354fd80cd4c0830c5035456babfb305cc6e7ab72832765c2c7173fb92b","observation_id":"048fb8c5-b98c-48b1-9830-16cf3d3797b8","resolution":{"observed_at":"2026-08-15T15:22:26.375995Z","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":"2026-08-15T15:22:26.378885Z","title":"Communications on Pure and Applied Mathematics , volume=","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.378885Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:f9f539cce311d203a6283ab88cd12f97b53ac2bcb95d263031211eade1f8bb9a","observation_id":"0afbd4b7-8c44-4d83-9a71-0fb77b9b87e4","resolution":{"observed_at":"2026-08-15T15:22:26.378885Z","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":"2026-08-15T15:22:26.381669Z","title":"Communications in Partial Differential Equations , volume=","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.381669Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:201f41e464bcc97d84404176e5eb15ea4db5939683c1cf9a175c1ba3900ee58f","observation_id":"9760d6fc-312a-4515-b653-6e29a8d09f72","resolution":{"observed_at":"2026-08-15T15:22:26.381669Z","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":"2026-08-15T15:22:26.384590Z","title":"European Congress of Mathematics , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.384590Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:7739096571a9fe360743505dde92fa53ea59e508820807c95bc1c4e2988c92cd","observation_id":"ef0f9cb0-9991-483f-93c3-c04576d6211a","resolution":{"observed_at":"2026-08-15T15:22:26.384590Z","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":"2026-08-15T15:22:26.387565Z","title":"Sharp conditions to avoid collisions in singular","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.387565Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:01d69bc250ad4dbf1746f316eab17426c36a17355b5628cb68e38ae2c1718794","observation_id":"2964a6b5-aaae-42f2-8784-baaf9083e859","resolution":{"observed_at":"2026-08-15T15:22:26.387565Z","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":"2026-08-15T15:22:26.391256Z","title":"Uniqueness of the solution to the","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.391256Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:9b1d27242d7efc64706cf2691af6fec23e20a9d6a8628237e6bc03edaa94dcfb","observation_id":"ca8b32f7-bcdc-45f1-b32f-c6d6e71b5c1f","resolution":{"observed_at":"2026-08-15T15:22:26.391256Z","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":"2026-08-15T15:22:26.394626Z","title":"Communications on pure and applied mathematics , volume=","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.394626Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:08892fd44d23e02a24d4880d1f2821193a607c81552372f51c055677650569c9","observation_id":"da3c2883-e66b-42f1-8a65-b1059f83f503","resolution":{"observed_at":"2026-08-15T15:22:26.394626Z","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":"2026-08-15T15:22:26.398070Z","title":"A computational fluid mechanics solution to the","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.398070Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:d3ca87d5122bfb46e9f57ad9d3b4684edcc32af8fa4b6505513c6113d8d0e148","observation_id":"4341a327-6e7e-42b2-b8c5-7e8107fcf44c","resolution":{"observed_at":"2026-08-15T15:22:26.398070Z","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":"2026-08-15T15:22:26.401409Z","title":"Acta Mathematica , volume=","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.401409Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:70c929b423787bb07ae59282500cf334388299022646552b74f2a86b2dda73f5","observation_id":"ff96bef4-14c1-494f-9d34-b141f69048ad","resolution":{"observed_at":"2026-08-15T15:22:26.401409Z","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":"2026-08-15T15:22:26.404694Z","title":"Advances in mathematics , volume=","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.404694Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:6c42004a6192f1bceac5e153159b7bd22ea237925465ea3220b8292af249f45e","observation_id":"ee33c4d8-19b0-489f-9509-b793009751d0","resolution":{"observed_at":"2026-08-15T15:22:26.404694Z","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":"2026-08-15T15:22:26.408080Z","title":"Finite-time blow-up