{"as_of":"2026-08-13T16:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:32834d94d033ce8f509f8e1818191ede85d97c4010eae719442c612aeb76c031","coverage":[{"denominator":42,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":42,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-30T05:33:59.018587Z","state":"measured"},{"denominator":42,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":42,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2606.29913/citation-record","integrity":"/paper/2606.29913/integrity","json":"/paper/2606.29913/citation-record.json","paper":"/paper/2606.29913"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:33:59.018587Z","title":"Kadets-type theorems for partitions of a convex body","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:abe9ef369818078e1558860da98cca80c2bf41a2f7b46a7e7203f5e8245ade92","observation_id":"09a2a952-9ae3-42f4-bf49-d3a834f2d6de","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:dc1a745fab5192a048b729a524c92dd025ec9de097196345cba757b3f050e047","observation_id":"a3cf7e44-54c9-45f8-b731-3697d572eead","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Sampling of probability measures in the convex order by Wasserstein projection.Annales de l’Institut Henri Poincar´ e - Probabilit´ es et Statistiques, 56(3):1706–1729, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:b54c965758bc204e48e7175d62a83097602218c7fde78a13e9df921a6bdc49f6","observation_id":"86dd7c60-1b31-49e5-8415-b545614c3003","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"A criterion for the affine equivalence of cell complexes inR d and convex polyhedra inR d+1.Discrete & Computational Geometry, 2(1):49–64, 1987","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:95843badddeb8843c2e265b561dbbdabfbec8c76980dad0274f6ac4737cefa9e","observation_id":"4f3597b9-42d7-4e8d-9583-cb69c54395b2","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Power diagrams: properties, algorithms and applications.SIAM Journal on Computing, 16(1):78–96, 1987","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:589c5a1b18badbe10a4306640d68fd26841e68a1add6dfd0503c4c8f2cede6d8","observation_id":"427aa0a4-e4de-4746-b9e7-6807d8d27796","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Minkowski-type theorems and least- squares clustering.Algorithmica, 20(1):61–76, 1998","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:373bb2d81fce4c460b0c89a4109802d84fb37fa69b9ec565785896c6f899d3c5","observation_id":"24cf0c7b-bb28-481f-8e12-7150f2eb0d59","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Bauschke and Walaa M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:c91112f6a1e05f01359243389ad869224ddc4468f4ae524e51cceef4bd725e9e","observation_id":"8b7cbb3a-4ed3-42a7-8aa8-4261b2b17cbd","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"SIAM, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:3b6df544b31918f11e1a559eb8867fb457a925ab74329f16391dce6696df7424","observation_id":"a2ccfb35-1eeb-4d17-8853-f4c2b7cdf4b7","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":null,"venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:222d7426b98e5b0e945bd83c2cf7f5a21e73e4c19b9df1658a1004d342d94b95","observation_id":"b7ab6f52-2294-46b2-973e-0316420455fd","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Generalized Voronoi tessellation as a model of two-dimensional cell tissue dynamics.Bulletin of Mathematical Biology, 72:1696–1731, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:deb3478014f021550bdfde4a69637b8090dd50ef9505533bdb1c66a60b2336bc","observation_id":"60b2eac1-bf3a-4516-aa34-1ae7a556f6c5","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Bourne, Piet J","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:6c97eaf508d49be05a962f8f35533246fbd3a12946822098cdb0d40723b5320f","observation_id":"dd20a955-ac18-45af-ad5a-f78d1a1b678c","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Bourne, Mason Pearce, and Steven M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:48d30569492d9b9c621f36f36d9b3d8533604038be2c0875af24eaa162e353a6","observation_id":"6b623b63-6210-45e3-b24f-c6bd0c9d53df","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Bourne and Steven M","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:6b449149d35ded7f21bec5280641b2f92312e50f7edaad69959909f8b69b8214","observation_id":"a8ebc4b5-f2b8-4840-9e39-eca28d445e55","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"On optimal weighted balanced clusterings: Gravity bodies and power diagrams.SIAM Journal on Discrete Mathematics, 26(2):415–434, 2012","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:5d0ba31e7f78c1a433ca11a6a8de8c1499ff6e864e411a3730221e48ad232fc1","observation_id":"d689766c-2dc4-4b94-ae49-7ecf3f70ecd4","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Constrained clustering via diagrams: A unified theory and its application to electoral district design.European Journal of