{"as_of":"2026-08-21T23:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6c3e6660ceebfc10f29e1ed956053471531b4818036c1278ddac2c2a94f699c8","coverage":[{"denominator":48,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":48,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:24:29.675432Z","state":"measured"},{"denominator":50,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":50,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:24:29.655182Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-16T15:48:03.793150Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.09362","snapshot_observed_at":"2026-08-10T20:24:29.655182Z","title":"A revisit to rate-dis tortion theory via optimal weak transport,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.655182Z"},"links":{"cited_paper":"/paper/2501.09362","citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:a8b41990ac2e5f6aa01d0e9cf4cef9fb2308f6b333aef2afab47e9e4b233eeff","observation_id":"8b6beba7-e082-4a5b-8b70-63f4fec0b9fb","resolution":{"observed_at":"2026-08-10T20:24:29.655182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"cited_work":{"arxiv_id":"2501.09362","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.09362","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A revisit to rate-distortion theory via optimal weak transport","venue":null,"work_id":"f09367a4-fafa-4513-9fe1-e8fe5f5ca1d5","year":2025},"citing_paper":{"arxiv_id":"2601.07246","last_updated":"2026-05-03T04:01:14Z","snapshot_observed_at":"2026-08-15T15:02:32.249005Z","submitted_at":"2026-01-12T06:29:34Z","title":"Rate-distortion Theory with Lower Semi-continuous Distortion on Noncompact Alphabets","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-16T15:47:39.863456Z"},"links":{"cited_paper":"/paper/2501.09362","citing_paper":"/paper/2601.07246"},"observation_digest":"sha256:221f018665ef8bb346efae86816958a802cfad476413d386f16869216aa5d12a","observation_id":"abc4ae4a-396f-4efb-9188-b480244b5134","resolution":{"observed_at":"2026-05-16T15:48:03.795657Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2501.09362/citation-record","integrity":"/paper/2501.09362/integrity","json":"/paper/2501.09362/citation-record.json","paper":"/paper/2501.09362"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:24:29.504459Z","title":"A mathematical theory of communication,","venue":null,"work_id":null,"year":1948},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.504459Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:233f5dd0bb9e7f15846c33955bda89295b36d45015f7a12763e74b083496eb08","observation_id":"283a40b9-3908-4be9-ace7-9ef00a5c29fc","resolution":{"observed_at":"2026-08-10T20:24:29.504459Z","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":"2026-08-10T20:24:30.227098Z","title":"Coding theorems for a discrete source with a ﬁdelity criterion,","venue":null,"work_id":"d06fd584-ac47-47e6-b149-bff598ca1626","year":1959},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.509094Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:493297ea9001d0d83da947e252eef334398ec7abdae0e4880cfd8658159ac790","observation_id":"02de3392-9ae8-4116-bb20-a34d56ce07c2","resolution":{"observed_at":"2026-08-10T20:24:30.230784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.216269Z","title":"Berger, Rate-distortion theory: A mathematical basis for data com- pression","venue":null,"work_id":"4289311d-f732-4721-b97c-9645fc289763","year":1971},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.513573Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:12d5371e9a18bdd46b6f9b682b8abbad8ec555beeb8511d9b5f437dd72734486","observation_id":"4123d86b-490e-4d4c-bfef-7fc496f32e1e","resolution":{"observed_at":"2026-08-10T20:24:30.220137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.205829Z","title":"Computation of channel capacity and rate-di stortion