of","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.408080Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:8d0d50e2f8ee782907301f6c6ad1bb355b24acb79515ae4b4ea32894afba6546","observation_id":"add4073e-1681-485e-bbb0-3724740a0f6d","resolution":{"observed_at":"2026-08-15T15:22:26.408080Z","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":"2026-08-15T15:22:26.411595Z","title":"Classical","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.411595Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:c4332bcc6bea81973ea9159a6fa44a9031cde1ee88903f1e0b424d98136ccb1b","observation_id":"3b8018e7-5e1c-407c-bdec-d179896a96d9","resolution":{"observed_at":"2026-08-15T15:22:26.411595Z","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":"2026-08-15T15:22:26.414744Z","title":"The Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.414744Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:dbfc2d9b4629f0c99e5c5cc3fe6c4896a022e4c388831a08b2d63db0d61aa18f","observation_id":"e4843fbc-b8eb-4957-8b30-4b785d5ef3e1","resolution":{"observed_at":"2026-08-15T15:22:26.414744Z","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":"2026-08-15T15:22:26.418065Z","title":"On the global convergence of","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.418065Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:f6acd22ee4246e2e7abf52ad39c3653339d56b717ca69ec534db397edbc8e757","observation_id":"7fef37c0-84ec-4364-b62d-97c2332a40f6","resolution":{"observed_at":"2026-08-15T15:22:26.418065Z","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":"2026-08-15T15:22:26.421481Z","title":"Journal of Differential Equations , volume=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.421481Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:5351aa51c10ad2321b30572fb47d53a29368c97187bfbf3d202d82a6cbb9c337","observation_id":"04a0c7c4-99a0-49ed-938b-25131cab66ea","resolution":{"observed_at":"2026-08-15T15:22:26.421481Z","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":"2026-08-15T15:22:26.424916Z","title":"Characterization of translation invariant","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.424916Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:deae3dbff10c3f2a3fffe9abfe4a6dce4c4400841a91c20b13775a790cd197fb","observation_id":"4704fa8e-6709-4525-84d3-b6eb4813b3bf","resolution":{"observed_at":"2026-08-15T15:22:26.424916Z","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":"2026-08-15T15:22:26.428529Z","title":"2021 , publisher=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.428529Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:3ddeaf59e7f8ac634e6050ee29e8f037bc348417db2d8d0e909527291336181e","observation_id":"ba030052-d3f2-4ea7-b2c7-69eef73eb4bd","resolution":{"observed_at":"2026-08-15T15:22:26.428529Z","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":"2026-08-15T15:22:26.431850Z","title":"SIAM Journal on Mathematical Analysis , author=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.431850Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:fc282dd9e6c70724af8881be162a271471e7a2bfc468c5c6f5ae50695c0c9bcb","observation_id":"1420a26a-4d2b-43ff-b6b4-4bbd7db9a425","resolution":{"observed_at":"2026-08-15T15:22:26.431850Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.21194","last_updated":"2024-07-30T21:02:49Z","snapshot_observed_at":"2026-08-14T02:42:49.931618Z","submitted_at":"2024-07-30T21:02:49Z","title":"Lectures on Coulomb and Riesz gases","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.21194","snapshot_observed_at":"2026-08-15T15:22:26.435780Z","title":"Lectures on","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.435780Z"},"links":{"cited_paper":"/paper/2407.21194","citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:12ce479a92afff5fdd131a7a397e218824c02f147d1836efe4644f477b340b61","observation_id":"aa209e4e-b14b-45f7-b6c4-5ee2413a2011","resolution":{"observed_at":"2026-08-15T15:22:26.435780Z","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":"2026-08-15T15:22:26.439599Z","title":"Sharp commutator estimates of all order for","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.439599Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:3527818be890420a6c17b5d284a2b61b1257e3e970fa3b8277d0bd936939fa2c","observation_id":"c34a2b60-fea7-49fa-a2b9-56623ff6b1de","resolution":{"observed_at":"2026-08-15T15:22:26.439599Z","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":"2026-08-15T15:22:26.443167Z","title":"Mean field limit for","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.443167Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:e87fc2e01c1f48d860111252aaac6efaf4777500b6c38000aef699636f933e5a","observation_id":"f16c537f-fe14-4f83-84a8-708cc251343c","resolution":{"observed_at":"2026-08-15T15:22:26.443167Z","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":"2026-08-15T15:22:27.606280Z","title":null,"venue":null,"work_id":"d4b2ad7e-df9e-42dd-ac1b-9e0afd31372a","year":2009},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.447597Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:a162432d700ade4d9f124efb49afafc72ad58ed542417671043d892600e2b113","observation_id":"eb8f11fd-d028-47a5-9314-bcda1b6eaeb8","resolution":{"observed_at":"2026-08-15T15:22:27.609608Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.450993Z","title":"Mean-field