{"as_of":"2026-08-16T05:40:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9da0a02ee744e27bceaaba98081ed16ea9b6c437b2d112712ce9e96e76ca7042","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T11:27:18.024273Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/1908.09322/citation-record","integrity":"/paper/1908.09322/integrity","json":"/paper/1908.09322/citation-record.json","paper":"/paper/1908.09322"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.350863Z","title":null,"venue":null,"work_id":"615c189d-a7f7-4eaa-a012-c9730e56524a","year":1948},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.920042Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:9ac52c9e1b7ee1ba5a9f9333929e7bbcf25b958f6f812f4ea83b593fc5ad0758","observation_id":"387df630-719f-486c-adf3-c6615dfe8a99","resolution":{"observed_at":"2026-08-14T11:27:18.354600Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.341516Z","title":null,"venue":null,"work_id":"885f42cd-9099-4644-bf5e-996eda88a781","year":1976},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.925206Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:4213d58d6667153256346fdb83ea13e9e708e6690f90fd24fc239c72f27ba056","observation_id":"41889c2c-70fa-4bd2-bad0-ae42e129ccb7","resolution":{"observed_at":"2026-08-14T11:27:18.344528Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.332441Z","title":null,"venue":null,"work_id":"76b50a1d-1f4d-418d-a3d3-07c4633ae1df","year":1961},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.929164Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:392aafb8eac53596e0e527bd90d62b4244a2b64152d3196e64ad2e71beffe535","observation_id":"9814087b-91c8-44ba-851b-ea7d7d898757","resolution":{"observed_at":"2026-08-14T11:27:18.335503Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.321505Z","title":"Feﬀerman, A","venue":null,"work_id":"db7a6509-1d8b-4932-af86-fa2979043b57","year":2014},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.933072Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:abd0c279c60c7b021b63753eb7db55817c1159b6d7b4cd31396150dc19595e01","observation_id":"da3510a6-9e75-464e-bae9-f0751fa2e14c","resolution":{"observed_at":"2026-08-14T11:27:18.325265Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.309761Z","title":"Gol’dshtein, V","venue":null,"work_id":"b7c18d73-0fd3-431e-a264-37e2489b4d96","year":2020},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.937008Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:7b5658e719083568c6f3dc81e643398e3c62875163d1ebfe780981bca5196f93","observation_id":"512cdabf-d788-4e44-a186-8c617e66613f","resolution":{"observed_at":"2026-08-14T11:27:18.313493Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.299254Z","title":null,"venue":null,"work_id":"c0250dfe-5967-43ec-b2be-19ac825a0813","year":null},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.940980Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:e164dc3d5cc449bb0f59c54537197fca2c520447a4dcff0089d7d49d32c8cf8e","observation_id":"570036a1-fdbf-4167-9a31-27da86c33f08","resolution":{"observed_at":"2026-08-14T11:27:18.303281Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.288237Z","title":null,"venue":null,"work_id":"839c4384-453b-467b-b54e-5c2ca394c4bb","year":1982},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.944910Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:26f0373ea6902ebd664fdfde3bbf591996cad37b108a04ce773fd90480d0d926","observation_id":"bffcabe5-6de2-4ff7-8a26-b5a8253ea25e","resolution":{"observed_at":"2026-08-14T11:27:18.292251Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.278042Z","title":null,"venue":null,"work_id":"9483558d-0140-435a-bfb8-048429d05c1a","year":1996},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.948844Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:dff3da9d551e0062500f9dab31ac91aaa8f8158c0aa71dae648287e137be9c59","observation_id":"f1e25086-3798-4aeb-a041-6570a544edf5","resolution":{"observed_at":"2026-08-14T11:27:18.281632Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.268812Z","title":"Hajlasz, P","venue":null,"work_id":"cee1917b-ba9c-4c3a-99ce-ffe41e2ea770","year":2008},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.952266Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:b737f791ac79b02fc5be975e8db68f30f1cf43230ab291a80d7d81047fdff745","observation_id":"0e382610-f59e-4bed-a1ab-b4fd9af4b441","resolution":{"observed_at":"2026-08-14T11:27:18.271846Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.258836Z","title":"Hajlasz, P","venue":null,"work_id":"281d3074-c76a-4dfc-9cfc-45dcff13eb26","year":2008},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.955784Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:a0533a8ec73f376a7dfa1e544cd08f64405bf38b56be3af0a3dbf192353b73f0","observation_id":"01f38f02-15be-4eba-9fb6-0e275b5178e8","resolution":{"observed_at":"2026-08-14T11:27:18.262310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.248985Z","title":null,"venue":null,"work_id":"044d7076-c959-4af2-8c99-be2e17fff8b8","year":1981},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.959441Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:8279c27a15836ffc8e532697db5e61148f644e70c32ab57b93023968e8196fab","observation_id":"8095fcaa-d32a-4b38-ae39-bb8c0e1c6a2b","resolution":{"observed_at":"2026-08-14T11:27:18.252287Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.238056Z","title":"Koskela, Extensions