func- tions,","venue":null,"work_id":"7981896d-da9c-48b6-80b9-d346f3020da9","year":1972},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.517403Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:be4163dedc3bdb9efcc33e0ef0c803362ff6c3f1b70e47eec8b83633d38b5df8","observation_id":"a92515b4-6fc2-42dd-92f6-1129b06b961b","resolution":{"observed_at":"2026-08-10T20:24:30.209578Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.194756Z","title":null,"venue":null,"work_id":"d70849ee-3b19-46f6-bc84-69d1ebda432a","year":1987},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.521474Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:066d492c229b57b107a7080bfcbad1e0c1866b5b6d8899ed2cceb08a085184b4","observation_id":"3cba4dee-4305-47f2-8f25-084d581d2e92","resolution":{"observed_at":"2026-08-10T20:24:30.198512Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.183817Z","title":null,"venue":null,"work_id":"1db48f23-73cd-496c-9f2e-ce9588ebcb17","year":2006},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.525483Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:e25b060da28c6de152f5eb84044fd764d0865ebe52f2d6c339179ebfc6b76be1","observation_id":"4c370efd-ed61-44f8-8492-87ff6564e86e","resolution":{"observed_at":"2026-08-10T20:24:30.187334Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.173079Z","title":"On an extremum problem of information theor y,","venue":null,"work_id":"1db71004-ad45-45d2-8413-f16eb629f86a","year":1974},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.529530Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:16311616973a85cd684a4e04c5849655869ceb86f7bab5caf54e79fd9f764bbd","observation_id":"e7c23b14-6b22-45d1-9e57-94ab62eeb1e6","resolution":{"observed_at":"2026-08-10T20:24:30.177154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.162729Z","title":"An algorithm for computing the capacity of a rbitrary discrete memoryless channels,","venue":null,"work_id":"1de18745-d5fb-4acb-883c-0e5794731148","year":1972},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.533009Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:b1853a618d63c7451bf738f371a8e10c6a14e772b37379b96dd369ae4e58f2b8","observation_id":"9b2a8e90-b3b5-40c9-9b02-850ecd150a43","resolution":{"observed_at":"2026-08-10T20:24:30.166581Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.152089Z","title":"Rate distor tion theory for general sources with potential application to image com pression,","venue":null,"work_id":"1b2b7127-3bc0-4421-a9bf-e53017b39e5b","year":2006},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.536380Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:73efd8c642d9e682753afbc97cbce003e28d988b522366cfc83d575caf996394","observation_id":"0e33b915-2ee8-45a0-9e19-fd81dcaeeced","resolution":{"observed_at":"2026-08-10T20:24:30.156021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.140817Z","title":"Rate-disto rtion theory for general sets and measures,","venue":null,"work_id":"93ffe388-70a5-4551-9658-e7eb3223c94f","year":2018},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.540141Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:4712e627ccf5c033ca56922f9027dc1e6239ec47791170c150aae7c250d842fa","observation_id":"37077752-c065-4f41-96f0-05150abce08c","resolution":{"observed_at":"2026-08-10T20:24:30.144697Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.129932Z","title":"Lossy compr ession of general random variables,","venue":null,"work_id":"23baf40b-baa3-45aa-b105-189b41e69d0e","year":2023},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.543579Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:66318137af9701fa38897e0633a63417708801106a9417cb96a3b900b3f69189","observation_id":"39fc8422-be1d-407d-9936-80ffb5745c14","resolution":{"observed_at":"2026-08-10T20:24:30.133855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.119384Z","title":"The rate-distortion dimensi on of sets and measures,","venue":null,"work_id":"3931b8fd-3f89-4f6c-9237-d22bd347cf2e","year":1994},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.547095Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:8ae69408b6f104499bb61dfc667ed24f7c333691716aa154940bac0492c2691b","observation_id":"2f98803f-3e1d-41d5-b12b-58e8a7ea0d92","resolution":{"observed_at":"2026-08-10T20:24:30.123129Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.108327Z","title":"Successive