limits of","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.450993Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:302d7ca2510eb7c0c84a55261befc55ce4f7c2a3a67c46515f2a2a37f295c016","observation_id":"4da9d2a0-d7c5-479a-9da1-a813a53410f3","resolution":{"observed_at":"2026-08-15T15:22:26.450993Z","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":"2026-08-15T15:22:27.597390Z","title":"Hitchhiker's guide to the fractional","venue":null,"work_id":"6b49195c-ab88-4f15-82bb-124b8ea085b6","year":2012},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.454460Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:ba4bdb7541646347944bf72fc704510722bcff378e79100f28b84d6a2525c928","observation_id":"bc7bf9cf-682f-4396-b37b-04637f90c241","resolution":{"observed_at":"2026-08-15T15:22:27.600300Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.588171Z","title":"Sharp constants in the","venue":null,"work_id":"6b4dd5e7-1b3a-43f1-ac68-b9bf22981486","year":1983},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.457838Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:1ad7c20420cc87192bd6c055c09896c1dfdb65dd727be2822290f01c8fc349cb","observation_id":"ac8d41c6-9ccb-4a4b-ab2a-8f0913b166bb","resolution":{"observed_at":"2026-08-15T15:22:27.591132Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.461589Z","title":"2001 , publisher=","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.461589Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:d4986d1dbb289593a492c0d15944c373d047fb2193f7dbd48f5e7210f22fb1c1","observation_id":"2525c7fb-34fa-4e07-8599-95e4eab06b9a","resolution":{"observed_at":"2026-08-15T15:22:26.461589Z","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":"2026-08-15T15:22:27.572704Z","title":"On the Best Values of the Constants in the Theorems of","venue":null,"work_id":"59335ab6-9ca3-45a7-bfd3-9e049b8f26e3","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.465203Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:d5c108ac2e5d8426965132ec452a7fd4a35174bce5ebd79177a440ae78497203","observation_id":"2da7cfa7-8822-4705-87b3-5bbc9393d4eb","resolution":{"observed_at":"2026-08-15T15:22:27.575733Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.562678Z","title":", author=","venue":null,"work_id":"26c59104-8cab-4aca-b4db-3e66e8241344","year":1996},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.469393Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:7779d8f3e08ddad55e008f4d47b0fbc6c3720bf8c8400aa0ef6348433eca3534","observation_id":"b3c7dce9-0fe2-42a2-81ca-499771697495","resolution":{"observed_at":"2026-08-15T15:22:27.565967Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.552269Z","title":"1970 , publisher=","venue":null,"work_id":"a2654a63-ce59-4f91-9061-7015c51fd42e","year":1970},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.472665Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:d47dd4e6b33b2ccce7a95acbd16adfb0ae6c3267d31caf63c34dbd8d8f39573b","observation_id":"e336a959-5357-4531-8cb4-89049165b160","resolution":{"observed_at":"2026-08-15T15:22:27.556068Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.541342Z","title":"Sharp inequalities for martingales with applications to the","venue":null,"work_id":"d282c60e-8da5-4b69-bff7-8b7fdc56b545","year":1995},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.476554Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:853bcdefaad28c71b5df36bcfce2403d4d38b58a2e3f71ae456b15f85c39574d","observation_id":"78775176-ce43-43b2-b305-bee6d20031b0","resolution":{"observed_at":"2026-08-15T15:22:27.545419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.480155Z","title":"The variational formulation of the","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.480155Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:fc3ceeda2fd35f273db96a95f72b039eded8fbb2cfb90fbfebd9dac1c17475c0","observation_id":"843192ea-3b06-4ae7-ab8c-4c15b2d71041","resolution":{"observed_at":"2026-08-15T15:22:26.480155Z","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":"2026-08-15T15:22:26.483953Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.483953Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:1452cd316a6ce3a66ab21b329a62be4563ba68eec9840ec49019871ffa99b2f5","observation_id":"469cabcc-32d1-4319-bdba-1b42813236f6","resolution":{"observed_at":"2026-08-15T15:22:26.483953Z","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":"2026-08-15T15:22:26.487095Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.487095Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:d53c939f3828c54cd8ade6d4fdebdaa82d31146fcf4146da2a7054c30a6b665c","observation_id":"936b229e-0627-45ba-b94a-3ef345202508","resolution":{"observed_at":"2026-08-15T15:22:26.487095Z","