{"as_of":"2026-08-13T11:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:cd3127cbccfa5c06cd8e949817e1affe1970c1204455507fae071ab51e5b73c3","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:52:14.924778Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T14:14:46.724181Z","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":"2026-07-01T17:05:50.928763Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"cited_work":{"arxiv_id":"2507.14955","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.14955","snapshot_observed_at":"2026-07-01T17:05:50.928763Z","title":null,"venue":null,"work_id":"1cf00135-1ba3-4b5d-bbed-a876a11dee42","year":2025},"citing_paper":{"arxiv_id":"2606.27691","last_updated":"2026-06-26T03:32:29Z","snapshot_observed_at":"2026-07-07T00:01:54.432346Z","submitted_at":"2026-06-26T03:32:29Z","title":"Singular Limits for Three-Dimensional Global Minimizers of Ginzburg--Landau-Type Functionals: Uniform Estimates and Singular Sets","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-29T04:14:28.284048Z"},"links":{"cited_paper":"/paper/2507.14955","citing_paper":"/paper/2606.27691"},"observation_digest":"sha256:5dcc3c599048778db101bd503d3a355cef8ba17e8c9f88e02051868245904f80","observation_id":"5a4bf091-42d0-44d6-b156-8c2c2cdcb993","resolution":{"observed_at":"2026-07-01T17:05:50.930112Z","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":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.14955","snapshot_observed_at":"2026-08-06T14:14:46.724181Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.04908","last_updated":"2026-08-05T14:35:42Z","snapshot_observed_at":"2026-08-10T10:28:36.746620Z","submitted_at":"2026-08-05T14:35:42Z","title":"On the absence of point defects in biaxial Landau--de Gennes models","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T14:14:46.724181Z"},"links":{"cited_paper":"/paper/2507.14955","citing_paper":"/paper/2608.04908"},"observation_digest":"sha256:91987fca6cd9358d31b52b94a2b51ebe6439a93aa97f32e51215edcfb96c1195","observation_id":"62309c45-d655-4141-8ab0-802ee1d7d19b","resolution":{"observed_at":"2026-08-06T14:14:46.724181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.14955/citation-record","integrity":"/paper/2507.14955/integrity","json":"/paper/2507.14955/citation-record.json","paper":"/paper/2507.14955"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.326734Z","title":"Bethuel, H","venue":null,"work_id":"9a6624f3-f870-49df-aca0-4178b5d7f0cd","year":1993},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:12.712979Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:5300f83cb03d007e115790f93b8b8890891ad08f58011cbc004560689ab49567","observation_id":"7a7c8fa9-ace6-4f15-b709-f18fc1f57e91","resolution":{"observed_at":"2026-08-06T15:52:15.330982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.312345Z","title":"Br´ ezis, J.-M","venue":null,"work_id":"d892c1f1-5ef7-4ef4-b05b-a7a9a42a1bec","year":1986},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:12.775146Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:bca7f0c81e0377110da09f8db2f0eed54fc8b5b0b05abcaa34ade5c967f1ca10","observation_id":"e5013b5c-03dd-4889-8421-6d81d2565b7c","resolution":{"observed_at":"2026-08-06T15:52:15.316765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.298837Z","title":"Canevari","venue":null,"work_id":"f0ad9bab-06e6-4e93-8ed5-d03cf6cb9b21","year":2017},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:12.801065Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:c72dfaabd84e100ec9ddaf3406631f91340d3b14821c2b992c033ebe23059d62","observation_id":"ec3a1029-f93b-4d80-8706-60ddb7fb69e8","resolution":{"observed_at":"2026-08-06T15:52:15.302961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.284325Z","title":"Contreras and X","venue":null,"work_id":"717264b7-13cc-4057-9c06-6864cc76a77a","year":2022},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:12.890166Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:094db2459dcc8af4b627614e3ef32b623d5a19a7f5e15da6ec9b417d0fbb36dc","observation_id":"337739b7-646e-423b-aea3-e802dfb93800","resolution":{"observed_at":"2026-08-06T15:52:15.288593Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.270350Z","title":"de Gennes and J","venue":null,"work_id":"7eb3edff-e48e-40a1-b194-2cf3e31bc3c8","year":1993},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:12.965291Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:8fb4ebae62cc796c298ca4d4ead1148c2810a80602891ff968277fcdf01a3b55","observation_id":"73020705-4311-44a5-9868-576bc3c6d5cf","resolution":{"observed_at":"2026-08-06T15:52:15.274568Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.256818Z","title":"Dipasquale, V","venue":null,"work_id":"96a880ba-9898-4a61-8d8b-8f48d99391ac","year":2021},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.073203Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:4c7a8591b70d0c2968e89a452e9dbe26c55df03047e273f252f4616c775996e1","observation_id":"a5416ca4-6397-4540-a42a-9a2785597781","resolution":{"observed_at":"2026-08-06T15:52:15.260786Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.243368Z","title":null,"venue":null,"work_id":"b68bd69a-acfa-45a7-b5f2-0862558d4d56","year":1991},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.214439Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:320c088dc6eb148ad7858bdb75ddac27d5f0ffe16ae3112091f8514622acff1c","observation_id":"a80033c9-94d6-4e45-9e97-5c141a2e3551","resolution":{"observed_at":"2026-08-06T15:52:15.247428Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.229291Z","title":"Fatkullin