reﬁnement of abst ract sources,","venue":null,"work_id":"e6979294-f668-46eb-952d-36583de67d08","year":2019},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.550428Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:7fefdd9969533a4aa0b1af58099a2067e66c0ba9ffc43c35a384e71c6239c31d","observation_id":"9a2fe011-d9a3-4ed2-b663-04b3219617e1","resolution":{"observed_at":"2026-08-10T20:24:30.112286Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.097971Z","title":"Asymptotic evaluatio n of certain Markov process expectations for large time, I,","venue":null,"work_id":"8fe9d987-8bfe-4bb3-847c-b6171f0a6f54","year":1975},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.553766Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:ed7562e9ed2a748c4fd51b9a5246e6dbdbdc1541b7f7447508938872fff8d248","observation_id":"7e78ff5a-230f-4e7c-aec9-ab14f03d9d15","resolution":{"observed_at":"2026-08-10T20:24:30.101795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.087186Z","title":"Successive reﬁnement of in formation,","venue":null,"work_id":"9011a519-3411-43ac-92a6-151f6976244a","year":1991},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.556785Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:66024a6a0d1086c190a7d4a7965b738a714fc501c31b769d30fc30e647475067","observation_id":"164f52e2-77f1-4f0b-9a12-24253b1f78ed","resolution":{"observed_at":"2026-08-10T20:24:30.091150Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.076725Z","title":"Transportation distance, shannon informa tion, and source coding,","venue":null,"work_id":"774b12cd-d309-4705-99e9-a33494c14e47","year":2013},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.560144Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:f22982bbf2b367a59991fcff07a4f468f40271ad65c9d1acbf6ed2254243be4d","observation_id":"4a1371c4-ffbb-4b85-887e-01cb921deac1","resolution":{"observed_at":"2026-08-10T20:24:30.080426Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.066384Z","title":"Estimating the rate- distortion function by Wasserstein gradient descent,","venue":null,"work_id":"4a328af8-bb35-461f-87e6-78ffa9f4240e","year":2024},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.563442Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:ec9258f1be52f614fdd91e0a2087aaafbe128eed4fe0fb9bea53712c1390fa99","observation_id":"761c4d2e-9fd4-4731-8ecc-2f149a26c88c","resolution":{"observed_at":"2026-08-10T20:24:30.070345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.054461Z","title":"Kan torovich duality for general transport costs and applications,","venue":null,"work_id":"a590a8cc-d7fd-415d-8c6d-4594f49360b7","year":2017},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.566913Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:99b22185cec06464e2b9ee2f4e6bb4f5d544762b83a094d69b4646a39837c127","observation_id":"f3baca73-de96-4c6d-abf1-13933212e4f6","resolution":{"observed_at":"2026-08-10T20:24:30.058340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1308.0215","last_updated":"2013-08-01T14:16:38Z","snapshot_observed_at":"2026-08-20T09:55:59.656275Z","submitted_at":"2013-08-01T14:16:38Z","title":"A survey of the Schr\\\"odinger problem and some of its connections with optimal transport","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1308.0215","snapshot_observed_at":"2026-08-10T20:24:29.570270Z","title":"A survey of the Schrödinger problem and som e of its connections with optimal transport,","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.570270Z"},"links":{"cited_paper":"/paper/1308.0215","citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:a84afb1534a56ad729a31dab1afdcf2256f1e7496d7319b03a4f56eefe064d60","observation_id":"761629f7-ae93-4eb2-b4ff-476d5b9c359d","resolution":{"observed_at":"2026-08-10T20:24:29.570270Z","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":"2026-08-10T20:24:30.044081Z","title":"Ex istence, du- ality, and cyclical monotonicity for weak transport