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":"2026-08-15T15:22:26.490859Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.490859Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:3666753fc38c646290d1c3b15b27fc3dbb3eb2820529e4b15a1a79c60b9b46c9","observation_id":"a7c624d9-83cc-4894-9eb2-b2db2c9b33f2","resolution":{"observed_at":"2026-08-15T15:22:26.490859Z","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":"2026-08-15T15:22:26.494858Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.494858Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:524f6e3ac9f5b7f8f839a48f19b8e11adcdc5fb3cc045f992c4914dcada03edd","observation_id":"3524516e-73a9-4f5a-9904-1f3758fca475","resolution":{"observed_at":"2026-08-15T15:22:26.494858Z","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":"2026-08-15T15:22:27.499473Z","title":"Sampling as optimization in the space of measures: The","venue":null,"work_id":"6aeaaeca-8f3a-4407-9952-1d91c17b0f5c","year":2018},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.497907Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:ebb1d23b49f74bccabe03c422db49f78fdd268cb17e8c4d713468e7608fb1bee","observation_id":"601c0387-8ec1-4a89-ba02-5427d425e4bd","resolution":{"observed_at":"2026-08-15T15:22:27.503164Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.500940Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.500940Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:7955ad98afa701a2169e14b8b520a6488417e951611c2576f0701234d7b1e6a6","observation_id":"22a0c254-cbe1-43f7-8669-34720fe8e5e4","resolution":{"observed_at":"2026-08-15T15:22:26.500940Z","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":"2026-08-15T15:22:27.482561Z","title":"Accelerating","venue":null,"work_id":"2a6135f0-11fe-4ac9-bed3-44f9d50d7021","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.504065Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:6735603b4d98332f908345218774ec8fbf3688014224966d7896baecbfa5e83c","observation_id":"03fd9638-f1ac-4ea2-9a8c-e731a6693c60","resolution":{"observed_at":"2026-08-15T15:22:27.486230Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.472021Z","title":"Variational inference via","venue":null,"work_id":"2b49707d-849b-44c6-ae6c-1886e690a856","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.507349Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:c1206b200e0b35e68b280499da3542f17efeec3c669524e0e75aded65fd6709b","observation_id":"c223af8f-08fa-4622-b7c9-c0f64752823e","resolution":{"observed_at":"2026-08-15T15:22:27.475699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.461384Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":"09725fc8-e083-4c9d-8f34-85cbfbb67d5f","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.510333Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:6c790a9e8e110278698eb2fbb13f783e865222551c0e41dd6c5eeea8798bfbbc","observation_id":"01e7a443-7d7f-4e26-ba21-4ad257422a35","resolution":{"observed_at":"2026-08-15T15:22:27.464949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.513175Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.513175Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:02b72cb087fa63922d1a47b7c1482ee28a86007fc4c1c8c536e323ab9d45fa48","observation_id":"b59e04b9-f769-42b8-a675-8e8d995a23d9","resolution":{"observed_at":"2026-08-15T15:22:26.513175Z","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":"2026-08-15T15:22:26.516549Z","title":"Interacting","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.516549Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:04e36a20c2012047b23f087e2ca6c175b029aaeb6088e228e5d7e17c8428d2aa","observation_id":"46c5bb06-629e-4037-aa60-6f8728878033","resolution":{"observed_at":"2026-08-15T15:22:26.516549Z","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":"2026-08-15T15:22:26.520873Z","title":"Communications in applied mathematics and computational science , volume=","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.520873Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:3bea7dcdac861e4f81da29bee9f353a46e4f9e55ca54958d7e65afa6f5db3e38","observation_id":"10487580-0100-4acf-86ef-c851dca24484","resolution":{"observed_at":"2026-08-15T15:22:26.520873Z","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":"2026-08-15T15:22:27.427826Z","title":"Nonlinearity , volume=","venue":null,"work_id":"3392ed6d-e539-43f5-89e0-e569e6cc14ab","year":2023},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.525077Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:d52ef443399bee8892d9d09d6d3e29381ed0f7b457dcc8a1bc75303e19e9350d","observation_id":"df303e9f-4afc-47de-9e9f-9f400c49ef83","resolution":{"observed_at":"2026-08-15T15:22:27.431563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.415521Z","title":"Ensemble","venue":null,"work_id":"ec36ce74-fe09-4821-b0a5-0b090592de8d","year":2022},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.529012Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:c82ad876a4bfe33131bcc598ee4b3b7838d822e779de28f9d0091bbac6c221a0","observation_id":"7df8f5c8-5899-4266-a5ce-b2b6a4ec2532","resolution":{"observed_at":"2026-08-15T15:22:27.419362Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.533241Z","title":"Studies in Applied Mathematics , volume=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.533241Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:f79181d496051b3435fca48d4e5405a553e7c8bf4e5f1979a9441d10d2402644","observation_id":"b948a375-9a48-4d46-acad-f1f380290e57","resolution":{"observed_at":"2026-08-15T15:22:26.533241Z","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":"2026-08-15T15:22:27.398589Z","title":"Communications in Mathematical Sciences , volume=","venue":null,"work_id":"71418e96-ef1e-4683-b657-3cf087e2b0b0","year":2025},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.537790Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:10897f085a17dc5a57ef57a06d37b432107d514525b565dd6f21e8c22895790d","observation_id":"63617ceb-0b88-4443-939f-39832f3cd965","resolution":{"observed_at":"2026-08-15T15:22:27.402200Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.541714Z","title":"Advances in applied probability , volume=","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.541714Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:508d5d143437da1c7797102c97d2c308571e743ff56bc2f9ecd9cc4224382a43","observation_id":"13cc1c06-da9b-4040-b721-4d8b9ed32dfb","resolution":{"observed_at":"2026-08-15T15:22:26.541714Z","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":"2026-08-15T15:22:27.380711Z","title":"Regularized","venue":null,"work_id":"54f8e90b-c43b-4032-a774-822fbe92028b","year":2024},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.545804Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:d134eb5ec7901db763bfaf00bafe379964d62c781a4977e7c372a32e32e6907f","observation_id":"a1fe40ee-ba85-44bd-adc8-a2a3132f37f1","resolution":{"observed_at":"2026-08-15T15:22:27.384520Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.369627Z","title":null,"venue":null,"work_id":"3879936c-26bb-4cee-8ab1-f9a5e0a56a55","year":2019},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.549842Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:cf24d62ac7556b50851b72af3418980d363b6a8dd60c9a400aa22b028c30c603","observation_id":"b3de983d-c0ae-4382-b0e7-fe8f819fd618","resolution":{"observed_at":"2026-08-15T15:22:27.372748Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.359368Z","title":"Proceedings of the National Conference on Artificial Intelligence , volume=","venue":null,"work_id":"4195a4b2-e781-48da-a2d8-150abe447b12","year":2007},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.553605Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:852243c4917647ff4ea4f79a9d8b6c59572028a30ee96279705a293feb3ccdb3","observation_id":"5d77050b-c062-4d30-a6da-ced3a167a170","resolution":{"observed_at":"2026-08-15T15:22:27.362718Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.348905Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":"8a1285df-c9cd-472b-b365-222819fe2e3e","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.557262Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:da47e63de749b41a446261de33f0fb3b9da4f5e116502a2b160fb8074b69385e","observation_id":"706b80b4-c10a-42e5-90f6-2376a2b91f00","resolution":{"observed_at":"2026-08-15T15:22:27.352039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.338101Z","title":"Bernoulli , volume=","venue":null,"work_id":"5d2287a2-1cbc-4a33-bca0-52d8bfacb985","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.561093Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:1a55efb847256acc750861c6df3c180ec15940df52e1c32915af7717d59bd393","observation_id":"86704deb-ed7e-4d44-a82c-7a195eff5060","resolution":{"observed_at":"2026-08-15T15:22:27.341902Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.326738Z","title":"Universality, Characteristic Kernels and","venue":null,"work_id":"3f2dd323-1c7c-4313-b3be-889e4a3caa84","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.565020Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:bdadacd42a3bfbdb52bd4b5f622c26fa5c6310c2595fc6894340241de45f52cc","observation_id":"83c46bc7-c98a-4d27-b198-0a51ba447dc3","resolution":{"observed_at":"2026-08-15T15:22:27.330585Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.568722Z","title":"2008 , publisher=","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.568722Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:8ed338c9da7d663685e5d0a0a9afd81b9a17ac9d62a14f1219ccbaf21681005f","observation_id":"4e667276-bf03-4c9e-bd60-e54b60100613","resolution":{"observed_at":"2026-08-15T15:22:26.568722Z","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":"2026-08-15T15:22:27.307799Z","title":"(De)-regularized","venue":null,"work_id":"d5f47413-0e8c-4043-bc57-6e81b49e9958","year":2025},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.572807Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:5e6c14e5c7e14c51f53a12f8d500c1af417896c75cf3ad01c7ac6ee25cba3f8c","observation_id":"e955b136-6e3e-4975-880b-012c1b53e648","resolution":{"observed_at":"2026-08-15T15:22:27.311397Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.295326Z","title":"Physica D: Nonlinear Phenomena , volume=","venue":null,"work_id":"796f54cf-7ec6-4f78-a2e3-1b13bb6eb6a9","year":2013},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.576877Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:c2b25c2d47aaa4105a6ccb7367935b471a8bbc4b558142368f0803b9ab1b5b85","observation_id":"36f93bd9-4107-4b23-9600-4388da356481","resolution":{"observed_at":"2026-08-15T15:22:27.299283Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.283899Z","title":null,"venue":null,"work_id":"90e6db5a-fc40-4ea2-8851-8b79429f9044","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.580635Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:7d3afc08da7d997ea0c27d35c1c07d4ddd7a622600a68c4317bd772e9f0450cf","observation_id":"7cdfdd4e-187b-4b6e-8622-f13de93b42e0","resolution":{"observed_at":"2026-08-15T15:22:27.287633Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.271766Z","title":"Posterior Sampling Based on Gradient Flows of the","venue":null,"work_id":"5ad94eff-910a-445f-b525-decfc85de80a","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.584376Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:4b3123e0a772ad26a642a7d520b22fc1f2da97a79e7f396434b7987fe18b53be","observation_id":"21de0ce5-6db5-4424-a23c-975f50801e6f","resolution":{"observed_at":"2026-08-15T15:22:27.275802Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.259850Z","title":"Generative Sliced","venue":null,"work_id":"ae8840f1-c5be-46ee-aa6a-850d2f6b47ef","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":88,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.588177Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:6275a88b2872185b659598e475874c3968497444ebd519086cf2792e40900768","observation_id":"0d942c80-26cf-4948-b0d1-2bcc0a7a4156","resolution":{"observed_at":"2026-08-15T15:22:27.263661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.248550Z","title":"Smoothed distance kernels for","venue":null,"work_id":"07f84402-a6c2-44f0-8d7f-9c88077f4cc1","year":2026},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":89,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.591930Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:93525f180bc47a4b71a8320850174aeb2882c3a2a0ef547f82c74f37e6071b84","observation_id":"adaa4a62-e97a-4c36-9a95-6da7d9d47df9","resolution":{"observed_at":"2026-08-15T15:22:27.252384Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.595821Z","title":"Journal of Multivariate Analysis , volume=","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":90,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.595821Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:b3fedb6d65b71536c648452a8e517df27df570fda0dda3266ac97b39bf3ba965","observation_id":"35cc554c-3adf-4859-b45c-e9b744dec11e","resolution":{"observed_at":"2026-08-15T15:22:26.595821Z","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":"2026-08-15T15:22:27.229534Z","title":"Bowling Green State University, Department of Mathematics and Statistics Technical Report , volume=","venue":null,"work_id":"a25adf9e-098f-458c-96f7-85e5b4924c3b","year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":91,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.599413Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:372a5c821964fe9aacd2988b93d8a2a1f63d08b42514bf3b94a9ebaa7ddfd3c2","observation_id":"88c29df9-0237-46bb-a492-b5ba765f0d47","resolution":{"observed_at":"2026-08-15T15:22:27.233232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.602896Z","title":"Journal of statistical planning and inference , volume=","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":92,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.602896Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:9bfae7768b8ed31bdb825ec04b9a08c19d666a03963a1dc1eb3133395472a761","observation_id":"2be34198-79c4-40aa-9d0e-11deccc39e46","resolution":{"observed_at":"2026-08-15T15:22:26.602896Z","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":"2026-08-15T15:22:26.606410Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":93,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.606410Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:25ab08ee8d9b4db9c5dcdf54b86c5c2026a7e3d6eebd8640dfdd533a4d65ba80","observation_id":"0034b72f-753a-4b69-8e05-95a1e50bc66c","resolution":{"observed_at":"2026-08-15T15:22:26.606410Z","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":"2026-08-15T15:22:27.201631Z","title":"Global-in-time