{"as_of":"2026-08-08T18:02:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:09b2ac83efaf286561471e198906e990d26c223ebcae40bcb5005c8c754da253","coverage":[{"denominator":76,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":76,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T10:38:33.256048Z","state":"measured"},{"denominator":76,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":76,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2507.23602/citation-record","integrity":"/paper/2507.23602/integrity","json":"/paper/2507.23602/citation-record.json","paper":"/paper/2507.23602"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:25.717409Z","title":"Barycenters in the Wasserstein Space","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:25.717409Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:dd2dd7870aa29de5e7f71b5c12e707ac360ce045813cda39a1489415153c108b","observation_id":"67b0046d-ff44-4965-9fe4-18e752d8bc49","resolution":{"observed_at":"2026-08-06T10:38:25.717409Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.02827","last_updated":"2019-05-15T15:21:50Z","snapshot_observed_at":"2026-07-06T07:13:13.692754Z","submitted_at":"2018-11-07T10:50:40Z","title":"Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference","version":2},"cited_work":{"arxiv_id":"1811.02827","doi":null,"metadata_source":"pith","pith_arxiv_id":"1811.02827","snapshot_observed_at":"2026-08-06T10:38:41.341312Z","title":"Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference","venue":"stat.ML","work_id":"d392767c-8a2d-43dd-8647-7dcf949468a9","year":2018},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:25.822612Z"},"links":{"cited_paper":"/paper/1811.02827","citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:2f5619b01183c3761e74ff5fa81149abce131ef08e3d9b142941ca18bd02a5ea","observation_id":"530f13e8-2961-457d-820e-b45119b1d401","resolution":{"observed_at":"2026-08-06T10:38:41.448200Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:45.016804Z","title":"Gradient Flows in Metric Spaces and in the Space of Probability Measures","venue":null,"work_id":"3fecb3e0-e495-4def-b1c4-754483e09639","year":2008},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:25.916360Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:8d0c6d3f5afc21c1cc76a537d2495c102668c40405783b204fa86b3d8c8403c7","observation_id":"0cb7efa1-a9a9-40f6-9f6b-6357f2f7b225","resolution":{"observed_at":"2026-08-06T10:38:45.115063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:25.990817Z","title":"Automated fault detection without seismic processing","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:25.990817Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:f35449211d2f7ac36a7368651559db65abf295b07e8459dae28966228917ae82","observation_id":"098db7b2-e5a6-4434-9e25-e70e34b3c608","resolution":{"observed_at":"2026-08-06T10:38:25.990817Z","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":"10.1145/116873","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:36.647999Z","title":"Voronoi diagrams—a survey of a fundamental geometric data struc- ture","venue":null,"work_id":"7e644ebb-582b-4aa5-bb4c-b067abab500a","year":1991},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.125441Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:93f09231c693bad202f3606e1104c04240d028559dd5bdf15d808e4984af425e","observation_id":"f88a2e5b-0222-46e8-bcff-86c03e08f3a8","resolution":{"observed_at":"2026-08-06T10:38:36.755628Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/pl00009187","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:36.338098Z","title":"Minkowski-type theorems and least-squares clustering","venue":null,"work_id":"438d65b9-c68e-49f5-a47c-1088c690a07f","year":1998},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.194058Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:56cf14feb07bd78702d297eb47e743136a3a84f01ce6af5f704b4e4c7f976e63","observation_id":"d961322c-29b2-40f7-921b-d745dfa2fc30","resolution":{"observed_at":"2026-08-06T10:38:36.525225Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3390/a15090311","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:36.032084Z","title":"Accelerating the Sinkhorn Algorithm for Sparse Multi-Marginal Optimal Transport via Fast Fourier Transforms","venue":null,"work_id":"08415ea6-f8c1-4ef1-8958-e2386f94c6ec","year":2022},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.269795Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:e30072385da92b352a30d0d988841384f1f38241b105e78f0108954096133138","observation_id":"331da25e-f3eb-4493-8a6b-fd9c2c213f9f","resolution":{"observed_at":"2026-08-06T10:38:36.209211Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:26.325037Z","title":"deal.II—A general-purpose object-oriented finite element library","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.325037Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:6c657df09b0a174422d3ab84f4ca664c1668d82b451594411097cccc6a562ec7","observation_id":"45bca663-33ca-451e-83ff-aae873e82061","resolution":{"observed_at":"2026-08-06T10:38:26.325037Z","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":"10.1137/20m1357226","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:35.854355Z","title":"A