costs,","venue":null,"work_id":"88d605a5-f1e0-4b48-8f3a-c1d9c27fb77b","year":2019},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.574457Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:f8955eddb202034e101bc2ca8e2be7e8c4fa240309300635b02a2636a6a09df1","observation_id":"ccaedf5d-3695-4e9c-b9df-819ba1701562","resolution":{"observed_at":"2026-08-10T20:24:30.047792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.033688Z","title":"Applications of w eak transport theory,","venue":null,"work_id":"c0efb236-829a-44d3-a040-a03674c5b344","year":2022},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.577889Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:16a3f1aaee96a114775b3c4694f66aa2f7b99b9aeafce303b16742e48f98f2e3","observation_id":"96652503-5ef7-4ae6-9b7f-d6a0bd437280","resolution":{"observed_at":"2026-08-10T20:24:30.037507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.022369Z","title":"A mapping approach to rate-distortion comput ation and analysis,","venue":null,"work_id":"1def084a-cb04-4439-ba49-e18352463466","year":1939},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.581595Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:94bd9f6364bef6ea43124121effeb3e65d24a63ad199fbb04226b2b56942d50e","observation_id":"673e75f3-061e-487e-a534-1355909b5a68","resolution":{"observed_at":"2026-08-10T20:24:30.026280Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.011298Z","title":"O ptimal transport for domain adaptation,","venue":null,"work_id":"870f0e02-8a37-49d7-a61c-31ebe4b18b0e","year":2016},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.585023Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:e03da8545ba9140d044baf04278c42b523d339a8f890257d474d1ec205a303b1","observation_id":"c47c0d1b-7093-4023-9a78-f26ae5e680c2","resolution":{"observed_at":"2026-08-10T20:24:30.015191Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.11937","last_updated":"2021-03-25T20:38:13Z","snapshot_observed_at":"2026-08-19T08:24:30.127542Z","submitted_at":"2021-03-22T15:31:53Z","title":"Regularized Optimal Transport for Dynamic Semi-supervised Learning","version":2},"cited_work":{"arxiv_id":"2103.11937","doi":null,"metadata_source":"pith","pith_arxiv_id":"2103.11937","snapshot_observed_at":"2026-08-10T20:24:29.766298Z","title":"Regularized Optimal Transport for Dynamic Semi-supervised Learning","venue":"stat.ML","work_id":"676403ea-79f4-461d-b5d4-d213b1dd21cd","year":2021},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.588753Z"},"links":{"cited_paper":"/paper/2103.11937","citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:786ce6bcdf434a69c49b91de19f8a05d568cf0bc6f30a7a96b315bc099176b93","observation_id":"86e72a17-d03a-4162-9bce-5f1281458bb9","resolution":{"observed_at":"2026-08-10T20:24:29.770351Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:30.000036Z","title":"Wasserstein g enerative ad- versarial networks,","venue":null,"work_id":"836b66bf-5853-48fe-9938-84bc3c6dc300","year":2017},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.592839Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:6ddb1802b82bfe39472814091fcac86c17d7b55d171675bcba6fc55b6e0ec97a","observation_id":"84122a7c-3b2e-4d06-9090-8ec12a0d2062","resolution":{"observed_at":"2026-08-10T20:24:30.004292Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.989348Z","title":"Multi-prototype space learning for commonsense-ba sed scene graph generation,","venue":null,"work_id":"d3ead616-d437-4254-a9d4-b2023a775ca9","year":2024},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.596492Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:21ffe1f1f2a707ace1b4de7f6958534142bc198595b8b1abfffe30bd7aee3c8a","observation_id":"2f3cd848-b40d-4f1a-8612-9d5047d792ff","resolution":{"observed_at":"2026-08-10T20:24:29.993098Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.978611Z","title":"Transportation cost for Gaussian and ot her product measures,","venue":null,"work_id":"8ba1978b-b7d5-46f5-be75-8f24752daf05","year":1996},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.600036Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:ed52333d639430cbb9d0ea182330e7b62ca417dad27e0e01e13cc5ae82458456","observation_id":"7d7c02b5-0f93-4a39-8c88-0902acc4ab1c","resolution":{"observed_at":"2026-08-10T20:24:29.982432Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.966880Z","title":"Connecting