{"as_of":"2026-08-15T08:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6cd5e492e6a39dfa0b63acd430ca469ba518f69dd8e033678c31338028838ccb","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:35:55.649920Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T23:35:16.248308Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-06-30T18:14:59.943084Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.05395","snapshot_observed_at":"2026-08-05T23:35:16.248308Z","title":"C., Tong, F.Boundary regularity of optimal transport maps on convex domains, preprint, arXiv:2507.05395","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.05551","last_updated":"2025-08-07T16:32:40Z","snapshot_observed_at":"2026-08-05T23:35:13.806705Z","submitted_at":"2025-08-07T16:32:40Z","title":"On a general class of free boundary Monge-Amp\\`ere equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T23:35:16.248308Z"},"links":{"cited_paper":"/paper/2507.05395","citing_paper":"/paper/2508.05551"},"observation_digest":"sha256:2f6cd0ba4e03cd4ce4dd11a255e1785539e39d456f739842a4a64704211d7413","observation_id":"65989be7-a18f-4825-8aa9-5e901422704a","resolution":{"observed_at":"2026-08-05T23:35:16.248308Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"cited_work":{"arxiv_id":"2507.05395","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05395","snapshot_observed_at":"2026-06-30T18:14:59.943084Z","title":"arXiv preprint arXiv:2507.05395 , year=","venue":null,"work_id":"2efa8e48-6bec-4396-8f52-bf8637eb94e7","year":2025},"citing_paper":{"arxiv_id":"2605.19142","last_updated":"2026-06-09T16:16:36Z","snapshot_observed_at":"2026-08-04T13:03:09.565145Z","submitted_at":"2026-05-18T21:49:28Z","title":"Solutions to Monge-Amp\\`ere Equations with Low Codimensional singularities","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-20T08:11:05.176246Z"},"links":{"cited_paper":"/paper/2507.05395","citing_paper":"/paper/2605.19142"},"observation_digest":"sha256:069c97fd748b792fd779bc041bdcb2ed1f8db30b376b15b55f4d8654930551d0","observation_id":"59c6b3de-5335-41b4-ae6e-5a7c0e8bc914","resolution":{"observed_at":"2026-05-20T08:13:08.254493Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"cited_work":{"arxiv_id":"2507.05395","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05395","snapshot_observed_at":"2026-06-30T18:14:59.943084Z","title":"arXiv preprint arXiv:2507.05395 , year=","venue":null,"work_id":"2efa8e48-6bec-4396-8f52-bf8637eb94e7","year":2025},"citing_paper":{"arxiv_id":"2605.19142","last_updated":"2026-06-09T16:16:36Z","snapshot_observed_at":"2026-08-04T13:03:09.565145Z","submitted_at":"2026-05-18T21:49:28Z","title":"Solutions to Monge-Amp\\`ere Equations with Low Codimensional singularities","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-30T18:10:52.141214Z"},"links":{"cited_paper":"/paper/2507.05395","citing_paper":"/paper/2605.19142"},"observation_digest":"sha256:d94ad72e794e25211418153fe558d478172e58332fb52ebe3ff3fb1cd9b763ae","observation_id":"53f58206-9f4d-4f0d-9571-bcc1ed46270c","resolution":{"observed_at":"2026-06-30T18:14:59.944741Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"cited_work":{"arxiv_id":"2507.05395","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05395","snapshot_observed_at":"2026-06-30T18:14:59.943084Z","title":"arXiv preprint arXiv:2507.05395 , year=","venue":null,"work_id":"2efa8e48-6bec-4396-8f52-bf8637eb94e7","year":2025},"citing_paper":{"arxiv_id":"2605.20122","last_updated":"2026-05-19T17:10:47Z","snapshot_observed_at":"2026-08-14T06:33:47.523674Z","submitted_at":"2026-05-19T17:10:47Z","title":"Optimizing Computational-Statistical Runtime for Wasserstein Distance Estimation","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-05-20T03:27:11.470079Z"},"links":{"cited_paper":"/paper/2507.05395","citing_paper":"/paper/2605.20122"},"observation_digest":"sha256:85b119fdcb2eed39716ac4d1d8c18e36545075c584ec39cab412e54124686b99","observation_id":"3c3e8396-1ecc-4272-90be-910c7e4ff723","resolution":{"observed_at":"2026-05-20T03:28:01.226694Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"cited_work":{"arxiv_id":"2507.05395","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05395","snapshot_observed_at":"2026-06-30T18:14:59.943084Z","title":"arXiv