Operational Research, 263(1):18–34, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:e31d5ba1c0c50b2438509c8b63458246eab5ad9b22f88ca0ce2a6fe63766bc66","observation_id":"a8d5615f-c3ed-40a0-b2b3-738835692b91","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Convex optimization: Algorithms and complexity.Foundations and Trends® in Machine Learning, 8(3-4):231–357, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:4892717b6b33fcb8fafaca27a04041bab1a070170860484736022e971cab8276","observation_id":"cf8195ae-7706-4612-9e66-2f71ec48e30c","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:bb0d22e53e9d14a2f02eb35602e65de2a88ca754aabe38386a357ca89d49912b","observation_id":"a42df37c-38b3-40bc-a8f0-b810e0ceddad","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Optimal transport and the geometry ofL 1(Rd).Pro- ceedings of the American Mathematical Society, 142(10):3585–3596, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:e50800326d8973929c54a8673a08f2c6fced829dce1237e4bb33a20184a61f68","observation_id":"c6292695-50d5-46eb-9bf0-404161c6510d","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"An algorithm for quadratic programming.Naval research logistics quarterly, 3(1-2):95–110, 1956","venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:0d1511010a0b7f6ca1c1e5c94ce196b8d89901590ebe20fd2521231794706c24","observation_id":"548618cb-60e3-4cab-aae2-e6b7f5afd382","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Gallou¨ et, Andrea Natale, and Gabriele Todeschi","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:8309221d5a368033125ccee7b649aaa5cdeb1c801f70a9d9d65f42b99882ab94","observation_id":"170dcb0d-5f81-4ac2-a5b3-64e528496de4","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"On a mixture of Brenier and Strassen theorems.Proceedings of the London Mathematical Society, 120(3):434–463, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:79d5664f4a03270726dba5a273bf260060683c8b24db52ea978a2fbf45fb73cc","observation_id":"0e5cde1d-4b63-4f44-8e0a-647541af3f62","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Kantorovich duality for general transport costs and applications.Journal of Functional Analysis, 273(11):3327–3405, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:4b51a9c8bc5384a5be2922b5bdce48969df5e33a4783971551cdaf2cd8a1b7d3","observation_id":"58147306-110a-44e7-adb4-5206c4cf9645","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Constrained clustering, diagrams, coresets, and their applications.Geometry, Analysis and Convexity, page 87, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:646c5f785c534c5d96afefc45b3bc672e74736da25e23564e9e30da8eef254be","observation_id":"58f2a673-e0e4-464f-8dc1-fdfe1a2a2f11","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Recursively-regular subdivisions and applications.Journal of Com- putational Geometry, 7(1), 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:b5eee37afd72ae3aa319a58fb4b25657a502b00e34e31a1c215296d0952158d3","observation_id":"b895caa6-3f3e-48b5-82f7-6bf72ae4c7d8","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.02840","last_updated":"2025-01-14T01:21:46Z","snapshot_observed_at":"2026-08-13T05:42:06.398201Z","submitted_at":"2024-06-05T01:30:58Z","title":"Statistical inference of convex order by Wasserstein projection","version":3},"cited_work":{"arxiv_id":"2406.02840","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2406.02840","snapshot_observed_at":"2026-06-30T05:34:19.959833Z","title":"Statistical inference of convex order by Wasserstein projection.arXiv:2406.02840, 2024","venue":null,"work_id":"e50cdf8e-6af5-4d12-9ccc-63aad75705cc","year":2024},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"cited_paper":"/paper/2406.02840","citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:7b712bd1bda90264c33a80a7aee692256f64120e8df0fc3d03948fc7dfa447b6","observation_id":"3085bc04-a96b-4cfe-88fb-c44a9b76bbe8","resolution":{"observed_at":"2026-06-30T05:34:19.961837Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-06-30T05:33:59.018587Z","title":"Backward and forward Wasserstein projections in stochas- tic order.Journal of Functional Analysis, 286(2):110201, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:ec6ddfcfee0752e464fee563ae2c187fdd85281cff7cd760f74e06c3c172fddb","observation_id":"80f22bb3-8423-46d8-acf2-67368699cf66","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Lagrangian discretiza- tion of crowd motion and linear diffusion.SIAM Journal on Numerical Analysis, 58(4):2093–2118, 2020","venue":null,"work_id":null,"year":2093},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:21d763ae73aabb0190b788949af57fd94e5a819d03694c0266fe688a1ff6daef","observation_id":"698a1893-9f15-4d88-85da-8dab264f5603","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:48a6bc431b24f999b7bfabb771cdbc096423549e3d8cb1042edc334900513e07","observation_id":"24295649-3e53-45bc-8512-ab7c7f21bc03","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"On