and imbeddings, J","venue":null,"work_id":"94904d46-57fb-4496-896f-e87d5db6da30","year":1998},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.963134Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:92f08750936241b17c89f798a77508c5359323de698ed24bb8a2c7238b383aad","observation_id":"bdc26653-6e4d-4134-b2d0-73102d7dfed8","resolution":{"observed_at":"2026-08-14T11:27:18.242081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.226626Z","title":"Koskela, D","venue":null,"work_id":"2d70ab22-4c9c-40df-9e9b-95aef1864252","year":2010},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.967433Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:03549a92691c05059af4c10034b0e319c5325a3b02a53b3d715bee5ec8b77f30","observation_id":"3abba8ac-6aab-4cae-afec-4f36c79defec","resolution":{"observed_at":"2026-08-14T11:27:18.230155Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1812.09037","last_updated":"2020-05-18T10:38:13Z","snapshot_observed_at":"2026-08-14T17:39:58.697459Z","submitted_at":"2018-12-21T10:38:17Z","title":"Sobolev extension via reflections","version":2},"cited_work":{"arxiv_id":"1812.09037","doi":null,"metadata_source":"pith","pith_arxiv_id":"1812.09037","snapshot_observed_at":"2026-08-14T11:27:18.056674Z","title":"Sobolev extension via reflections","venue":"math.FA","work_id":"dda32e49-a0fe-4ca9-b9f1-962841c38d82","year":2018},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.971348Z"},"links":{"cited_paper":"/paper/1812.09037","citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:2ce6e2a1e5206441c609fffbbc92f0442a69776a80b5ddcd88294f8afeb60290","observation_id":"3646a772-d08c-4030-8190-58fc1e4c2ea1","resolution":{"observed_at":"2026-08-14T11:27:18.063371Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.216210Z","title":"Maz’ya, Sobolev spaces: with applications to ellipt ic partial diﬀerential equations, Springer, Berlin/Heidelberg, 2010","venue":null,"work_id":"2cf8bdc8-44a4-4143-a0a6-7d7227e0c15c","year":2010},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.975565Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:b9821fe83a99381c5f384283f0d255d16812694afa5d2832e31865c3786b6ef2","observation_id":"a3d39ee0-1601-4d89-b43c-05f97ad175b5","resolution":{"observed_at":"2026-08-14T11:27:18.220113Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.206124Z","title":null,"venue":null,"work_id":"6c2f2128-43e9-4679-801f-27bcfcd9e191","year":1986},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.979240Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:52bb49171d19c424cfb1e03362fd34cbfc9d2f7e0cecfaa0f239f801e95a7866","observation_id":"1f8485d0-def1-4db2-9096-09001b6fb8e3","resolution":{"observed_at":"2026-08-14T11:27:18.209550Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.197320Z","title":null,"venue":null,"work_id":"14a0de4e-ec5c-4a3c-93a4-847cc70d1864","year":1987},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.982804Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:bb5d8c7fa2a0d491eb6274cd60328cf9f08374c7d407ae3f1505966fb3eee60f","observation_id":"f69a946e-815a-4d9d-9fd5-2cee7123a825","resolution":{"observed_at":"2026-08-14T11:27:18.200258Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.188044Z","title":"Maz’ya, S","venue":null,"work_id":"22dcad28-0f96-4fd9-9028-25a6a34c3e86","year":2007},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.986529Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:e741bbd4a92e49f1c76eb6f8110c04c75ba0a733aa89f77677c25cdac3d15019","observation_id":"849d5efb-309a-4ff7-ac1f-003752058e41","resolution":{"observed_at":"2026-08-14T11:27:18.191468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.177176Z","title":"Shvartsman, Whitney-type extension theorems for je ts generated by Sobolev