preprint arXiv:2507.05395 , year=","venue":null,"work_id":"2efa8e48-6bec-4396-8f52-bf8637eb94e7","year":2025},"citing_paper":{"arxiv_id":"2605.24232","last_updated":"2026-05-22T21:22:07Z","snapshot_observed_at":"2026-08-15T03:09:19.913757Z","submitted_at":"2026-05-22T21:22:07Z","title":"Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-30T14:48:46.558424Z"},"links":{"cited_paper":"/paper/2507.05395","citing_paper":"/paper/2605.24232"},"observation_digest":"sha256:276876991e460043cd5203a398b38155319a247313a7906f0e9a446afbad318a","observation_id":"2e235dac-3153-4c57-86bf-3fcf5c3f406a","resolution":{"observed_at":"2026-06-30T14:54:45.567920Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.05395","snapshot_observed_at":"2026-07-31T08:36:25.087119Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.24666","last_updated":"2026-07-27T17:08:26Z","snapshot_observed_at":"2026-08-13T19:41:49.558377Z","submitted_at":"2026-07-27T17:08:26Z","title":"Global $W^{2,p}$ Regularity in Optimal Transport","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-31T08:36:25.087119Z"},"links":{"cited_paper":"/paper/2507.05395","citing_paper":"/paper/2607.24666"},"observation_digest":"sha256:ba204b92bcb4b7cec76239562bed2f97512ee6a66cca72907ddf6f4e52275319","observation_id":"58eb198e-4b50-4357-8643-3adbe5076ad5","resolution":{"observed_at":"2026-07-31T08:36:25.087119Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.05395/citation-record","integrity":"/paper/2507.05395/integrity","json":"/paper/2507.05395/citation-record.json","paper":"/paper/2507.05395"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.412953Z","title":"J., Rankin, C.,A geometric approach to apriori estimates for optimal transport maps, J","venue":null,"work_id":"ff0fccf8-773c-466b-9880-00cea03fd1f4","year":2024},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.020961Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:9834965294882796f5e1e5b01a0032d885a451c1b23a6fd13dcdca752a1ec91b","observation_id":"9a8b7974-43d6-4592-9535-fb40007e12c3","resolution":{"observed_at":"2026-08-06T19:35:57.415927Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.403767Z","title":"Polar factorization and monotone rearrangement of vector-valued functions","venue":null,"work_id":"6286d122-f3ff-4277-b1e6-db93abb30611","year":1991},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.054775Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:d17b0d7d24675b6cecd7246d385db1245f1e164ebdb9ecd74ddacfd03a5ad133","observation_id":"a193da4a-4ca2-406e-9d64-4f73cc8196ea","resolution":{"observed_at":"2026-08-06T19:35:57.406976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.394079Z","title":"The regularity of mappings with a convex potential","venue":null,"work_id":"70bea2e9-86dc-428b-82e2-1ae6d2c13e6b","year":1992},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.073980Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:1832efac01562816f7aaad0c7a4ac70498fa4297cad64ea728164229f1eb264c","observation_id":"eea161d3-d3b0-422f-be19-812871e13986","resolution":{"observed_at":"2026-08-06T19:35:57.397415Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.383628Z","title":"Boundary regularity of maps with convex potentials","venue":null,"work_id":"57cffcca-c704-464b-aae7-2506c7afd9cf","year":1992},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.104077Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:7e3fb43f49b08147fc3d1ec633319f47bede5feb0951cf1c5cf93725fb69e94f","observation_id":"3a5e0e66-63d5-465a-9bb8-b38d62d1119c","resolution":{"observed_at":"2026-08-06T19:35:57.387096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.373868Z","title":"Boundary regularity of maps with convex