the use of Laguerre tessellations for representations of 3d grain structures","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:2aad9fdaf32cdc2abb66381e5c5a9f87bd242d39d3061dc1693f7c258cd233ca","observation_id":"66737fd6-93a9-47ce-adc3-5444667ef4d6","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Non-asymptotic convergence bounds for Wasserstein approximation using point clouds","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:4f70ca3dce23dfc7b552a37e40b968243edcbb16585077ffe2201b7a3f3bbfd4","observation_id":"22f35f3d-0ac0-43e3-9d21-e2e35b437c38","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Mirrors, lenses and Monge–Amp` ere equations.European Mathematical Society Magazine, (120):16–28, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:0a48a55232eb6cb7fcb80add618316476026ee30d979e2c8fa943e977ef19e41","observation_id":"96890af3-b1b2-4c28-9132-9a1290391af1","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Optimal transport: discretization and algorithms","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:559999bb94c59db5f4a89e561ff7a21abf98bc4d57d3f83ce33e20c9c9563b5f","observation_id":"82d0c25e-dabe-4831-aca1-0f20b521a3ff","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Initialization procedures for discrete and semi-discrete optimal transport","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:61056164f93034fa502f9e68f86e010317c2adf88ab835d28f4e6e3d64f09ceb","observation_id":"6870ff27-2848-4377-9ff8-41aec06c59ae","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Reconstruction of grains in polycrystalline materials from incomplete data using Laguerre tessellations.Microscopy and Microanalysis, 25(3):743–752, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:ce494207f70015b1ca0f4e5fa372050c4e9843c5a81fa5a685f927be64293105","observation_id":"1ccd2498-8086-4272-b60b-460290b6824e","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"On the sequential convergence of Lloyd’s algorithms.Mathematics of Operations Research, 51(2):1120–1138, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:266641196b8127358c99e9a230cf04ddd89f847257a8214c3bfbab000c28ab2e","observation_id":"ea906b12-49ab-491a-ba1d-2e60daa19e6b","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:386c1795077c25e1f1b43fe1c14646ee058770363524731829a9499ffbd6f418","observation_id":"53743ad3-126c-427c-bb57-c9437c095b29","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Birkh¨ auser, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:6d10d6ea0b7aa0f74d496334011fd8b167343924a668473bd89e8703036d7d4d","observation_id":"655231a4-b96e-42f2-a27c-950d47f9e0c8","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"The existence of probability measures with given marginals.The Annals of Math- ematical Statistics, 36(2):423–439, 1965","venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:828b41188d02afc509a1f732586159dd36ab461ddeb45ce919f8450f2dcd71e2","observation_id":"3c3ba061-90a2-434c-8292-c703f418ee0a","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"¨Uber exponierte punkte abgeschlossener punktmengen.Fundamenta Mathe- maticae, 24(1):139–143, 1935","venue":null,"work_id":null,"year":1935},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:423ca64ef7de591bf9f72de8cc6e4da0a36da4be366c58bc23d166dad2e4591b","observation_id":"b597df37-972f-4d39-8b05-8ad770ec6ef8","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:4f4cb8b5b21d0252934aa728c4b6c4f6df7031947e712a810d58d2abfaefddba","observation_id":"f051c697-08ef-40fc-99eb-7e64fd820978","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Springer, 2009","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:a070e4612d6b5fe9d88b02e2bf19815aff2da92ab99718c6d612d931367c81a2","observation_id":"4d89be80-0a7c-4873-bdf7-814569af4de4","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","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":"2026-06-30T05:33:59.018587Z","title":"Centroidal power diagrams with capacity constraints: Computation, applications, and extension","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-06-30T05:33:59.018587Z"},"links":{"citing_paper":"/paper/2606.29913"},"observation_digest":"sha256:170ce6224587290a662169dbb4970389c4145305be26ff482399b980feda05aa","observation_id":"ca445f82-0a70-4a21-8a89-877d7c413510","resolution":{"observed_at":"2026-06-30T05:33:59.018587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.29913","last_updated":"2026-06-29T07:51:04Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-04T00:18:35.141805Z","submitted_at":"2026-06-29T07:51:04Z","title":"Semi-discrete convex order and Laguerre tessellation fitting"},"reference_resolution":{"displayed":42,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":41,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":42},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2606.29913."}