GANs, mean- ﬁeld games, and optimal transport,","venue":null,"work_id":"4900bcd1-94af-4c78-b86d-00bbf1b05257","year":2024},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.604350Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:823c5e96cf930ec7c7f248e3370626ff69c6f88afb4f06de793886da0ae7cd1c","observation_id":"fbba0974-1af1-43f0-9395-b9fec615c38e","resolution":{"observed_at":"2026-08-10T20:24:29.971386Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.04398","last_updated":"2022-07-09T07:16:41Z","snapshot_observed_at":"2026-08-19T10:07:01.938585Z","submitted_at":"2021-12-08T16:45:31Z","title":"Matching for causal effects via multimarginal unbalanced optimal transport","version":2},"cited_work":{"arxiv_id":"2112.04398","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.04398","snapshot_observed_at":"2026-08-10T20:24:29.750721Z","title":"Matching for causal effects via multimarginal unbalanced optimal transport","venue":"stat.ME","work_id":"ddaa62a2-64f7-4f4d-ba3c-b72feb11f7a1","year":2021},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.608071Z"},"links":{"cited_paper":"/paper/2112.04398","citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:9c134e989e76bf6515e8aed69942cd90b34e70b3bcf8d0e72dc6a215e2b3666d","observation_id":"6e3259b0-8213-4916-bb60-e11a21856622","resolution":{"observed_at":"2026-08-10T20:24:29.755441Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.956321Z","title":"Convexity of mutual informatio n along the Ornstein-Uhlenbeck ﬂow,","venue":null,"work_id":"e1ce3575-9faa-444b-964f-c3a57d950231","year":2018},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.612188Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:e8890860828d5a84f9d8a0ad376a06fae4fba54ffcafc94a31b0c97466fc42a8","observation_id":"1c7268a5-dbbe-4c60-b170-57b930e37670","resolution":{"observed_at":"2026-08-10T20:24:29.960087Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1901.10893","last_updated":"2019-01-31T06:27:44Z","snapshot_observed_at":"2026-08-16T10:54:30.824687Z","submitted_at":"2019-01-30T15:18:29Z","title":"Transportation Proof of an inequality by Anantharam, Jog and Nair","version":2},"cited_work":{"arxiv_id":"1901.10893","doi":null,"metadata_source":"pith","pith_arxiv_id":"1901.10893","snapshot_observed_at":"2026-08-10T20:24:29.730688Z","title":"Transportation Proof of an inequality by Anantharam, Jog and Nair","venue":"cs.IT","work_id":"b3a41742-86e7-41a9-9e8a-177949faa4e3","year":2019},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.615972Z"},"links":{"cited_paper":"/paper/1901.10893","citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:f02b99dfd792f5018ec64cb7e81d08f3ce3fb630ce946794be52e040a13759e1","observation_id":"c7621bf1-bc05-4307-bdc9-d1475b53211e","resolution":{"observed_at":"2026-08-10T20:24:29.737296Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.945846Z","title":"Optimal transport meets information science: from measure concentration, to information theory, to machine learning ,","venue":null,"work_id":"e5056398-354d-4c4f-ac89-e90fdd223e4c","year":2022},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.620066Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:5b3ee26a955e86e2e87c56c2eaefb911a314dbdc6c61a0a21d7082e08c32a78c","observation_id":"f8e69cbe-9def-48bf-9bca-b540eb8c2945","resolution":{"observed_at":"2026-08-10T20:24:29.949609Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.934841Z","title":"Information constrained op timal trans- port: From Talagrand, to Marton, to Cover,","venue":null,"work_id":"8dc20f7a-4b44-4cca-b886-d4849ac5a5d0","year":2023},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.623605Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:abb9702f967ee8a4cf70652f3814c4924b539ac687ea946d614b6752fa511cd3","observation_id":"c2d45a86-0ea6-4e64-9669-77a6b4ed1079","resolution":{"observed_at":"2026-08-10T20:24:29.938715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.923826Z","title":"Villani, Optimal transport: old and new , ser","venue":null,"work_id":"98c150dc-392b-423e-9265-bd72225f0eee","year":2009},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.627162Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:4aefaf33d96eb6c74bbee85f2c706608519d6738940680dc43438bbc2baa3a35","observation_id":"8b53d647-d838-4b2f-b7f6-2927e5e40e7c","resolution":{"observed_at":"2026-08-10T20:24:29.927729Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.910355Z","title":"Charac- terization of a class of weak transport-entropy inequaliti es on the line,","venue":null,"work_id":"f3ca3d7d-54d7-46fb-9798-26a9de129ee8","year":2018},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.630931Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:13fdde260fc028534878b5b166c7d3f37bd21d0469d7a779b35b9f6a27a85adb","observation_id":"1ec7139d-1b19-4f78-a65d-3aa9eb0db33a","resolution":{"observed_at":"2026-08-10T20:24:29.914843Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.897859Z","title":"On a mixture of Brenier and Str assen theorems,","venue":null,"work_id":"00de16b7-16cf-4746-a0a8-55ad5712d805","year":2020},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.634722Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:934cb1b4e23cfdf5420a6db051264a888bead034a3fc3e871fe1188a66dc898a","observation_id":"1c7e863c-d9b7-4f5b-8654-32b59abfcf47","resolution":{"observed_at":"2026-08-10T20:24:29.902177Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.886293Z","title":"We ak monotone rearrangement on the line,","venue":null,"work_id":"b3abb1cb-4507-4cca-a113-159494da85b2","year":2020},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.638276Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:5ea4a298bb609a71d5413b20a9c8acadef77c1d5bf4c54476fcbee98d84b12d8","observation_id":"bc350a43-4ce4-4767-8d86-60b2a8bed5f2","resolution":{"observed_at":"2026-08-10T20:24:29.890104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.873940Z","title":"Stability of mart ingale optimal transport and weak optimal transport,","venue":null,"work_id":"6799cd3f-1787-4df6-b732-d703a45952b7","year":2022},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.641860Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:a639e4553eafa8db32568d8d639b2fee16e5f31e593276c72289a873273519f9","observation_id":"4196542e-0683-4b1e-bfb6-ce09d2ee54eb","resolution":{"observed_at":"2026-08-10T20:24:29.877973Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.863129Z","title":"Weak transpor t for non- convex costs and model-independence in a ﬁxed-income marke t,","venue":null,"work_id":"7c463f57-5371-4475-8f7d-4ff57b20387e","year":2021},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.645415Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:002a15fa0dc06fd69fa25229047043f65c0cf91627b067d809448a9990d8cd4b","observation_id":"54677309-6bbf-4f6e-91c1-0d8edfaf9100","resolution":{"observed_at":"2026-08-10T20:24:29.866953Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.852191Z","title":"Über die umkehrung der naturgesetze,","venue":null,"work_id":"e83376d4-1bff-48b7-907c-0ddeb3081547","year":1931},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.648721Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:5dc37ca1adc1f56dd9be8ad0b30abeab4e1c81a48231d7a724d7c11b45b0022c","observation_id":"3735ee4c-350f-4517-b53b-85292bb3d62c","resolution":{"observed_at":"2026-08-10T20:24:29.856029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.840595Z","title":"Introduction to entropic optimal transport,","venue":null,"work_id":"e7e5577f-9ef3-4ae3-98e1-65b5b6877649","year":2021},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.651835Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:9ecb8f0e7a36c283428f7fbb7e0ea07fdc4c367622f15ae10234b031f51e6e5c","observation_id":"1da1b975-d07e-4070-8c53-b42b17103ab8","resolution":{"observed_at":"2026-08-10T20:24:29.844435Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.09362","snapshot_observed_at":"2026-08-10T20:24:29.655182Z","title":"A revisit to rate-dis tortion theory via optimal weak