potentials","venue":null,"work_id":"e73cfa59-642f-4365-a850-3654c1d1a042","year":1996},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.156213Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:417af5ff8667c47c9e0363f2f9fdd1f323ab420b1a9c62a6d9a7383fa5cb7db1","observation_id":"615de6e2-74b5-4615-936b-a0ba662874b8","resolution":{"observed_at":"2026-08-06T19:35:57.377212Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.364687Z","title":null,"venue":null,"work_id":"8bec0147-bba7-49dd-ad7f-a6149ba516be","year":1990},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.215925Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:e3beb677c6d92d30250d994c7553ed8e7090b603b8b9889c0cd9c7e697122f34","observation_id":"7a18aab9-944e-4550-94ec-dbb6e0751dc5","resolution":{"observed_at":"2026-08-06T19:35:57.367891Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.355315Z","title":null,"venue":null,"work_id":"d796d37d-8993-4e0c-8952-833e1ecf41b5","year":1984},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.254246Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:9d7f74b744d6bbab69113efb598073a1fe6f37f422314c7aca813385f4f65717","observation_id":"e7546a1f-2c86-44b1-8fe2-565332fe17c7","resolution":{"observed_at":"2026-08-06T19:35:57.358538Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.346335Z","title":null,"venue":null,"work_id":"3d1e1253-88a7-42ce-8471-046d3b6bbe97","year":2017},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.336825Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:92b463b4a227f8cb3c55046967c6349b440b081176790e7b07409d815186e710","observation_id":"d8e13c4c-8cd4-4ff4-b31d-e02595f01683","resolution":{"observed_at":"2026-08-06T19:35:57.349292Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.336110Z","title":"Wang Global regularity for the Monge-Amp` ere equation with natural boundary condition","venue":null,"work_id":"e9fb77ec-57ae-45a0-9266-286794eb9fec","year":2021},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.420565Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:d19b207a3db0a80c22389c2106543b0fa810717f284ac669b95a1880d60aa447","observation_id":"f10c2275-974a-4f08-9a8d-30299d03b2ae","resolution":{"observed_at":"2026-08-06T19:35:57.339286Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.327087Z","title":"Pure Appl","venue":null,"work_id":"b68dd3c5-856a-4dc6-ba4c-efa6763b7fff","year":1977},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.473251Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:79f4ec4f886fa5eaa33bff5442c3f3aab4f461b2b8d7173b8c5ce04ceea9b90e","observation_id":"2b747a69-f845-4b61-a256-229301ac9e52","resolution":{"observed_at":"2026-08-06T19:35:57.330079Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.317387Z","title":"On a general class of Free Boundary Monge-Amp` ere equations, to appear","venue":null,"work_id":"bdbf6633-9cde-49a8-8296-03ffc383f30b","year":null},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.531168Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:b824e276e2787a9687ecc1fe961d44a733385a01e7d8f174b2a1b507357e859f","observation_id":"e15c18cc-051b-4896-9ef9-959650d5e9c8","resolution":{"observed_at":"2026-08-06T19:35:57.320620Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.306780Z","title":"Complete Calabi-Yau metrics in the complement of two divisors","venue":null,"work_id":"f646d7e7-7314-4343-800a-d37e382a5f25","year":2024},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.608654Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:8ac1246a47c81e35b698dc81b6301558cd0551c4fdb083ce3d053c9a40173018","observation_id":"ac64ef0c-2f1d-48f8-a221-9d46c636c2a1","resolution":{"observed_at":"2026-08-06T19:35:57.310281Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.10111","last_updated":"2024-02-15T17:07:52Z","snapshot_observed_at":"2026-08-13T04:18:10.290130Z","submitted_at":"2024-02-15T17:07:52Z","title":"A free boundary Monge-Amp\\`ere equation and applications to complete Calabi-Yau