{"as_of":"2026-08-19T19:32:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4b5a893f4be34dc97893a40fa7f535d6f3575308b4fe2a2f80c1b9706d5ed0fd","coverage":[{"denominator":64,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":64,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T13:49:10.895966Z","state":"measured"},{"denominator":66,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":66,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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":"2026-08-10T00:37:59.027086Z","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":"2026-06-29T09:53:17.559455Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.12889","snapshot_observed_at":"2026-08-10T00:37:59.027086Z","title":"Detaille and J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.18149","last_updated":"2025-01-30T05:32:04Z","snapshot_observed_at":"2026-08-19T16:08:14.712001Z","submitted_at":"2025-01-30T05:32:04Z","title":"Generic topological screening and approximation of Sobolev maps","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T00:37:59.027086Z"},"links":{"cited_paper":"/paper/2412.12889","citing_paper":"/paper/2501.18149"},"observation_digest":"sha256:d415552155691e08fe985c17d3cd675be4964cd96912220ecea81280329dd3a0","observation_id":"135ce5e5-00f2-4fda-a7cd-2a3029c20c3b","resolution":{"observed_at":"2026-08-10T00:37:59.027086Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"cited_work":{"arxiv_id":"2412.12889","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.12889","snapshot_observed_at":"2026-06-29T09:53:17.559455Z","title":"Detaille and J","venue":null,"work_id":"4f8238e8-3523-412b-b1d7-4af8d463d4c5","year":2024},"citing_paper":{"arxiv_id":"2605.28622","last_updated":"2026-05-27T15:30:34Z","snapshot_observed_at":"2026-07-06T23:38:09.179597Z","submitted_at":"2026-05-27T15:30:34Z","title":"Topological singular set of manifold-valued maps weakly approximable by smooth maps","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-29T09:45:31.272703Z"},"links":{"cited_paper":"/paper/2412.12889","citing_paper":"/paper/2605.28622"},"observation_digest":"sha256:d9552a230e78443307e92a476fb1b88b0e7f79db8919559e8fda625e2ac62c85","observation_id":"aece2c29-9744-4107-bb2d-de85c7a77a6e","resolution":{"observed_at":"2026-06-29T09:53:17.561023Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.12889/citation-record","integrity":"/paper/2412.12889/integrity","json":"/paper/2412.12889/citation-record.json","paper":"/paper/2412.12889"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/1970147","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.876290Z","title":null,"venue":null,"work_id":"9390bc25-c399-49cf-b0c4-f4ab2d21fc0f","year":1960},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.550463Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:3ac3a5d8c07a4c6915cad2aa7cbb5929b2ff751edd70fe4e6fb6ec9ab8257023","observation_id":"d8aab363-6642-4ae9-b7f4-6e6125c1795e","resolution":{"observed_at":"2026-08-11T13:49:11.881885Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10097-003-0053-5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-19T11:03:45.297681Z","title":"Alberti, S","venue":"Journal of the European Mathematical Society","work_id":"ee6b3134-9984-4e77-aaf6-6ab8c06a287a","year":2003},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.556757Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:d893e08e545535333023dc2b5538b7b1f355a4c1b6c5db58da9e2747dbaac4c7","observation_id":"ebdce2fe-6c5d-4802-afa3-e1443d4ea75b","resolution":{"observed_at":"2026-08-11T13:49:11.864649Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bfb0082921","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"Almgren, W","venue":"Lecture notes in mathematics","work_id":"ead29a8e-0c3b-4988-a1eb-e84c898412d4","year":1988},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.562400Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:7842e23afb10c9521f77488407b0c1eef2789bef2e8ecfaeb1220313e8f2b0b5","observation_id":"dea31ae6-e2ca-4298-b739-829df1490ccf","resolution":{"observed_at":"2026-08-11T13:49:11.845295Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-540-69315-4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-13T11:03:48.094449Z","title":"Bernot, V","venue":"Lecture notes in mathematics","work_id":"4b2891c3-7e2b-41b1-853e-ae54cd38ff5a","year":2009},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.568290Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:cc57034900fea98f8a70611ab4dfb2b9db819b0ff0f393dcf5800f42836c8ba2","observation_id":"971c91bd-bd25-4dd9-9e61-8a2b077ea251","resolution":{"observed_at":"2026-08-11T13:49:11.827529Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.574384Z","title":"Bethuel, A characterization of maps in H 1(B3,S 2) which can be approximated by smooth