Newton Algorithm for Semidiscrete Optimal Transport with Storage Fees","venue":null,"work_id":"f40df3bf-b570-46c0-9288-20af08ccd6ff","year":2021},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.404808Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:7fc5110375b9b3f6310e4ff60f43357b56ef123b4fe744faa5d2dc8258d52dbe","observation_id":"44e50365-a15b-4bee-9498-c99e9c966624","resolution":{"observed_at":"2026-08-06T10:38:35.933611Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:26.478434Z","title":"A hierarchical O(N log N) force-calculation algorithm","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.478434Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:73196e6e7c1339dff47ab7b1d993a6cf033196a49f996e9cc3c1a9aaa4347f0f","observation_id":"9824d604-5e85-4b33-b8ec-82b18adda874","resolution":{"observed_at":"2026-08-06T10:38:26.478434Z","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":"2026-08-06T10:38:26.540720Z","title":"Iterative Bregman Projections for Regularized Transportation Problems","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.540720Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:50b620327b9d80a0232880e92dd65a6bf53822d6297156c4ffbed0d081adda17","observation_id":"2ec0cdd7-0984-4f4d-8478-15b1fbc1b9b5","resolution":{"observed_at":"2026-08-06T10:38:26.540720Z","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":"2026-08-06T10:38:44.802275Z","title":"Auction algorithms for network flow problems: A tutorial introduc- tion","venue":null,"work_id":"4644e1f7-821c-4848-9b8a-1b6d71253cc0","year":1992},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.658014Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:ba8766b44f6695bd1727887a6d22cbde37fda3ec2d34158ec6849bf3d0c0971d","observation_id":"bb110f47-d3ac-40e1-95c0-6a11ca7b6b4c","resolution":{"observed_at":"2026-08-06T10:38:44.894233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1111/cgf.14778","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:35.612082Z","title":"A survey of Optimal Transport for Computer Graphics and Computer Vision","venue":null,"work_id":"ff7fc292-b6ab-4d7d-bffc-3b6634530e72","year":2023},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.729241Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:eea14abce6504eaf58e9b1ef6b487bc4ca35b21ef25b60d0b80da4e61b38f337","observation_id":"af9e2aa5-258a-4361-982a-41a1ec91599f","resolution":{"observed_at":"2026-08-06T10:38:35.681791Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:26.788930Z","title":"Brenner and L","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.788930Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:fd71ccc67b19feb2e9c60a0a90993fa5317004d18f3a776ced09f801a6be598c","observation_id":"ed504bd3-7e64-47dd-8624-06f2e449873b","resolution":{"observed_at":"2026-08-06T10:38:26.788930Z","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":"2024.11331","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:40.939793Z","title":"Anisotropic power diagrams for polycrystal modelling: Efficient generation of curved grains via optimal transport","venue":null,"work_id":"7e4a8172-d381-42f2-9a70-bdf415b84025","year":2024},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.855967Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:d50fb3326f082504dff53803a7c226d8c2833882d247f9a59f301d92b76c0546","observation_id":"f5102aae-4254-4ba7-a4b8-929519865ecf","resolution":{"observed_at":"2026-08-06T10:38:41.056631Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:26.923457Z","title":"A Fast Adaptive Multipole Algorithm for Particle Simulations","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:26.923457Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:0c7203c9047de858b977968337d44bda54f382240b45969a2cb1b2c3df8ab93e","observation_id":"952b5da5-22b9-4c30-9a45-ac5968f0742d","resolution":{"observed_at":"2026-08-06T10:38:26.923457Z","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":"2026-08-06T10:38:27.028042Z","title":"An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:27.028042Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:c9a982f2f90e48d43811b5105ac2a6ee4f452deb125d563a0d8815450fb0aca2","observation_id":"061f4dbd-f659-4962-bdde-078eb359b595","resolution":{"observed_at":"2026-08-06T10:38:27.028042Z","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":"2026-08-06T10:38:27.176539Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:27.176539Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:f2d05ee3895cd05d3c5e0213b4cdf6b8df747d0873050cbe42d10f37b6ae290a","observation_id":"25e089df-261f-4913-8e69-bc20c3cd5dda","resolution":{"observed_at":"2026-08-06T10:38:27.176539Z","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":"2016.26159","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:40.583063Z","title":"Optimal Transport for Domain