metrics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.10111","snapshot_observed_at":"2026-08-06T19:35:53.697783Z","title":"arXiv:2402.10111","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.697783Z"},"links":{"cited_paper":"/paper/2402.10111","citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:89cce6bbee371b80a0daa552ccc2bae274f04ab8e649b1bb7f1eb454e591a92d","observation_id":"4dcd2b70-9384-4b26-b8cb-ebaaf1b8aa33","resolution":{"observed_at":"2026-08-06T19:35:53.697783Z","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":"2026-08-06T19:35:57.290773Z","title":null,"venue":null,"work_id":"f62bd7d8-e184-48f4-8a17-7ee32f9f2dd1","year":2014},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.776633Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:ac99ce1e9105b07aae4e7dcf893403f231c6d6484563f6981dd8d9b76f84fefa","observation_id":"d109244b-9d86-4b7b-9ec7-7d589905512b","resolution":{"observed_at":"2026-08-06T19:35:57.293706Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.280024Z","title":null,"venue":null,"work_id":"3db1acf9-a721-4081-9ec0-ed1b0727e2f8","year":1991},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.864236Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:a1ec2189a9c0ab42caac84da63a9ed4b8e1e0d733d9fea41ce292b0cd194a726","observation_id":"8cd77511-e256-4954-b720-0c0382c35414","resolution":{"observed_at":"2026-08-06T19:35:57.283850Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.270204Z","title":"C., Partial differential equations and Monge-Kantorovich mass transfer, Current developments in mathematics, 1997 (Cambridge, MA), 65–126, Int","venue":null,"work_id":"5c2cefa0-8344-4e84-a646-9a2442b53323","year":1997},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.884402Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:7883643b0f26bc0fba9897e3512061f42c2d095581c4906a3020cfbf255a003b","observation_id":"c592b990-43d6-416a-99a3-4fa63fc3f496","resolution":{"observed_at":"2026-08-06T19:35:57.273363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.260866Z","title":"The Monge-Ampere equation","venue":null,"work_id":"0199abb8-7454-4764-b2be-bff9b2e5653c","year":2001},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.911571Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:18e5bbc7b80f8cebe22a5f75bf866229ded0bd7f4e402a8a919876bf127b41cd","observation_id":"4dcacf6b-e4b7-43f6-94be-992460a9c789","resolution":{"observed_at":"2026-08-06T19:35:57.263869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.250845Z","title":"On the regularity of optimal transports between degenerate densities, Arch","venue":null,"work_id":"6d0dd772-9d74-4498-a938-12d39bca01d5","year":2022},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:53.973414Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:09916752c7ea0e89cac46f9494fe33ef83547fe768277bf07e632cf79180e2ba","observation_id":"67a5bd56-a7a8-4a7e-9b6c-6a93167b21aa","resolution":{"observed_at":"2026-08-06T19:35:57.254269Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.15263","last_updated":"2023-09-26T20:46:40Z","snapshot_observed_at":"2026-08-13T10:04:21.989006Z","submitted_at":"2023-09-26T20:46:40Z","title":"Singularities of the solution to a Monge--Amp\\`ere equation on the boundary of the 3-simplex","version":1},"cited_work":{"arxiv_id":"2309.15263","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.15263","snapshot_observed_at":"2026-08-06T19:35:55.777802Z","title":"Singularities of the solution to a Monge--Amp\\`ere equation on the boundary of the 3-simplex","venue":"math.DG","work_id":"4b8ebde0-ad6e-41f2-94c7-cb77d63c6640","year":2023},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.071831Z"},"links":{"cited_paper":"/paper/2309.15263","citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:37f1cbb35afa35416f2a9707c75af3e21126b529f5300631b082bf9d16f98f21","observation_id":"b36dab0d-caff-4068-b311-5611e8d71b04","resolution":{"observed_at":"2026-08-06T19:35:55.859271Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.240829Z","title":null,"venue":null,"work_id":"c21ef03e-017f-4951-8d17-72955caeb909","year":2010},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.144473Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:29cf138a53d4a249d26501480a7642404979e2fcb48189b38e47b6897125d4c1","observation_id":"b546447b-fa2c-43fa-a25a-cffd86b86703","resolution":{"observed_at":"2026-08-06T19:35:57.244186Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.230015Z","title":"Pseudo-Riemannian