maps, Ann","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.574384Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:5851e130227902039d103f3068528e6222726803b1e816e74b565743d9bf13b6","observation_id":"0989ddcf-8a60-43f4-a3f1-8a6d43cc4e93","resolution":{"observed_at":"2026-08-11T13:49:10.574384Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02392449","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"Bethuel,The approximation problem for Sobolev maps between two manifolds, Acta Math.167 (1991), no","venue":"Acta Mathematica","work_id":"8ef09423-a018-407e-98ab-a2bd3074e670","year":1991},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.579865Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:138c7cfeeee5cb38a171436d9a1c6df1b04b280132d1610da008f16b9f39edc9","observation_id":"9501ae83-b7be-4608-9015-0f014696544f","resolution":{"observed_at":"2026-08-11T13:49:11.796284Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11784-014-0185-0","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.770758Z","title":"Fixed Point Theory Appl.15 (2014), no","venue":null,"work_id":"6a636584-0679-4271-b71f-7edb5e024902","year":2014},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.585957Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:2042bdc2cf92584ff29f81dd7e0ad7497f6ab4f8704cb7ee242d9eab3478ac29","observation_id":"f9ce9d4a-d526-4a39-b6f0-56db09ddf6fa","resolution":{"observed_at":"2026-08-11T13:49:11.776259Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-019-00911-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":"Math.219 (2020), no","venue":"Inventiones mathematicae","work_id":"8bb15d5f-ac48-42b2-b846-3bac40185ef6","year":2020},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.591096Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:80a4f65f655fb4fa5a04851ad6ede457b6b27d61db067dd0d609ab17b1154026","observation_id":"544cb598-e2e9-451d-94fe-eb87e260450a","resolution":{"observed_at":"2026-08-11T13:49:11.758549Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/conm/446/08628","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.735391Z","title":"Bethuel and D","venue":null,"work_id":"54a648d5-ddd1-4fc6-9d5d-e838e4dc18ca","year":2007},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.596375Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:d4b2533f8545a5896141a13b12f1d5f885aa151487ab617f619b2f86533ae691","observation_id":"32729dfe-eda2-467a-81f9-addf2123c403","resolution":{"observed_at":"2026-08-11T13:49:11.740753Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01187897","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"Bethuel and F","venue":"Calculus of Variations and Partial Differential Equations","work_id":"710a3089-c7ed-4fc6-a2a7-15433a16f906","year":1995},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.601392Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:929f55c3bb426f2f569dedfdcd3f0051f8ef4dfb0b98238f396da978c1e82aa6","observation_id":"f11a18f8-6155-4af6-bc23-1e7117fd43bd","resolution":{"observed_at":"2026-08-11T13:49:11.723532Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0022-1236(88)90065-1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.699869Z","title":"Bethuel and X","venue":null,"work_id":"1b5aede2-43e9-4d1b-a775-b3cc794cbd91","year":1988},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.606607Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:8f4d429147442e63d58cf4ab1eb46e899a0b6cb7e5fb76dafa890f6b4ede2c7e","observation_id":"81c20396-339e-4cb4-8ac8-c67c50669195","resolution":{"observed_at":"2026-08-11T13:49:11.705455Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.612064Z","title":"Bourgain, H","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.612064Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:5e03d40b2a809530255c4d4110fda2598477219ae9ed4a9907e8278dc75bab05","observation_id":"dc891a9d-ab71-4e89-a4f9-a96410e1297f","resolution":{"observed_at":"2026-08-11T13:49:10.612064Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/cml.5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.670329Z","title":"Bousquet, A","venue":null,"work_id":"12bb54a1-0360-490f-864d-5e3bd075c29c","year":2013},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.617146Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:2fc36d5fd4656e52688ff3781669832d8382d604765bb7fdfdd5e91af89bfc86","observation_id":"eefa127f-f613-4ab6-be2c-a59c4f634e55","resolution":{"observed_at":"2026-08-11T13:49:11.676415Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/jems/518","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.653483Z","title":null,"venue":null,"work_id":"f0b62012-638a-4022-b019-a47c012625e4","year":2015},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.621938Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:20539f7e7b7cbb98cbd9dd891b08261a5efb629c1fbef6f2911d3187d55345dc","observation_id":"c47d5a2d-0ebd-46cb-a3c3-7a7ce50dbe90","resolution":{"observed_at":"2026-08-11T13:49:11.658730Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.crma.2018.01.017","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.636381Z","title":null,"venue":null,"work_id":"00615fa8-e57d-4deb-8f80-4b9e6f54e8ab","year":2018},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.627308Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:3cf09aad27d447ab46234456ac6044897b7fcbc9d1ce2c634c02b7bae827695e","observation_id":"68ed1563-de70-406b-b10e-1519d488ba11","resolution":{"observed_at":"2026-08-11T13:49:11.642027Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.632214Z","title":"Brezis and J.