Adaptation","venue":null,"work_id":"155b863d-f223-4e15-9250-11568927dd01","year":2017},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:27.284974Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:80c7b72fd2f78f4dff2086625d2b58325cc8e1f6a66174e6bedfc066ee33fd7f","observation_id":"1ca4f7c0-cbb6-4d47-b5fc-22b6a18c2ff0","resolution":{"observed_at":"2026-08-06T10:38:40.745942Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:44.606935Z","title":"Sinkhorn Distances: Lightspeed Computation of Optimal Transport","venue":null,"work_id":"f0b2d729-f16e-418e-b120-bf6acf09be5f","year":2013},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:27.388277Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:b08483c5de6ca4d336cdedf56ea012e99ec9d8421b25b911ad38bb1bbc8b8b95","observation_id":"b9167b5c-f52a-415d-9e83-6c3a8052bb9a","resolution":{"observed_at":"2026-08-06T10:38:44.685475Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:44.394086Z","title":"Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method","venue":null,"work_id":"47f2ddfd-fccc-45e6-9093-f6aef1f8663e","year":2024},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:27.575703Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:e6007bc581a385e83293f4d39d0f4039abda05e2e8857fabb082c04fe37653ea","observation_id":"6ea7f243-347c-432e-8ba4-63a96f48329a","resolution":{"observed_at":"2026-08-06T10:38:44.461139Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.17086","last_updated":"2026-05-19T05:51:29Z","snapshot_observed_at":"2026-08-01T03:28:42.074300Z","submitted_at":"2024-02-26T23:53:18Z","title":"Multicellular simulations with shape and volume constraints using optimal transport","version":4},"cited_work":{"arxiv_id":"2402.17086","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.17086","snapshot_observed_at":"2026-08-06T10:38:40.274253Z","title":"Multicellular simulations with shape and volume constraints using optimal transport","venue":"q-bio.QM","work_id":"a48c7415-451c-4790-8318-7e94385184da","year":2024},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:27.888110Z"},"links":{"cited_paper":"/paper/2402.17086","citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:9cf84b581a3142889780a67c0ebca5d02a15353ce88bafa605928b03c1842560","observation_id":"705327ec-ee06-44fc-adcd-9f498a214124","resolution":{"observed_at":"2026-08-06T10:38:40.362429Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:44.202930Z","title":"Centroidal Voronoi Tessellations: Appli- cations and Algorithms","venue":null,"work_id":"8d94fd31-7ed6-4077-9b36-019789bb71ba","year":1999},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:28.077917Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:4a9a49a25f0c68af2627469bb4d5d0b4551d0f8d421fdd88b429c99a44abf182","observation_id":"9e6cf05e-b8eb-4ac4-99c7-a39d031c34ed","resolution":{"observed_at":"2026-08-06T10:38:44.306817Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:44.010802Z","title":"Analyse de données géométriques, au delà des convolutions","venue":null,"work_id":"774499e1-f345-4c54-9079-601855d4421a","year":2020},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:28.200493Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:167679cbf136d7fe9d76f13da4dabc61459410daa2b49b592f8511f4da0ff463","observation_id":"bfffa80a-55f2-488e-9183-b5368ad0c946","resolution":{"observed_at":"2026-08-06T10:38:44.088284Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:43.826946Z","title":"Interpolating between Optimal Transport and MMD using Sinkhorn Diver- gences","venue":null,"work_id":"a7497400-5184-4a7f-b85d-f488df92cde2","year":2019},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:28.380554Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:9f66683ca98278223e05f9852749dbe4381b8edb1f22bc0362464e45c0c49611","observation_id":"94dfd5da-0dd2-49c6-b0c6-54ad2c318d25","resolution":{"observed_at":"2026-08-06T10:38:43.937128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:43.628225Z","title":"Sample Complexity of Sinkhorn Divergences","venue":null,"work_id":"fbe311ff-be1d-45b3-be64-91afc0c83cf1","year":2018},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:28.535072Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:e5025f48181b5792bdaf7f53905f01f013838394451a68e6d7ba94985b4f2663","observation_id":"ed4decb8-8c34-4bc7-b132-d1e4ecfda5f7","resolution":{"observed_at":"2026-08-06T10:38:43.727986Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:43.464852Z","title":"Stochastic Optimization for Large-scale Optimal Transport","venue":null,"work_id":"1deff405-9f72-4956-ba07-5891f1d2094e","year":2016},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:28.750238Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:3d80d837a7837ad8b9360e8e82c88c514bc15cd2846dd7c9f825dc48cb57196a","observation_id":"edfdda6b-84f6-4c47-9f67-9fd044be17c6","resolution":{"observed_at":"2026-08-06T10:38:43.535160Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1201/9781003281344-13","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:35.168341Z","title":"Wasserstein Generative Adversarial Network (WGAN)","venue":null,"work_id":"253adf6c-0aa7-4ce1-8352-33ab03a3a78b","year":2023},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:28.846281Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:af9ee0d4fcb23f512914f72598258abc3ced6070a770fdecb41a20f81b1e524c","observation_id":"bb3429c1-6d12-4605-a656-3bb48d1e284d","resolution":{"observed_at":"2026-08-06T10:38:35.222165Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:28.901921Z","title":"Blue noise through optimal transport","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:28.901921Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:0f02acabcb17e99e4f8bc8337ca652376a8fd993585ed09b6618b268deadb241","observation_id":"4794299f-8199-4ae0-88cd-0e1c362363ec","resolution":{"observed_at":"2026-08-06T10:38:28.901921Z","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":"2026-08-06T10:38:43.262256Z","title":"Power particles: an incompressible fluid solver based on power diagrams","venue":null,"work_id":"0ad35259-3ee7-4686-9dcf-15511fd46d68","year":2015},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:28.991601Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:7031bfe672044bc0c2d93a9d5cf7a244de986e8b9840a8e35baa2d2b80ef6286","observation_id":"d2adeaf7-51c6-42c3-84f2-4ec62f5f0c38","resolution":{"observed_at":"2026-08-06T10:38:43.354758Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:29.128646Z","title":"A fast algorithm for particle simulations","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:29.128646Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:5c44b1627d3cee1d1d86c87c3b9b8157695aa9b2f2834773acfaef2a6607529f","observation_id":"2dd0292f-e0bd-4f22-90bd-f5ef6fa38eb3","resolution":{"observed_at":"2026-08-06T10:38:29.128646Z","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":"10.4310/ajm.2016.v20.n2.a7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:35.015947Z","title":"Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge–Ampère equations","venue":null,"work_id":"a3e08b0d-c8b5-46d7-90f8-399821e6b49c","year":2016},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:29.282562Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:366a00224c5d3189ac888146e1728dc7b8f3eed9a7112ae6cc1c3e0a8ef85ad6","observation_id":"bdcf165e-18cb-43eb-a9f8-4eea58f15361","resolution":{"observed_at":"2026-08-06T10:38:35.054152Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"1697.60226","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:39.943690Z","title":"R-trees: a dynamic index structure for spatial searching","venue":null,"work_id":"a1a96b34-61a4-4962-9ec1-4b7944bd5e64","year":1984},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:29.428741Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:04348b76fac7c8f4ad68ea7179712e2279799c88f6615763a67a2c6a8aff74e8","observation_id":"8f0ad6af-4d99-474a-ad0e-526e1ffe95ed","resolution":{"observed_at":"2026-08-06T10:38:39.991028Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"6836.66311","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:39.712398Z","title":"Optimal Mass Transport for Registration and Warping","venue":null,"work_id":"c2451116-1049-403f-bf74-40420978819e","year":2004},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:29.549900Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:6303bd9d46115444a84626463e2397cef08b7c19da124a6e6759f6f482cb97bc","observation_id":"492a8236-8dca-4a07-965b-cf6e8d60dc19","resolution":{"observed_at":"2026-08-06T10:38:39.808664Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:43.041143Z","title":"Computer Simulation Using Particles","venue":null,"work_id":"fbf8bb22-c19c-4562-babe-35a23905898b","year":null},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:29.665851Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:6787419ed5be8e6bcf4a432c975ba714a6bc10fd93bd65960270e29d28957b81","observation_id":"6414ee94-212c-4985-bb3b-6d1cf736c956","resolution":{"observed_at":"2026-08-06T10:38:43.152386Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:42.854404Z","title":"Billion-scale similarity search with GPUs","venue":null,"work_id":"3fb097e0-aaa9-4cad-b497-6b8fce1d7a19","year":2019},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:29.887618Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:55332f17b0c52a6e2b265e5aae13bc09d7760ec159e79af13dd90602171b3eb6","observation_id":"0325e8da-5524-4944-9fae-39fc29e55b1a","resolution":{"observed_at":"2026-08-06T10:38:42.964530Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:29.980353Z","title":"The Variational Formulation of the Fokker–Planck Equation","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:29.980353Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:8ca9a2d2ba90f3eeae728ae59d07e1b1e6f218e4b412b490c3fa0d402a230752","observation_id":"1cdf50cf-567f-4575-8a00-f9288edb09b3","resolution":{"observed_at":"2026-08-06T10:38:29.980353Z","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":"2026-08-06T10:38:30.044652Z","title":"On the translocation of masses","venue":null,"work_id":null,"year":1942},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.044652Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:deb52401a80f6f6eb8b46cf08c8bea715a51f6eeadc92a2caea8484b25e4306a","observation_id":"7a204362-c052-4e95-ab52-99527820c3c3","resolution":{"observed_at":"2026-08-06T10:38:30.044652Z","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":"2025.11393","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:39.466031Z","title":"Optimal