transport,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.655182Z"},"links":{"cited_paper":"/paper/2501.09362","citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:a8b41990ac2e5f6aa01d0e9cf4cef9fb2308f6b333aef2afab47e9e4b233eeff","observation_id":"8b6beba7-e082-4a5b-8b70-63f4fec0b9fb","resolution":{"observed_at":"2026-08-10T20:24:29.655182Z","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":"2026-08-10T20:24:29.658678Z","title":"Dupuis and R","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.658678Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:3ff3aebc0fc4146e889bd3ec75d3946d594ccd7591f90842bac9522eed57cd84","observation_id":"86308450-9460-4497-89d4-b124744f6c72","resolution":{"observed_at":"2026-08-10T20:24:29.658678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.11686","last_updated":"2024-08-21T15:07:25Z","snapshot_observed_at":"2026-08-16T13:24:51.917326Z","submitted_at":"2024-08-21T15:07:25Z","title":"Plug-in estimation of Schr\\\"odinger bridges","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.11686","snapshot_observed_at":"2026-08-10T20:24:29.662147Z","title":"Plug-in estimatio n of Schrödinger bridges,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.662147Z"},"links":{"cited_paper":"/paper/2408.11686","citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:38ded15377cbcb606de47bfc5c8d48389af1c1758223e7dc01acc256984dddb9","observation_id":"734c9850-7e2e-44f6-a64d-0d2803c1cc9a","resolution":{"observed_at":"2026-08-10T20:24:29.662147Z","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":"2026-08-10T20:24:29.822369Z","title":"Wasserstein proximal algorit hms for the Schrödinger bridge problem: Density control with nonlinea r drift,","venue":null,"work_id":"a88ee11a-73bb-4a9b-b763-c66b0db74e85","year":2021},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.665900Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:a88409ef682c102864f553ad4e880108f508d4730c640b4f87c920bff521826a","observation_id":"8f2c65aa-9b71-449c-bb90-c595da24c45d","resolution":{"observed_at":"2026-08-10T20:24:29.826483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.810279Z","title":"An optimal transport approac h for the Schrödinger bridge problem and convergence of sinkhorn alg orithm,","venue":null,"work_id":"d8a6197b-f8d3-46b4-8ca5-b94c920d81cf","year":2020},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.668993Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:4b138ea0207193645fc36b87183da02b25df7ba447436bcfb430323bccce8f51","observation_id":"514c0341-061d-4830-8949-17ab57a8c354","resolution":{"observed_at":"2026-08-10T20:24:29.814637Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.798931Z","title":"Random coding strategies for minimum entro py,","venue":null,"work_id":"5b0ee65b-41b9-4d3d-85e4-3e08bcf5b397","year":1975},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.672212Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:d90a066795dd299c1d64110d0786ad0c6e36969a9401297cdd19a394b9ecca83","observation_id":"628a5a6d-3262-4db5-81e6-08d768398573","resolution":{"observed_at":"2026-08-10T20:24:29.802802Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-10T20:24:29.787671Z","title":"Polyanskiy and Y","venue":null,"work_id":"3c8949ed-97ee-4876-8c5c-836654c1e05a","year":2025},"citing_paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-10T20:24:29.675432Z"},"links":{"citing_paper":"/paper/2501.09362"},"observation_digest":"sha256:fe08b2a456cccd458a1fb439d23b068efe9a811eb12dfea13742c759b1fcd21b","observation_id":"baa39612-3e09-4b21-bbfe-bf71f0f80e85","resolution":{"observed_at":"2026-08-10T20:24:29.791243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.09362","last_updated":"2025-01-24T08:11:45Z","latest_version":3,"primary_category":"cs.IT","snapshot_observed_at":"2026-08-15T15:40:12.746858Z","submitted_at":"2025-01-16T08:17:38Z","title":"A Revisit to Rate-distortion Theory via Optimal Weak Transport"},"reference_resolution":{"displayed":48,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":3,"verified_fuzzy":38},"total_outbound_references":48},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 2 inbound Pith citation observations for arXiv:2501.09362."}