{"as_of":"2026-08-21T21:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b10ebae637d6eef34af65dcb3e15e7e5c5c8ca2be37c14e47b8977b1faea7b09","coverage":[{"denominator":14,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T23:01:21.129965Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+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/2412.03120/citation-record","integrity":"/paper/2412.03120/integrity","json":"/paper/2412.03120/citation-record.json","paper":"/paper/2412.03120"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T23:01:21.479972Z","title":"Altschuler, Jonathan Weed, and Philippe Rigollet","venue":null,"work_id":"13c0432a-230f-40d3-b9b6-42d9bd5db8b7","year":1964},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.085776Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:2fef894fe4f609029d9264d856b8626a1ccdc08162d0e37e5ef3aacb30325326","observation_id":"eee06af7-279a-4611-97df-d5b1e9e2ff04","resolution":{"observed_at":"2026-08-11T23:01:21.482794Z","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":"2026-08-11T23:01:21.471048Z","title":"We refer Boyd and V andenberghe(2004) as a reference for the Lagrange duality, including the definition of the Lagrangian","venue":null,"work_id":"5495595d-fb0e-40dd-b3c6-257b77e225af","year":2004},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.127071Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:10e367200a1257d922a5d2046225110fce26189928f879c647712ec7c28c28fc","observation_id":"a1089a5e-7200-467c-8f73-4c89b287ecab","resolution":{"observed_at":"2026-08-11T23:01:21.474135Z","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":"2309.11666","last_updated":"2025-04-09T06:18:45Z","snapshot_observed_at":"2026-08-19T08:14:15.906696Z","submitted_at":"2023-09-20T22:19:49Z","title":"Error estimate for regularized optimal transport problems via Bregman divergence","version":2},"cited_work":{"arxiv_id":"2309.11666","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.11666","snapshot_observed_at":"2026-08-11T23:01:21.317724Z","title":"Error estimate for regularized optimal transport problems via Bregman divergence","venue":"math.OC","work_id":"fbabdbdd-774e-425c-b0cb-5792f4a775f1","year":2023},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.110502Z"},"links":{"cited_paper":"/paper/2309.11666","citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:b849e05b8d4939d6e906c47d7fe389397db30dfae18929f1ac3d431540978db8","observation_id":"512142ba-34c2-4783-b2e7-08124eee4c1d","resolution":{"observed_at":"2026-08-11T23:01:21.322003Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T23:01:21.116889Z","title":"URL http://projecteuclid.org/euclid.mmj/1028990177","venue":null,"work_id":null,"year":1945},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.116889Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:b91d6a2c52cdbc696751a192aac863ac7ad40d2bc461c60c5e438b5f092ea5b8","observation_id":"d762dd42-4d22-4f05-813d-1d7b537b17b0","resolution":{"observed_at":"2026-08-11T23:01:21.116889Z","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":"2026-08-11T23:01:21.460575Z","title":"Slivkins et al","venue":null,"work_id":"12a52eb4-c87f-4a00-8ddb-bb7c96b256f2","year":2019},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.129965Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:ad708720db3a4da178c6665bcf1309b99f4546d855b509a13034454e5fe617f4","observation_id":"d6396dee-b81e-4e50-b696-f8bc114a6082","resolution":{"observed_at":"2026-08-11T23:01:21.463694Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T23:01:21.089849Z","title":"doi: 10.2307/19 92971","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":1957,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.089849Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:2344a8fa4587a42d1cb9be56513b86c1c668b77504465c3d6599eadbbac52cae","observation_id":"86245929-0da8-458c-afa0-0cc8da631fc1","resolution":{"observed_at":"2026-08-11T23:01:21.089849Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-11T23:01:21.096193Z","title":"doi: https://doi.org/10.1016/0024-3795(89) 90490-4","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":1989,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.096193Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:d1f0deb71d1184b49352b903a4cb1c9e4eeb993f27df959a75b206ccb25951c0","observation_id":"82fb86e4-9a80-4e31-b7b2-d89b9a445126","resolution":{"observed_at":"2026-08-11T23:01:21.096193Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/(sici)1097-0312(199801)51:1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T23:01:21.148103Z","title":"URL https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0312%28199801%29 Giacomo Greco, Maxence Noble, Giovanni Conforti, and Alain