transport-based displacement interpolation with data aug- mentation for reduced order modeling of nonlinear dynamical systems","venue":null,"work_id":"61250154-325e-4dcc-9d09-8882fc767c6e","year":2025},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.193241Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:cc665450e4ba81344829693b97b8b22867a642295980e7b7d7cee6cd790092b8","observation_id":"17b7df7f-cd27-4bdd-a67e-3d0fb4b68f52","resolution":{"observed_at":"2026-08-06T10:38:39.544297Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:30.234520Z","title":"Optimization by Simulated Annealing","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.234520Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:fcf22f2b8adc8b5bd49cb3ac636e806ae34b60417c2cc2c1ec8b72d139904652","observation_id":"a43dec15-3aeb-4455-9beb-ee8d16f8ca1d","resolution":{"observed_at":"2026-08-06T10:38:30.234520Z","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":"2026-08-06T10:38:30.320589Z","title":"Convergence of a Newton algorithm for semi-discrete optimal transport","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.320589Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:83520f12eafc98eb2deec89331c710e7e2022ff79550ee03e23ea745a9f79868","observation_id":"db2a4917-ee8a-4058-b113-42d22e2a4e5b","resolution":{"observed_at":"2026-08-06T10:38:30.320589Z","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":"2026-08-06T10:38:30.445075Z","title":"A Comparison of Methods for Generating Poisson Disk Dis- tributions","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.445075Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:3b34e0acb7dc691dd673e7a0a3af6224791d14bc8db054a9ba1ca03308b22eb8","observation_id":"f5b115b8-ba79-4773-a4cd-90ea3d243163","resolution":{"observed_at":"2026-08-06T10:38:30.445075Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:42.686353Z","title":"A survey of the Schrödinger problem and some of its connections with optimal transport","venue":null,"work_id":"7b4f8109-a0e0-4f0a-8920-615d75fed419","year":2014},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.515709Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:692da68ce8304ae965236b1b6fb1daba8be5b55d7f667da1d2e4f223371ac647","observation_id":"826b23cb-d539-4b70-bc0a-d9b0e3989f2c","resolution":{"observed_at":"2026-08-06T10:38:42.776352Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:30.689976Z","title":"A Numerical Algorithm for L2 Semi-Discrete Optimal Transport in 3D","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.689976Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:6a22dcd0d92bd02889a38edd7f8e592d3909f2d0ce9704fc1d271ed6fb3120a6","observation_id":"923813cf-531f-4ccb-8aaa-aefee4954854","resolution":{"observed_at":"2026-08-06T10:38:30.689976Z","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":"10.1007/978-3-642-33573-0_21","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T11:07:33.414567Z","title":"Variational Anisotropic Surface Meshing with Voronoi Parallel Linear Enumeration","venue":null,"work_id":"b2fefe33-c2c1-474a-b9ec-f8a1ee16e228","year":2013},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.762344Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:1d214ecee5e867da77a8d6cbf230b215caab71b4c24214796c5915b7c43f1be8","observation_id":"4e354524-e026-46bd-aa85-16ccb232f75b","resolution":{"observed_at":"2026-08-06T10:38:34.820728Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:30.801857Z","title":"Notions of optimal transport theory and how to imple- ment them on a computer","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.801857Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:da96d3d025a97100a7616f9c21d335a2c5342d3a8bfebc82c743944992fb29be","observation_id":"24f4cd2a-7a39-4cd6-a738-94dcd0679ccd","resolution":{"observed_at":"2026-08-06T10:38:30.801857Z","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":"10.1137/18m1219813","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:34.559768Z","title":"Multilevel Optimal Transport: A Fast Approximation of Wasserstein-1 Distances","venue":null,"work_id":"e12a0e0b-733b-4112-8d66-83262c77ca69","year":2021},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.913570Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:49a1baebd6904924e87bf7c405ec87b8913db30204e78acfdf3fdd3f072306b8","observation_id":"a43eb921-0d54-47e3-8f9b-f96283cc8d2b","resolution":{"observed_at":"2026-08-06T10:38:34.666606Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:38.791562Z","title":"On centroidal voronoi tessellation—energy smoothness and fast computa- tion","venue":null,"work_id":"09e2f493-c5e9-49b1-b8eb-2fa7a9d4b7f3","year":2009},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.978975Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:bcb820d6a3b4315484f54c86730e62ae81f4bc1dcfd5a3dfe223c6bed1c1cbcc","observation_id":"23316197-bf8a-49fc-ad52-9c381e14e986","resolution":{"observed_at":"2026-08-06T10:38:38.955502Z","resolver_source":"arxiv_id_nonexistent","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:31.089484Z","title":"Plugin