-M","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.632214Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:f4cc9888d67eecc9996973832dca916219a15b26d329a6e6e84d653e847f043e","observation_id":"0b9271f8-06b3-4e39-a78d-71340837c39f","resolution":{"observed_at":"2026-08-11T13:49:10.632214Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01205490","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"Brezis, J.-M","venue":"Communications in Mathematical Physics","work_id":"bc214bd2-5b17-413b-92f3-24849b6144b7","year":1986},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.636968Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:ea0f76face4a0d298ea1d826943a93d85df54bc77741dd74a0f01a287a260071","observation_id":"a7c8c465-a2a1-451b-800c-44d20b3268ff","resolution":{"observed_at":"2026-08-11T13:49:11.611033Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.641466Z","title":"Brezis and P","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.641466Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:48b8ebd3a0cbbba51cf31dc12db69d9e5d868694f5623336e03ebbbb7faadc14","observation_id":"a3004927-33ce-48a9-9198-b7bf1509f28b","resolution":{"observed_at":"2026-08-11T13:49:10.641466Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jfa.2015.04.005","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.574414Z","title":null,"venue":null,"work_id":"aad02f14-91f7-4a8e-a724-f5c621ed930d","year":2015},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.646143Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:fc3f3192be6661a534982469b58e55c726ebf40766f4ee357b2adf349421f798","observation_id":"188e1c02-dd94-43a4-a109-b08209c381ff","resolution":{"observed_at":"2026-08-11T13:49:11.580307Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.651655Z","title":"Brezis and L","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.651655Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:d2998a206e07c3f9c477a27a844f802a399d478a763d453c3e13887378a97c0c","observation_id":"288907f0-25bc-4832-ba7d-5efc720f1206","resolution":{"observed_at":"2026-08-11T13:49:10.651655Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00526-019-1501-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":"Canevari and G","venue":"Calculus of Variations and Partial Differential Equations","work_id":"8dd357f1-362b-46a5-8d97-830ffdcdabe4","year":2019},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.656250Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:d5ac17409dac7d783c5a9ed62b14cb2ad3d52c83a2984d37c581e7076de8c31b","observation_id":"2a452d40-9f0d-4f88-949b-b61b07a7d69e","resolution":{"observed_at":"2026-08-11T13:49:11.550115Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.660999Z","title":"Da Lio and T","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.660999Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:01a55a62435d97b0162a26f3735afd06be489d780b440154251c120ac11abe8f","observation_id":"8a6715f9-93cc-4638-864c-755a4052e8cb","resolution":{"observed_at":"2026-08-11T13:49:10.660999Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/aif.55","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.513282Z","title":"Deny and J.-L","venue":null,"work_id":"ffea749b-4813-4bfc-bc56-a0d613cf8674","year":1954},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.666490Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:dc89fa585f1b4746264c619702194dfd10552abce0723dfa07010c6a4fe332ea","observation_id":"b4a1e497-4a6e-433d-aeae-bd264a1afbe8","resolution":{"observed_at":"2026-08-11T13:49:11.518894Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.672474Z","title":"Detaille, A complete answer to the strong density problem in Sobolev spaces with values into compact manifolds(2023), available athttps://arxiv.org/abs/2305.12589","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.672474Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:b4db1d744a763ed758e28fbf7cb4296744ee68069b5a8c68eb660fbbba2d06b6","observation_id":"de85c273-3762-4fd6-8555-b321cff78a6a","resolution":{"observed_at":"2026-08-11T13:49:10.672474Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.678834Z","title":"Eells and