geometry calibrates optimal transportation, Math","venue":null,"work_id":"54243b3f-817b-436c-ba5f-14fe0877f096","year":2010},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.337699Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:f63445d5d7280226a451c6d026a92ba6649faefd66d88b9ebcc31b951d813e1a","observation_id":"8273fa19-785a-41f4-bc9f-a574322f21f8","resolution":{"observed_at":"2026-08-06T19:35:57.233991Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:54.397015Z","title":"Intermediate complex structure limit for Calabi-Yau metrics","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.397015Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:6e74717c361b6e4ae09bc7968cc9aab1fa7de6cf227a091705b7f3a47d3eeb98","observation_id":"2abeb0b3-1267-4a26-b727-07c1cdcefe1f","resolution":{"observed_at":"2026-08-06T19:35:54.397015Z","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":"2026-08-06T19:35:57.212974Z","title":"T., R¨ uschendorf, L.,Mass transportation problems","venue":null,"work_id":"f3e7d476-58d0-4bc0-b645-af3ece662bb3","year":1998},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.492417Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:a9ce5465c6bbed4232b126de13654346577d16b865a08662f541023135c11a4d","observation_id":"39164cd1-096c-4541-bb17-efcef27bc60a","resolution":{"observed_at":"2026-08-06T19:35:57.216478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.202869Z","title":null,"venue":null,"work_id":"37b3b995-878c-42ac-ba04-cdebeff83cdc","year":2013},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.566421Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:985d28a070f6004cbddb1b19db58caba153ae7dbaf5b9bf901cf7c57db49e3a1","observation_id":"51a9e598-9309-47a2-a676-e5ac660a03b9","resolution":{"observed_at":"2026-08-06T19:35:57.206000Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.192867Z","title":null,"venue":null,"work_id":"0f05c1cf-e779-4267-ab5f-ca50fc74ed57","year":2013},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.631655Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:1f6f6e955ee7c8f7ba430bc99bfe36208f10e172cd7ce0b9ac0fcf3dd2c61b49","observation_id":"ac110725-89c3-478f-919c-1778b3747895","resolution":{"observed_at":"2026-08-06T19:35:57.195767Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.182677Z","title":null,"venue":null,"work_id":"76f9871b-3359-4360-b3b0-2f2ebc690950","year":2020},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.707457Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:ca28c74e48a2c3bf69f83a919c2c1d467869911f1837d1b9f5ffb95f155bac67","observation_id":"1bfb66f1-e2d1-4008-a8ae-94c6a96e697c","resolution":{"observed_at":"2026-08-06T19:35:57.185550Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.173439Z","title":"Convex Bodies: The Brunn–Minkowski Theory , Encyclopedia Math","venue":null,"work_id":"165394b3-d4b9-4180-83cd-7afdf5d7df3d","year":1993},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.773512Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:417ff61a66912f0bef4f2c1890395237f679c76bede00f57c3727d6742fe42c8","observation_id":"acc9a4ac-b522-4cdf-afa9-07c43e39b38d","resolution":{"observed_at":"2026-08-06T19:35:57.176437Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.164216Z","title":"Complete K¨ ahler manifolds with zero Ricci curvature","venue":null,"work_id":"9e4c867a-34f4-4a32-83ab-fa0f79a71b36","year":1990},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:54.885588Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:6ea742a28d9c74a9f3ba170eade7b3e3686c62e76f7fa9001f19e1cf63c289dc","observation_id":"d3912db7-45ba-4962-bac8-9ed3628dd47d","resolution":{"observed_at":"2026-08-06T19:35:57.167453Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.153581Z","title":"S., Wang, X.