Durmus","venue":null,"work_id":"4263bf60-f9c3-4dc3-b32b-a400d618ae29","year":null},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":1998,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.102914Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:04bd27704f2876348aadcd2a52ebfcdaeb993cf5c403c0f0276b95ff0354759d","observation_id":"39478ab4-1419-43d6-b649-b19ccce4453a","resolution":{"observed_at":"2026-08-11T23:01:21.152157Z","resolver_source":"doi","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":"2407.14186","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T23:01:21.449321Z","title":"doi: https://doi.org/10.1 016/j.laa.2003.05.002","venue":null,"work_id":"c787d0dd-ba48-4056-9e53-135e08453e19","year":2003},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":2003,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.093133Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:1b5ffed6639def628d8f8580a1b59e49359827556bafd78e4addc608a531a48d","observation_id":"77c4c43a-4b38-4c87-85d6-11ae09f36921","resolution":{"observed_at":"2026-08-11T23:01:21.454138Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T23:01:21.099721Z","title":"URL https://doi.org/10.1214/13-AAP925","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.099721Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:7a0b47257d91c3b52a6451de6e68ca17b5adff23f53b602d9152bd9bbea6415e","observation_id":"e4a646f3-15f6-4596-859e-7b68d8e5902b","resolution":{"observed_at":"2026-08-11T23:01:21.099721Z","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":"2026-08-11T23:01:21.114050Z","title":"URL http://www.numdam.org/articles/10.1051/m2an/2015020/","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.114050Z"},"links":{"citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:51737232a7945fb9b42829ef198c5a318005a7e5ec1ef78d28ca6fb0c869cbaf","observation_id":"a386c0e9-fb98-4076-a921-0da1b3b0e9c9","resolution":{"observed_at":"2026-08-11T23:01:21.114050Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.05054","last_updated":"2024-03-08T05:01:43Z","snapshot_observed_at":"2026-08-21T14:47:16.566029Z","submitted_at":"2024-03-08T05:01:43Z","title":"A Sinkhorn-type Algorithm for Constrained Optimal Transport","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.05054","snapshot_observed_at":"2026-08-11T23:01:21.120294Z","title":"A sinkhorn-type algorithm for constrained optimal transport","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.120294Z"},"links":{"cited_paper":"/paper/2403.05054","citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:79d5387bca5b1ec1372bad0d89d68b012ea9c53ab65126518414086c0b1e814f","observation_id":"28ea866a-78bc-48de-81e7-bf7ea148ec16","resolution":{"observed_at":"2026-08-11T23:01:21.120294Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.20238","last_updated":"2024-03-29T15:31:13Z","snapshot_observed_at":"2026-08-16T14:05:10.250290Z","submitted_at":"2024-03-29T15:31:13Z","title":"An ordinary differential equation for entropic optimal transport and its linearly constrained variants","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.20238","snapshot_observed_at":"2026-08-11T23:01:21.106621Z","title":"An ordin ary differential equation for en- tropic optimal transport and its linearly constrained vari ants","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.106621Z"},"links":{"cited_paper":"/paper/2403.20238","citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:d71bb86c90c484876597b2f604f07b558fe643e2b67f7e103d2fe748239a21a7","observation_id":"45663369-8feb-4822-a478-72dfbc30ef49","resolution":{"observed_at":"2026-08-11T23:01:21.106621Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.08550","last_updated":"2025-01-25T04:50:05Z","snapshot_observed_at":"2026-08-16T13:26:05.717715Z","submitted_at":"2024-08-16T06:33:56Z","title":"String Diagram of Optimal Transports","version":2},"cited_work":{"arxiv_id":"2408.08550","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.08550","snapshot_observed_at":"2026-08-11T23:01:21.170280Z","title":"String Diagram of Optimal Transports","venue":"cs.AI","work_id":"7d36c29d-76ff-43da-a04f-b3c423c2b71b","year":2024},"citing_paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports","version":4},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-11T23:01:21.123898Z"},"links":{"cited_paper":"/paper/2408.08550","citing_paper":"/paper/2412.03120"},"observation_digest":"sha256:8cabc8e7028cb2ee0838b1b4628352cfaf559e8e95f2db2b505da8730a81dd39","observation_id":"484c81cb-92fb-4c62-be41-1015b27f71b9","resolution":{"observed_at":"2026-08-11T23:01:21.174187Z","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"}}],"paper":{"arxiv_id":"2412.03120","last_updated":"2025-01-12T08:12:17Z","latest_version":4,"primary_category":"cs.DS","snapshot_observed_at":"2026-08-16T18:49:11.102998Z","submitted_at":"2024-12-04T08:39:45Z","title":"Sinkhorn Algorithm for Sequentially Composed Optimal Transports"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":3,"verified_fuzzy":3},"total_outbound_references":14},"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 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2412.03120."}