estimation of smooth optimal transport maps","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.089484Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:7e00854bac1dfe3efcf26eb7ca3417d3c8b34bc77a01639c354bb41d3a96e411","observation_id":"2c3c9f98-4f64-449c-8121-ae43a8c1137d","resolution":{"observed_at":"2026-08-06T10:38:31.089484Z","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":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:38.320582Z","title":"A Convexity Principle for Interacting Gases","venue":null,"work_id":"7bda64b6-c26b-42f1-8b86-22f905cd726f","year":1997},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.187657Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:75b86fbe66d8683a5161639f9b4a095d4d264a221114b16eec231f1608899a03","observation_id":"86dc4a6a-0d5a-42c6-a9d6-d28ae0e550fb","resolution":{"observed_at":"2026-08-06T10:38:38.452043Z","resolver_source":"arxiv_id_nonexistent","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:37.721174Z","title":"A Multiscale Approach to Optimal Transport","venue":null,"work_id":"395512ee-b9bd-465b-b035-6b55c8b97e03","year":2011},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.304691Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:880671b75a72ad9b6e88d4e4a45b8ce8887a8c24dd00eeb56c53431fdd689fe0","observation_id":"581eea6f-c019-481c-80a4-22e06ef4f5b3","resolution":{"observed_at":"2026-08-06T10:38:37.903268Z","resolver_source":"arxiv_id_nonexistent","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:42.538729Z","title":"Mémoiresurlathéoriedesdéblaisetdesremblais","venue":null,"work_id":"a6f8886e-4929-4231-a0fe-194e024e863f","year":null},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.373910Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:287933202503855edfaf02818512e97c3215707dc6ba2e147d0f5d87c8fc1017","observation_id":"36702746-660d-4ef6-a1d0-583895270423","resolution":{"observed_at":"2026-08-06T10:38:42.595499Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:42.341899Z","title":"Optimal Transport with Proximal Splitting","venue":null,"work_id":"f6a97be1-4d01-4d0e-9a69-d5e6f9edf003","year":2014},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.433677Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:88fa22b90077bfa6ea7dcf6b1c5b2f4614533e66656f4eeeff7513556580a014","observation_id":"43d1c39a-a83c-4a3d-92cd-5f5e01f22b69","resolution":{"observed_at":"2026-08-06T10:38:42.403767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:42.170298Z","title":"Computational Optimal Transport: With Applications to Data Science","venue":null,"work_id":"cdb9e697-aa8c-4db1-9953-edeac0f181a5","year":2019},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.538074Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:97b7a29748b2cadc487134ac04da55e4014456f3cfff39053807ce3cf521742f","observation_id":"4afc25ea-bc49-4312-bcbd-bffa52f5b2fc","resolution":{"observed_at":"2026-08-06T10:38:42.254207Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2139/ssrn.3276147","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:34.307862Z","title":"On the computation of Wasserstein barycenters","venue":null,"work_id":"b1421e76-e7df-4e30-97df-1ca164cf2c0e","year":2018},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.716451Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:830fe4ab61180c2e25e381865c04614a54ae2b00ac0701e830afe3d02f9e576c","observation_id":"290d0a0b-5e51-45b7-9717-6cb3daed90b5","resolution":{"observed_at":"2026-08-06T10:38:34.423499Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1145/3119910","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:34.139617Z","title":"Wasserstein Blue Noise Sampling","venue":null,"work_id":"cc14524e-6bb3-4d9f-807a-04171df59310","year":2017},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.771246Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:041529c02170239ddd32eef9c4660afd9780575536895b1d3efcc5f06c73bb90","observation_id":"90d5a6f6-7430-4d5d-ba0b-cf5486c35406","resolution":{"observed_at":"2026-08-06T10:38:34.240182Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.12097","last_updated":"2025-02-17T18:15:09Z","snapshot_observed_at":"2026-08-07T18:11:30.232418Z","submitted_at":"2025-02-17T18:15:09Z","title":"Data assimilation performed with robust shape registration and graph neural networks: application to aortic coarctation","version":1},"cited_work":{"arxiv_id":"2502.12097","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.12097","snapshot_observed_at":"2026-08-06T10:38:37.326574Z","title":"Data assimilation performed with robust shape registration and graph neural networks: application to aortic