L","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.678834Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:5cc6aafab47f8c8319118aa6ef9838c52471333e34a5ba16e4cee8272cf0f1c8","observation_id":"454cc9ee-cf8c-4955-83f3-c8ed5d84b1ff","resolution":{"observed_at":"2026-08-11T13:49:10.678834Z","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":"2026-08-11T13:49:12.418341Z","title":"Eells and J","venue":null,"work_id":"eaef28c7-d27f-43b2-9e74-0a94a5e37d15","year":1965},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.684099Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:070ed4c65edb247301a8d5ec99c762fcd358846ef86b22a4ca38dbf6a21ea0b3","observation_id":"c068cb97-3a0b-4cb6-ab45-77774d193204","resolution":{"observed_at":"2026-08-11T13:49:12.423705Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf00298012","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":null,"venue":"Archive for Rational Mechanics and Analysis","work_id":"c23c92af-b5ab-463d-b083-67fa1e39a447","year":1958},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.689504Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:29830b1beca285e09410dc1d0be540ce628c9c5d1dedc245d9acccf82fa5047f","observation_id":"2717639d-9857-41df-9cc8-fe7f49a9496b","resolution":{"observed_at":"2026-08-11T13:49:11.488789Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/zaa/1571","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.465621Z","title":"Gastel,Partial regularity of polyharmonic maps to targets of sufficiently simple topology, Z","venue":null,"work_id":"dc5e4843-151b-466d-8ee9-d1f02558a36d","year":2016},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.694888Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:51e636438ef3be4affbf08d41930d44a217775201095fa3ef1a4b27c2e4a0f57","observation_id":"1cb14286-3f64-4be9-a67e-bbfc54837b32","resolution":{"observed_at":"2026-08-11T13:49:11.471156Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-662-06218-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-13T11:03:48.094449Z","title":"Giaquinta, G","venue":null,"work_id":"28d5af24-efc5-4e29-85e3-daec1f9eace5","year":1998},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.700927Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:8bb94932e75b07c084db8ced8151501e69822bfe2e49b07fb0356dde9ff71a8b","observation_id":"8a435490-ce32-46b2-8bba-f193f4328a86","resolution":{"observed_at":"2026-08-11T13:49:11.454118Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0362-546x(94)90190-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.432554Z","title":"Hajłasz, Approximation of Sobolev mappings, Nonlinear Anal","venue":null,"work_id":"4dbacec4-1a47-4a38-a9e5-b912e5848bba","year":1994},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.706665Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:ae136cbe1c5963c4d368c18cb673b540df8d285f2e71131724c902a77362ca13","observation_id":"4a14e9b2-4603-47f7-88ca-d660b12fefdd","resolution":{"observed_at":"2026-08-11T13:49:11.437511Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/cpa.3020","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"Hang,Density problems forW 1,1(M,N ), Comm","venue":"Communications on Pure and Applied Mathematics","work_id":"b85537eb-95a2-4717-86a0-4b4ba226a615","year":2002},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.711661Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:1beb7bc4bb7ad6f0ee71270feb368678857a2b6abae87bf3fb7a3df60adbb540","observation_id":"ed6045e0-95f2-493a-84d6-bb11d09d9635","resolution":{"observed_at":"2026-08-11T13:49:11.419925Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02392696","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"Hang and F","venue":"Acta Mathematica","work_id":"363b1d74-01cf-41ef-9632-b1b643cf4435","year":2003},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.717094Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:789b9b6a55e970eee472b879e5de061e7ccc354207ff339bf9ab0d01c52242fd","observation_id":"5b21ce83-5f13-4d6d-9df3-1486c0ff061e","resolution":{"observed_at":"2026-08-11T13:49:11.397837Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/cpa.10098","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"III, Comm","venue":"Communications on Pure and Applied Mathematics","work_id":"55407a54-493d-4a08-bc69-2bf9c9ebeabb","year":2003},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.722624Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:32583b7f498c6ee9c16910f6a2175c400c1cf3d7f1bfe0dc09991b56759fc1e7","observation_id":"1c9395b0-0aa0-4073-b751-1364243c5864","resolution":{"observed_at":"2026-08-11T13:49:11.373609Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:12.400492Z","title":"Hardt and T","venue":null,"work_id":"9a7f10cf-0b4c-400a-be10-494cf9b3655a","year":2003},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.727784Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:ce53b80c33214de40dd59c2c0a3c06cd547f49a3f25cff4365602fe9090e26de","observation_id":"1aa2b72b-33f2-448d-be34-f049127382f2","resolution":{"observed_at":"2026-08-11T13:49:12.405927Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11511-008-0023-6","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.348872Z","title":"200 (2008), no","venue":null,"work_id":"5bbd07e1-fb09-4c0b-bf37-d9a0a0b3fb1e","year":2008},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.733456Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:b4fc3dbb500416f1973a55c90601488ddc88a55378d04207ec93e9c55040e2d1","observation_id":"51294e51-9c8e-46e4-a248-f93ed178640c","resolution":{"observed_at":"2026-08-11T13:49:11.355138Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00526-015-0881-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":"Hardt and T","venue":"Calculus of Variations and Partial Differential Equations","work_id":"b17311f0-60f2-4245-b127-51c666c5d2c7","year":2015},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.738806Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:74f273a9de86515e346ed1e700b68b8d0d65737fdc1a7da886a861e5244756c4","observation_id":"502bd47e-a766-4fa3-8ac1-7554300a3e8f","resolution":{"observed_at":"2026-08-11T13:49:11.336436Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.743978Z","title":"Hatcher,Algebraic topology, Cambridge University Press, Cambridge, 2002","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.743978Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:8efb1487a014164a3d340c07e11756f9696a7ecbf0a13cfaf2d85541273cc54d","observation_id":"9159ee42-1cc4-45c7-84da-25ebe32f53fb","resolution":{"observed_at":"2026-08-11T13:49:10.743978Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/b978-044452833-9.50009-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.310359Z","title":"Hélein and J","venue":null,"work_id":"92bb7904-8e84-4757-b6c6-3c993a48770a","year":2008},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.749417Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:9789709f2efd450cc1f0e91c0ec54fc5fed3937f40e32566043f144f92533601","observation_id":"2c4359fa-c85d-4720-ad84-241f944002e8","resolution":{"observed_at":"2026-08-11T13:49:11.316584Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.754803Z","title":"Huang, Y","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.754803Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:1d8926d6fdaad8618f8af8967961e5652881cb08701dfe0e55bae277d9f68c58","observation_id":"49a017c2-d0a9-408a-8759-0f9416ff4b48","resolution":{"observed_at":"2026-08-11T13:49:10.754803Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.760000Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.760000Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:a84ca0df8e83d017c00db3d8a1b88e17299a6cefaaf02181049f2c7ddc75453a","observation_id":"8bf08421-3814-43be-870a-d2f5c41e3188","resolution":{"observed_at":"2026-08-11T13:49:10.760000Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.765461Z","title":"Jost,Harmonic maps between surfaces, Lecture Notes in Mathematics, vol","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.765461Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:e243d20d927c01c0b8cd3794c24984a4569eebeb9b4a86bbeb640a322917e599","observation_id":"325a2106-2681-4827-a331-105282dfb264","resolution":{"observed_at":"2026-08-11T13:49:10.765461Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.770624Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.770624Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:bd4b81b48fd00df9d1f012d5f75c50adca623df7a00d97f67868766afc66ec9a","observation_id":"c27f6122-de15-4e2c-b7fe-03e2e6dee48e","resolution":{"observed_at":"2026-08-11T13:49:10.770624Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.776168Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.776168Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:252520d2322b1672df24e7ad7de93e6746e0022fc853ba2934dec442e58ba54d","observation_id":"ee4296cb-5bcd-4f8b-8905-af87449464e7","resolution":{"observed_at":"2026-08-11T13:49:10.776168Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.781906Z","title":null,"venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.781906Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:5bfedca2fecdd06629bf33aae2fa9c57ea6be3b2e289e615b4bd500e18bacb1f","observation_id":"1bbf6c71-f946-41f2-bb1f-7ba1f0b39f2f","resolution":{"observed_at":"2026-08-11T13:49:10.781906Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.787467Z","title":"Mironescu and