and V","venue":null,"work_id":"8fbd37b6-e76f-4c09-82ca-de02cbe93040","year":2008},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.297342Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:141c402cb77c2d455917d2eec550746c5f7a3f479dfb86fed491089b9e12794c","observation_id":"f558307b-4fb4-4348-b71e-94cdf7edb48a","resolution":{"observed_at":"2026-08-06T15:52:15.233382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.215478Z","title":"Feng and M","venue":null,"work_id":"74e57cc0-e77a-48c5-acdc-9ba4a093283d","year":2022},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.420910Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:ea8a4a90739d764e54e547551a77fae4559f319ff98fad618a256c5ef312d14f","observation_id":"45cfc493-d0e7-41b8-844e-7ac5be13a661","resolution":{"observed_at":"2026-08-06T15:52:15.219925Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.201102Z","title":null,"venue":null,"work_id":"a97efe11-f358-4528-a361-c1c39e9c27e1","year":1958},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.496202Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:7c9437ab9d5affb9e0d9485c928b206e3adbf4e1dd193640f9e26be003460d53","observation_id":"5e453bb0-1cf5-4749-9893-e6ef94a2d839","resolution":{"observed_at":"2026-08-06T15:52:15.205454Z","resolver_source":"raw_fallback","status":"unresolved"},"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":{"arxiv_id":"2408.06726","last_updated":"2024-09-07T07:46:26Z","snapshot_observed_at":"2026-08-13T04:13:44.896499Z","submitted_at":"2024-08-13T08:37:12Z","title":"Quantitative stratification and sharp regularity estimates for supercritical semilinear elliptic equations","version":2},"cited_work":{"arxiv_id":"2408.06726","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.06726","snapshot_observed_at":"2026-08-06T15:52:15.005983Z","title":"Quantitative stratification and sharp regularity estimates for supercritical semilinear elliptic equations","venue":"math.AP","work_id":"14d0de99-0e3f-41ab-9327-d1f97abd5807","year":2024},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.598316Z"},"links":{"cited_paper":"/paper/2408.06726","citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:0ad5abb90135f200e4693fd12eefd6a8c463a67753e104bf9dc3abffe18ecda7","observation_id":"e4ad8dc7-8de5-42a0-908b-be004404c809","resolution":{"observed_at":"2026-08-06T15:52:15.010941Z","resolver_source":"local_arxiv","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.186768Z","title":"Geng and A","venue":null,"work_id":"a9d83bab-e31d-40ba-bb9c-7327a4c8c0a8","year":2023},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.685064Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:a1e4f27326abbc86cc90e771cad1805981925a2c04bb4750d43ac3f91249450a","observation_id":"5a5f76a8-0200-4b7a-a8d1-766796701f11","resolution":{"observed_at":"2026-08-06T15:52:15.191322Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.172300Z","title":"Huang and J","venue":null,"work_id":"7767dff1-5351-4917-aa53-6a7a4de80d92","year":2022},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.835594Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:624e8d4627bd070e4c68053d662e82b183f2f129e34c24d5a630a7adbbcc8f79","observation_id":"9d20a134-15de-47ea-8891-48a694b0d598","resolution":{"observed_at":"2026-08-06T15:52:15.176686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.157155Z","title":"Lin and C","venue":null,"work_id":"79d95c80-dea0-460f-80b9-1245914a3c0d","year":2008},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:13.900034Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:2f4089b7f19e805a316dbd36367330524c776a55c268c65d3a684a64ff2c17c3","observation_id":"fb7e9030-feaf-41ca-8631-1d67dff05b2e","resolution":{"observed_at":"2026-08-06T15:52:15.161172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.143363Z","title":"Partial H¨ older continuity for minima of certain energies among maps into a Riemannian manifold","venue":null,"work_id":"49be700f-b56b-4010-86b6-ecfcdb4ce354","year":1988},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.008303Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:873efb4081a7ff62a61513a5f12daf4d8bdaf113b70c036129913a93c5c8304d","observation_id":"20e59d5a-7e07-4780-aedf-1a38822dee1b","resolution":{"observed_at":"2026-08-06T15:52:15.147674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.129239Z","title":"Majumdar and