coarctation","venue":"math.NA","work_id":"a616960d-1b4f-48eb-85e9-7b7cb0adc958","year":2025},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.848466Z"},"links":{"cited_paper":"/paper/2502.12097","citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:4df60d6383f67648d186bd083a699138a584d491b3f6910fdd8e0ee9438d15d5","observation_id":"997d7639-f1ab-4ae9-8319-e17f22598536","resolution":{"observed_at":"2026-08-06T10:38:37.366627Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2139/ssrn.4038042","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:33.969981Z","title":"LearningDeepOptimalEmbeddingswithSinkhornDivergences","venue":null,"work_id":"2397c9a7-e8a8-4f0e-a410-3825922091d3","year":2022},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.923222Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:72cd1d2f6f916174ce495682a3923214a47394c1be5b4cb34f8a3473d914393b","observation_id":"4fd9c08c-bcb0-4993-83d4-11b4bb07c29c","resolution":{"observed_at":"2026-08-06T10:38:34.047104Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:41.990030Z","title":"Geometrical optics and optimal transport","venue":null,"work_id":"fb650a30-b4a1-49c6-8095-7769a7713282","year":2017},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.015625Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:146c7326e6673d520b7ca2202468899bb4e49a11409d97bcd1d184a4d1e30c0c","observation_id":"b5f78ff9-6c1f-45a3-b232-e31491f22f2d","resolution":{"observed_at":"2026-08-06T10:38:42.087073Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:32.141641Z","title":"Stabilized Sparse Scaling Algorithms for Entropy Regularized Trans- port Problems","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.141641Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:36c16785c9abe3bc6b6cf6626a5015fac39589c31d58a8ce481b145f39acc701","observation_id":"185d951f-b522-4976-b9c7-6ffdb12b8f11","resolution":{"observed_at":"2026-08-06T10:38:32.141641Z","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":"2026-08-06T10:38:32.243003Z","title":"TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.243003Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:1ad59048359047b65942e7d56593105adedf0122390271db8c855c84df60268e","observation_id":"cea51c5f-b4cf-40d0-987d-5cefcb50b5ad","resolution":{"observed_at":"2026-08-06T10:38:32.243003Z","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":"2026-08-06T10:38:32.414514Z","title":"Convolutional wasserstein distances: efficient optimal transportation on geometric domains","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.414514Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:db295c9aa6ebae08f4f2f07aef82bc4cbbd356c1535e1ca901a0f49120a50866","observation_id":"486ae57b-6f30-4e39-b17b-403ce5a4c775","resolution":{"observed_at":"2026-08-06T10:38:32.414514Z","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":"2026-08-06T10:38:32.517334Z","title":"Semi-discrete optimal transport: hardness, regularization and numerical solution","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.517334Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:6cd145a95d76823fd9a7daf3616baefaf02dde82a47e041ad9349dfde980f7a2","observation_id":"2ec482b3-3e04-4405-9663-3aa04a31bee1","resolution":{"observed_at":"2026-08-06T10:38:32.517334Z","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":"10.3390/a14050143","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:33.643786Z","title":"Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport","venue":null,"work_id":"b397bd22-4de7-451f-b584-3c24cfa54219","year":2021},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.620039Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:a8787bdf1d24bc70d8e002709783f3df04bd658a590a4c47d6a1168d574e5103","observation_id":"cd0e3841-7d14-42eb-95f1-bb330a5fbc2b","resolution":{"observed_at":"2026-08-06T10:38:33.709545Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:37.115107Z","title":"Kokkos 3: Programming Model Extensions for the Exascale Era","venue":null,"work_id":"55888509-77da-4816-8165-873605ebefd6","year":2022},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.697142Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:9fe24a294dec7cec406e763e8973cde1597575b5383cbad435cf1e319f1617fd","observation_id":"35343eea-f5bc-4794-bbd5-3dd523edd23e","resolution":{"observed_at":"2026-08-06T10:38:37.173203Z","resolver_source":"arxiv_id_nonexistent","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:32.753839Z","title":"Optimal Transport","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.753839Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:254a72abfa77f69beabbece76ab2e70fb8197be66b63b348fc203adeb178a8a3","observation_id":"9740fadc-7331-4b94-918b-1d07da700cd5","resolution":{"observed_at":"2026-08-06T10:38:32.753839Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:41.778052Z","title":"Topics in Optimal Transportation","venue":null,"work_id":"42e42d2d-1e7d-4bae-a825-dbf939f993fa","year":null},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.820928Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:76f6df60422eb9f287be7afcd69b987a73abbd93f3a96d999db1643a1f6db013","observation_id":"93eca387-344d-4532-82d0-0a85b6efc33b","resolution":{"observed_at":"2026-08-06T10:38:41.912596Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:41.530898Z","title":"Self-supervised non-rigid structure