mean-field convergence for singular","venue":null,"work_id":"ad93e15a-1abe-420b-98ba-dd9df8824a0f","year":2023},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":94,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.609941Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:f6ef918db3109f65cf7ec38fdbb71952ffaa131f19e2037993026493aeb04cfe","observation_id":"7d0fa61e-cfc6-41ea-bb23-c067bb9f1931","resolution":{"observed_at":"2026-08-15T15:22:27.205751Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.189415Z","title":"Commutators, mean-field, and supercritical mean-field limits for","venue":null,"work_id":"1e429b0b-da7a-4cfe-bec6-5dcccd3c24be","year":2025},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":95,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.613443Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:0c12b5688276ffd077d9099f0792e1830d93cf0497733986098e2b35741c01fc","observation_id":"60d53c4e-dc51-4a27-8cab-f3b106ed2183","resolution":{"observed_at":"2026-08-15T15:22:27.192714Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.178069Z","title":"Wasserstein distances for vortices approximation of","venue":null,"work_id":"47f8684a-a4d6-4090-bb01-1ac0e72e0a62","year":2009},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":96,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.617019Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:6c48ba82bff731b6b25d3294f0211280c8c081d6a3fb3a7b916782a11a475570","observation_id":"b1c3481e-3346-448f-8d35-8175d377b0bc","resolution":{"observed_at":"2026-08-15T15:22:27.181438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.167448Z","title":"Ecole d'","venue":null,"work_id":"871fc2cb-7404-48aa-b8dd-1de8b1c7e062","year":1991},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":97,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.620501Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:c1de0d3f468c26d4fe67137ac611efd8d496d1a17f59f34410e50dfd16cc43e7","observation_id":"3dbe5353-9495-41be-9419-e6ee3c4126f5","resolution":{"observed_at":"2026-08-15T15:22:27.170695Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:26.624331Z","title":"Quantitative estimates of propagation of chaos for stochastic systems with","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":98,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.624331Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:6eafaf7ac554a0259cb53a50d2b85ae6cc2218aefb4b508a62ff6c42f4746899","observation_id":"6ab86f1f-8a06-4fe8-a559-ea76b97e3666","resolution":{"observed_at":"2026-08-15T15:22:26.624331Z","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":"2026-08-15T15:22:27.148789Z","title":"Active Particles, Volume 4: Theory, Models, Applications , pages=","venue":null,"work_id":"2239dd46-a24f-428e-b177-1790050a2dd2","year":2024},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":99,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.627709Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:30b2936016371ec177b9e9e3ce9785cfc750cc23361e39a84f805e11346c761b","observation_id":"aa163f18-5b4d-4510-99ab-e661eeeacd95","resolution":{"observed_at":"2026-08-15T15:22:27.152648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:22:27.137687Z","title":null,"venue":null,"work_id":"5f286a08-62ad-46b7-b0fc-cf9d52a001f4","year":2019},"citing_paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels","version":1},"reference_index":100,"source":"arxiv_source","source_observed_at":"2026-08-15T15:22:26.631108Z"},"links":{"citing_paper":"/paper/2608.01182"},"observation_digest":"sha256:4a7cf6ab85cd7e885a572d391076c769653ee92330227d0e944bd3015783047d","observation_id":"5b449f2a-8411-43c3-9e40-4f1a26931a29","resolution":{"observed_at":"2026-08-15T15:22:27.141409Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.01182","last_updated":"2026-08-02T11:59:43Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-15T15:08:33.357391Z","submitted_at":"2026-08-02T11:59:43Z","title":"Wasserstein gradient flows of Maximum Mean Discrepancy with energy kernels"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":5,"parse_uncertain":0,"unresolved":65,"verified_exact":1,"verified_fuzzy":29},"total_outbound_references":113},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 100 of 113 outbound references and 0 inbound Pith citation observations for arXiv:2608.01182."}