A","venue":null,"work_id":"f880ae75-0670-4de0-8357-d6f973686219","year":2010},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.067172Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:9a1f63c61ad857547484910b1367bf3028162a6da39bd7e99caa4a47e54b6896","observation_id":"b59a8c0b-830e-44a9-b79e-c38e926e411a","resolution":{"observed_at":"2026-08-06T15:52:15.133557Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.115498Z","title":"Millot, Y","venue":null,"work_id":"f4de43d1-90b2-46f5-9fee-4c437448986d","year":2019},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.172263Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:4e2d5d3062ea49d0f3a4c5d20a1f107c1330ac394faa11e7a679f93d26bda345","observation_id":"5b4017c3-936d-417a-bf94-062a4565ac02","resolution":{"observed_at":"2026-08-06T15:52:15.119553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.101617Z","title":"Monteil, R","venue":null,"work_id":"7a84746d-c8dd-430f-bb25-ea04bee7bf31","year":2021},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.248099Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:821250f0ce7b8c44f1f061b09527af2b519d72b707c2bcb01f71f0fc89347727","observation_id":"f0c65db9-4633-4bb5-bfa0-93a6d2f52bba","resolution":{"observed_at":"2026-08-06T15:52:15.105831Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.086556Z","title":"Naber and D","venue":null,"work_id":"9448254e-4de2-42f0-bcf7-735420ad03e5","year":2018},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.346247Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:f5763eca0d27e4ec0b418536c2e23ab41657593dc69d6cc26846b5cd05f372ca","observation_id":"33c2eb18-2d7d-4b4f-81f9-c29c695c04f5","resolution":{"observed_at":"2026-08-06T15:52:15.091128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.070957Z","title":"Nguyen and A","venue":null,"work_id":"437b5cf6-7116-4afd-bcad-89f28e360158","year":2013},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.467298Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:1cdb1077c17c379ca5b2e4af96e9211206ca42a50ff3b69baa6b73e424eeec49","observation_id":"bdf8ba8a-3a97-4842-a093-87ed94f6fad4","resolution":{"observed_at":"2026-08-06T15:52:15.075572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.056228Z","title":"Schoen and K","venue":null,"work_id":"de25892e-846e-46f1-98e5-ec089c09eff9","year":1982},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.565168Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:a4004ed04d999ec7e27942ac602372e53ca3f43e54248583c8f14cf45b6ab21b","observation_id":"d4180d36-554d-47ad-bf33-eab6cdcfeae2","resolution":{"observed_at":"2026-08-06T15:52:15.060563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.039517Z","title":"Schoen and K","venue":null,"work_id":"351c6657-0142-4ecd-b8a6-33022923671b","year":1983},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.657522Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:fd4d995029b71a58cf2761858e0f13b88ddc27437c2ec5ed39351fd9bd67cfa5","observation_id":"2756e201-be7e-48f1-98b7-9ad6cc833966","resolution":{"observed_at":"2026-08-06T15:52:15.044048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":{"arxiv_id":"2503.16829","last_updated":"2025-03-21T03:54:41Z","snapshot_observed_at":"2026-08-07T16:47:35.074842Z","submitted_at":"2025-03-21T03:54:41Z","title":"Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface","version":1},"cited_work":{"arxiv_id":"2503.16829","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.16829","snapshot_observed_at":"2026-08-06T15:52:14.981105Z","title":"Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface","venue":"math.AP","work_id":"a07823cd-18eb-4007-965f-24b7b0aaf856","year":2025},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.763288Z"},"links":{"cited_paper":"/paper/2503.16829","citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:8b2384c85b3396d72a98f324d5ff86eb4f54e914b7f36b6770ab88151571d777","observation_id":"e711e138-f196-4fe5-8a3f-d1fd6d2cfe3a","resolution":{"observed_at":"2026-08-06T15:52:14.988004Z","resolver_source":"local_arxiv","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:52:15.023191Z","title":null,"venue":null,"work_id":"6d1d08e0-96c6-46a7-a3c7-1427a468eb60","year":2017},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.859550Z"},"links":{"citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:b52d8145dfc913f95cc911ad0a34866619cee2113f7fbbf046a787272b05e35b","observation_id":"e90791a3-3adc-4b60-9263-fde3c44611f2","resolution":{"observed_at":"2026-08-06T15:52:15.027728Z","resolver_source":"raw_fallback","status":"unresolved"},"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":{"arxiv_id":"2404.00677","last_updated":"2024-03-31T13:04:34Z","snapshot_observed_at":"2026-08-13T00:40:35.762561Z","submitted_at":"2024-03-31T13:04:34Z","title":"Landau-de Gennes model with sextic potentials: asymptotic behavior of minimizers","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.00677","snapshot_observed_at":"2026-08-06T15:52:14.924778Z","title":"Wang and Z","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T15:52:14.924778Z"},"links":{"cited_paper":"/paper/2404.00677","citing_paper":"/paper/2507.14955"},"observation_digest":"sha256:e0c963e1feea2cee804feeca11bca625fe4885aa81af63cd0abd42d2396ad587","observation_id":"38b52a35-48aa-4504-a91b-5ec2f49453c6","resolution":{"observed_at":"2026-08-06T15:52:14.924778Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.14955","last_updated":"2025-08-03T16:04:02Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T20:23:24.657578Z","submitted_at":"2025-07-20T13:26:57Z","title":"Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":2,"verified_fuzzy":19},"total_outbound_references":25},"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 25 of 25 outbound references and 2 inbound Pith citation observations for arXiv:2507.14955."}