from motion with improved training of Wasserstein GANs","venue":null,"work_id":"12495106-b4e6-44f6-bd84-1285db290a15","year":2023},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.988392Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:f7ab06d4fc711452d4d34a6e387beb9ae2befb2b195ff4f0075e656f9c285723","observation_id":"27027527-8175-40a9-a2cb-9f894c2e5bb7","resolution":{"observed_at":"2026-08-06T10:38:41.635179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.03749","last_updated":"2026-05-11T17:00:21Z","snapshot_observed_at":"2026-07-06T20:32:00.585460Z","submitted_at":"2025-02-06T03:21:48Z","title":"PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.03749","snapshot_observed_at":"2026-08-06T10:38:33.075906Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:33.075906Z"},"links":{"cited_paper":"/paper/2502.03749","citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:8959cc91832fc16552470ffb9b7125b76c0fc6fe28a179a2832b85c8faed21cb","observation_id":"c526779e-268d-458c-b2ce-d7437dabfe07","resolution":{"observed_at":"2026-08-06T10:38:33.075906Z","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":"10.5220/0013104100003890","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:33.459133Z","title":"Examination of Document Clustering Based on Independent Topic Analysis and Word Embeddings","venue":null,"work_id":"d07f936f-2d2a-4549-9055-df847e9b9e73","year":2025},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:33.155859Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:95530f034d96da88dcb1ccbbba4f24dce0402d372145960090d0a59ae925bc81","observation_id":"d6610b23-35a8-46c2-9b4a-39ead73b79c1","resolution":{"observed_at":"2026-08-06T10:38:33.530605Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:33.256048Z","title":"Sample Elimination for Generating Poisson Disk Sample Sets","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:33.256048Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:1f34140b234477ad78cf16b9b89ca4a3b2d9ba29677d2ffb641ceae43c046591","observation_id":"49aeb1c6-c0fb-47fb-8007-f66551c2c82b","resolution":{"observed_at":"2026-08-06T10:38:33.256048Z","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":"2026-08-06T10:38:31.627815Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":607,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:31.627815Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:2229c1d227d7e36d31d28dfe4abf6528b83328a3f28755f3f5d9ee5c5a05a3d3","observation_id":"09b8fe75-48b2-4917-9bee-b4499e1a46ec","resolution":{"observed_at":"2026-08-06T10:38:31.627815Z","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":"10.1007/s11075-024-01903-y","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:38:35.361533Z","title":null,"venue":null,"work_id":"e6c2bcde-b1ab-4f8c-addf-df60a118f2b8","year":null},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":1004,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:27.741542Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:b6900f62598edf7022cac78b8001023fb80e409cdbc4b77f8206cd46ca3aca2e","observation_id":"94c05b3e-dbbb-40a9-9b63-cca037c38625","resolution":{"observed_at":"2026-08-06T10:38:35.420740Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:38:30.594482Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":1574,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:30.594482Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:418138749971bb7bff7339b2c3ac94cb232a47090b539e71381b59f511eee837","observation_id":"868ce232-34dd-41d3-862e-221c9b14e72b","resolution":{"observed_at":"2026-08-06T10:38:30.594482Z","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":"2026-08-06T10:38:32.902648Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":2003,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:32.902648Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:75da09ce6f9520dbea0c948d1a59fec8df4640e259cd4da3b8c526b0ce5122e8","observation_id":"710df208-3ecd-4eba-84fb-db7637163ddd","resolution":{"observed_at":"2026-08-06T10:38:32.902648Z","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":"2026-08-06T10:38:29.799272Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-06T10:38:29.799272Z"},"links":{"citing_paper":"/paper/2507.23602"},"observation_digest":"sha256:ce14d1471c0ea9914af4c82afc89b9bde99959c98139073bac02c8dc6290607f","observation_id":"963cb518-1a2c-43ff-b93c-18d18cacd808","resolution":{"observed_at":"2026-08-06T10:38:29.799272Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.23602","last_updated":"2025-07-31T14:40:43Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-08T03:54:25.968305Z","submitted_at":"2025-07-31T14:40:43Z","title":"Efficient Numerical Strategies for Entropy-Regularized Semi-Discrete Optimal Transport"},"reference_resolution":{"displayed":76,"state_counts":{"malformed_identifier":5,"metadata_mismatch":4,"parse_uncertain":0,"unresolved":27,"verified_exact":23,"verified_fuzzy":17},"total_outbound_references":76},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 76 of 76 outbound references and 0 inbound Pith citation observations for arXiv:2507.23602."}