J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.787467Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:716348964911ee21482c3114521ed28c75c9028482bedd43c55f1b17473b3bdf","observation_id":"75c2d183-345e-46b9-be10-347222d87681","resolution":{"observed_at":"2026-08-11T13:49:10.787467Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/afst.1675","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.215541Z","title":null,"venue":null,"work_id":"02a46939-e75f-4e9d-8dab-95016b34c065","year":2021},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.792921Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:58fa89e88e104ae0317d8ce2152bce595afc0aaaa5a23f5f248f7021b9cabffc","observation_id":"de5b69e2-402a-4147-b70c-96e42a13fd1f","resolution":{"observed_at":"2026-08-11T13:49:11.221637Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.anihpc.2018.06.002","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.196201Z","title":"Monteil and J","venue":null,"work_id":"34d626ce-0d3f-443f-9507-f12725db7e7d","year":2019},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.798220Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:abd4fdbb159a41faea73cf1eef00d38709f9afffa11753d2f3808dffd60bd3fc","observation_id":"1503aa17-c860-4ed4-a8c7-1e3f697153f9","resolution":{"observed_at":"2026-08-11T13:49:11.202372Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0362-546x(94)00225-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.177584Z","title":"Nakauchi and S","venue":null,"work_id":"eda251df-9ffc-416b-b005-2a9c50a5d47b","year":1995},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.803687Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:7adfcf7cfbce5bd62878a93b8f7806ec2ec4d8920bf9425daae5314fed1f865c","observation_id":"c42f441e-0271-4d35-874c-827944dcaa46","resolution":{"observed_at":"2026-08-11T13:49:11.183560Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.808904Z","title":"Nash,C 1 isometric imbeddings, Ann","venue":null,"work_id":null,"year":1954},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.808904Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:ff6b78047aa8b1fc358e5f2e8f184763459cc6d6678ff20da1850d5be887d1c7","observation_id":"a294a17b-bcf4-4871-ab6b-d7c3ac451e60","resolution":{"observed_at":"2026-08-11T13:49:10.808904Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.813446Z","title":null,"venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.813446Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:82d97c34fc68b1881c72473c86dccb6677ebf1fd9cd0ef5269d5620c751848ef","observation_id":"34055da2-badf-481c-ba9a-e0b738333c9c","resolution":{"observed_at":"2026-08-11T13:49:10.813446Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1021227017504","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.133120Z","title":null,"venue":null,"work_id":"db62ad71-02d8-4b98-90de-012e939f01d1","year":2003},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.818581Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:9d38eb136728e9057e6ceae209f59f86b48775238f1d1323019fc51488e9acd1","observation_id":"4eb2afb1-84e2-467a-9857-46b0cde4851c","resolution":{"observed_at":"2026-08-11T13:49:11.139242Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s000390300006","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":null,"venue":"Geometric and Functional Analysis","work_id":"9796fb81-8200-4c2c-8f50-4df7e17331f0","year":2003},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.824012Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:dbd125cde72c8a8b51f2d39199a5ef1023b6d98dd4275173e39387d1739baf3a","observation_id":"034cafea-7073-4b4c-9db2-ca1581c0d6cc","resolution":{"observed_at":"2026-08-11T13:49:11.120365Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.829473Z","title":"Rivière,Minimizing fibrations andp-harmonic maps in homotopy classes fromS3 into S2, Comm","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.829473Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:cb74e4c279ab4bcad57e64f3b697dd9b521b1b8b021c21a9653a35ecea408825","observation_id":"d2644f96-8e8e-4b03-a3e4-4106bdeb4395","resolution":{"observed_at":"2026-08-11T13:49:10.829473Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01909369","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"Runst,Mapping properties of nonlinear operators in spaces of Triebel-Lizorkin and Besov type, Anal","venue":"Analysis Mathematica","work_id":"8e40f674-8455-4cca-8c86-48ef181e62e1","year":1986},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.835235Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:d13b48c75bd90bd72abdb035bf03ec19be8311e4ae9f39c1fcefa6e040491eb8","observation_id":"64d38565-688c-4bcb-ad12-b1fd442ae24c","resolution":{"observed_at":"2026-08-11T13:49:11.084571Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.840996Z","title":"Sacks and K","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.840996Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:4b09cd9da479c3f32ef37928bf5e5e02c47b1a974a650ee9d8e97f3dcdacddc8","observation_id":"aa6df02c-c96e-4ebe-ac9e-ef6272c8bd35","resolution":{"observed_at":"2026-08-11T13:49:10.840996Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.846523Z","title":"Sandier,Lower bounds for the energy of unit vector fields and