-J., Boundary regularity for the Monge-Amp` ere and affine maximal surface equations, Ann","venue":null,"work_id":"a0f640b3-fd72-4068-bd1f-c3716f2ba9ec","year":2008},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:55.016865Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:b0c5cb586dec47ce5e797c8547a101bbdd18a3dcc1a53419b62b03d486898fdb","observation_id":"759c1c5f-60e3-4d47-b7b9-a3113331dce0","resolution":{"observed_at":"2026-08-06T19:35:57.157488Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:57.139249Z","title":"Reine Angew","venue":null,"work_id":"fcf52318-a61b-4490-825c-e2ce3a066b28","year":1997},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:55.076736Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:1b0ae3660116b28da30d8567df1928f5ea8fb6c1aa23eb8f5cad471416b2565d","observation_id":"19a42d3f-72d1-441d-a22e-9a12302afb93","resolution":{"observed_at":"2026-08-06T19:35:57.146278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:56.919432Z","title":null,"venue":null,"work_id":"dccb5758-9390-408b-a0be-c7e2970f8e9a","year":2009},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:55.178410Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:74b15eeb3fbd982b7648feed48f210cd0854cd52d4f7fa25e0d52477cbd5db30","observation_id":"4e02056c-6e4c-4392-a9a6-278937273906","resolution":{"observed_at":"2026-08-06T19:35:57.027302Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:56.601539Z","title":null,"venue":null,"work_id":"fd822f86-255b-44f0-a4cf-b271f7efe9ea","year":2003},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:55.328906Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:6a72b9570cda62648283c98d877f1c97cd6baca1c8ef6e086c3ae8152707f823","observation_id":"67283853-2dd4-43b8-b397-43a0c8bb3143","resolution":{"observed_at":"2026-08-06T19:35:56.783203Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:56.382406Z","title":"On the Ricci curvature of a compact K¨ ahler manifold and the complex Monge-Amp` ere equa- tion","venue":null,"work_id":"78e9569d-33a4-490e-80c9-a881ad68d7b0","year":1978},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:55.437511Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:ab011745b131cdb2f7e2f58f36d32502a314bd24adada39f560a12c9f5b47e47","observation_id":"af62f1be-47b3-4a98-b1f4-3e3e46e00c6b","resolution":{"observed_at":"2026-08-06T19:35:56.514780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:56.157639Z","title":null,"venue":null,"work_id":"3d25d67e-3a22-409b-8327-fd5e1e9341eb","year":1978},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:55.563094Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:5b49f74b024f551f08b3d1b2c722914271cafd1e0714ce27b9c3b183d2b79ebc","observation_id":"33868f80-5397-4c0f-a742-7d7347cb591b","resolution":{"observed_at":"2026-08-06T19:35:56.255599Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:35:55.972703Z","title":"A monotonicity approach to Pogorelov’s Hessian estimates for Monge-Ampere equation","venue":null,"work_id":"d805edad-5c92-45d6-813e-125f8b456cc5","year":2023},"citing_paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T19:35:55.649920Z"},"links":{"citing_paper":"/paper/2507.05395"},"observation_digest":"sha256:13398ade67824290f8a43a6a19a95d7f186277591d67f8e29b13066ad5f134fa","observation_id":"c8245892-0fd0-4d8a-a541-2de1b7e7b5af","resolution":{"observed_at":"2026-08-06T19:35:56.062242Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.05395","last_updated":"2025-07-07T18:29:24Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-13T12:58:32.704834Z","submitted_at":"2025-07-07T18:29:24Z","title":"Boundary regularity of optimal transport maps on convex domains"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":1,"verified_fuzzy":20},"total_outbound_references":35},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 6 inbound Pith citation observations for arXiv:2507.05395."}