func- tions, Adv","venue":null,"work_id":"d1e5e85c-0d6f-4a63-8b75-b94606021d17","year":2017},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.990980Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:e65e83e9963f20a01a56d1beb3f082751d07cc59ba0f019aea9e9ad5dc6bf2b1","observation_id":"35e265f9-69bf-461b-8a6d-657c1bb8b066","resolution":{"observed_at":"2026-08-14T11:27:18.181006Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.164889Z","title":"Shvartsman, N","venue":null,"work_id":"4a17d789-babc-4cef-a131-e734a1a476a8","year":2016},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.994899Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:0a8355e4aff5beebb082e91c83422b70bd1f1c5020b0dc5970117d4247203ae4","observation_id":"7661b204-2a7e-4caf-b258-a915b0759483","resolution":{"observed_at":"2026-08-14T11:27:18.169588Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.154083Z","title":null,"venue":null,"work_id":"44d0f470-7f29-4087-8ea1-ae99feff419f","year":1970},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:17.998979Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:0a45ddc404ec9a3a247e2261ce70068beea007c865e73e562a8960eb531a25d3","observation_id":"f089c91b-1cb8-4417-b6bf-3cefa5f5d49d","resolution":{"observed_at":"2026-08-14T11:27:18.157941Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.141853Z","title":"Ukhlov, On mappings, which induce embeddings of Sobo lev spaces, Siberian Math","venue":null,"work_id":"9a2b9777-3f9b-49c1-9707-e202f26ddec4","year":1993},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:18.002905Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:0ca28280b86cee1fa8339733d146934daf1064858b06a2d07b40c69e53d3060b","observation_id":"0d04b44d-c915-4a96-aea8-cadc00ac5d3e","resolution":{"observed_at":"2026-08-14T11:27:18.146507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.129496Z","title":"Ukhlov, Lower estimates for the norm of the extension operator of the weak diﬀerentiable functions on domains of Carnot groups","venue":null,"work_id":"12b1929a-9231-4c48-8114-7d2bd3501bc2","year":1999},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:18.006672Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:66c43805f3e95f524131b644a1dd57782648b2442b328d54e462effe32e8f21a","observation_id":"5cf0e2fc-5b0f-421d-a05b-287d76c2c11d","resolution":{"observed_at":"2026-08-14T11:27:18.134459Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.116578Z","title":null,"venue":null,"work_id":"75278b70-7f60-4ea8-8318-65df013e1483","year":null},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:18.009785Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:7a96982991932f2b25dafe45d58e6aab84419eaa736cee4131b2bdfc5c622464","observation_id":"e8cdb314-5736-45ec-a84e-2cbeae8fc866","resolution":{"observed_at":"2026-08-14T11:27:18.120745Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.106112Z","title":null,"venue":null,"work_id":"e1e3bf52-44f9-407b-adce-2e87f9370dde","year":1988},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:18.013317Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:06fb881a21199bc7215661601f7212061884123363c07aa9f72930fba026694a","observation_id":"58815a23-48ef-47da-9b03-e5195c633304","resolution":{"observed_at":"2026-08-14T11:27:18.109382Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.095212Z","title":null,"venue":null,"work_id":"2fb083d9-db89-4df2-bd1a-f3a99c9f0670","year":1979},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:18.016915Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:b361fa67ef3dbc242578416c083a15b0b7b5ae6451966f68db31b74237f5fd92","observation_id":"59336df5-7636-4ff7-aa83-c9fa9f3f7df3","resolution":{"observed_at":"2026-08-14T11:27:18.099138Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.083179Z","title":null,"venue":null,"work_id":"bd56155f-4e79-4ab7-bc6c-7208fa85cb20","year":2002},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:18.020666Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:d0ae01feb31097dc97bc05c722895f7425f7ffa6be43928b1924a2b6705a9f67","observation_id":"55426fae-c52b-4a68-a0ec-bfc103a14d6b","resolution":{"observed_at":"2026-08-14T11:27:18.086943Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T11:27:18.071746Z","title":null,"venue":null,"work_id":"b0a85cc1-c53c-4fec-bf24-3c4eb7dcbc27","year":2004},"citing_paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability","version":4},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T11:27:18.024273Z"},"links":{"citing_paper":"/paper/1908.09322"},"observation_digest":"sha256:b30cb55b1c83962919e24e2472274c3df770abe548ef1e915d08dcb0414b0e0f","observation_id":"a12f598e-acf1-4705-8e12-5e8857afb0d5","resolution":{"observed_at":"2026-08-14T11:27:18.075633Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.09322","last_updated":"2020-10-15T09:24:16Z","latest_version":4,"primary_category":"math.FA","snapshot_observed_at":"2026-08-16T03:37:28.390138Z","submitted_at":"2019-08-25T13:21:43Z","title":"Extension operators on Sobolev spaces with decreasing integrability"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":1,"verified_fuzzy":12},"total_outbound_references":28},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:1908.09322."}