applications, J","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.846523Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:0824b9d699167c5e9886393000da6f46aa91e47368d7a5f2d59846cae0f3eef6","observation_id":"2bde67d2-b056-4be6-a072-4e5515a17122","resolution":{"observed_at":"2026-08-11T13:49:10.846523Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-0-8176-4550-2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"Sandier and S","venue":"Progress in nonlinear differential equations and their applications","work_id":"45346987-59e8-470f-bc51-63ddbd30c468","year":2007},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.852283Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:2daf7e8910547a38e124301ad4541c855e7891772c8ed0b819d68e243bd73fe9","observation_id":"28649317-cda4-4d88-9cdc-965715c3043e","resolution":{"observed_at":"2026-08-11T13:49:11.053123Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.857896Z","title":"Schoen and K","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.857896Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:08dc68e38c2fdf50a1393f949172dc0232eb9edf25be67cffe1250b4cde21ff7","observation_id":"5fb1e8b0-66c6-4a00-b835-0fc6828bac4e","resolution":{"observed_at":"2026-08-11T13:49:10.857896Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.862926Z","title":null,"venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.862926Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:a1b44ef31de69ba6bc6cda72047b0bc82481a40c1d1b4521f7a2c35e3d41965f","observation_id":"d2b5c4bd-1acd-4a18-b92a-41df0df2e55b","resolution":{"observed_at":"2026-08-11T13:49:10.862926Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/proc/15026","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:11.011729Z","title":"Schikorra and J","venue":null,"work_id":"890a5990-fec3-4db9-b1fd-28edb4b44c1e","year":2020},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.869260Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:2bbd2ec2079d0cd58e9c8c6f230abe89d83a5e967ddce8ff43f37194b310b22f","observation_id":"72261ee7-3ebc-4a59-955f-021ace6be6ca","resolution":{"observed_at":"2026-08-11T13:49:11.017576Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/10886","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.992393Z","title":"Urakawa,Geometry of biharmonic mappings: Differential geometry of variational methods, World Scientific, Hackensack, N.J., 2019, doi:10.1142/10886","venue":null,"work_id":"f6ff029c-b55f-4a8b-8ce7-403efd481def","year":2019},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.875014Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:f40bef7297a7002c9e5f7e5e9b74f506743c859b1d50ac84ad5464c6f59a69e4","observation_id":"15374271-b9e3-4bd4-802c-31dad8269c89","resolution":{"observed_at":"2026-08-11T13:49:10.999073Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02392271","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:08:50.044864Z","title":"White,Homotopy classes in Sobolev spaces and the existence of energy minimizing maps, Acta Math","venue":"Acta Mathematica","work_id":"46cf97c5-f622-476d-962c-9f1595af614e","year":1988},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.881887Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:5dcc74cd11aba49a91f7e22120c44e3af2666d6ca5c4d3613279a823a3bb031f","observation_id":"a98b1982-e175-427d-a783-ec681a944230","resolution":{"observed_at":"2026-08-11T13:49:10.978559Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/1968907","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T13:49:10.952069Z","title":null,"venue":null,"work_id":"c77d19b5-ce1e-4002-899a-437c466ebbce","year":1941},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.889041Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:045dcfb186f05ef1a5c8c03b9e04d2e3d6bb7b75df5304f66204080de6361ec6","observation_id":"99ee0de3-cf9c-498d-862a-3171dd2c42df","resolution":{"observed_at":"2026-08-11T13:49:10.958744Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-11T13:49:10.895966Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-11T13:49:10.895966Z"},"links":{"citing_paper":"/paper/2412.12889"},"observation_digest":"sha256:d636b8cd19f6a9267248b96c81cf2c3e6ee217c9e87629e0378e0cdfe729fa40","observation_id":"ec26f096-b7c3-4b1d-90a0-49269a483858","resolution":{"observed_at":"2026-08-11T13:49:10.895966Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.12889","last_updated":"2025-04-12T17:41:16Z","latest_version":2,"primary_category":"math.FA","snapshot_observed_at":"2026-08-18T00:24:18.695626Z","submitted_at":"2024-12-17T13:16:30Z","title":"Analytical obstructions to the weak approximation of Sobolev mappings into manifolds"},"reference_resolution":{"displayed":64,"state_counts":{"malformed_identifier":4,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":36,"verified_fuzzy":2},"total_outbound_references":64},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 64 of 64 outbound references and 2 inbound Pith citation observations for arXiv:2412.12889."}