{"as_of":"2026-08-08T08:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:55c6d9512e48dc685d6bf766d4de08b25b672d1d187959a29515113e056acf43","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:31:37.137202Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2506.08387/citation-record","integrity":"/paper/2506.08387/integrity","json":"/paper/2506.08387/citation-record.json","paper":"/paper/2506.08387"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:31:37.532856Z","title":null,"venue":null,"work_id":"4f936621-57bf-4d35-adf3-7c06ba83f078","year":1990},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.031041Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:486629d370ed12f5373a717a56bd0e2ace11fe273f5e8f8ccb1b570a9a096e91","observation_id":"7836358a-5421-4831-8247-4a2036de8639","resolution":{"observed_at":"2026-08-07T05:31:37.537567Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.516621Z","title":null,"venue":null,"work_id":"7ee98471-135b-4f32-a492-d9a2bca04cd9","year":1990},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.036324Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:15e5d4a3f387a202d6a2ccfc927e30f7c4dd0a78c6a48a592f55c3e03013fe73","observation_id":"b8020375-681b-4962-af89-50edaee794f3","resolution":{"observed_at":"2026-08-07T05:31:37.521382Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.501730Z","title":null,"venue":null,"work_id":"105d63d6-e7b1-4dbe-a139-e3558357af52","year":1991},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.040883Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:bdbec27f7b718c6bd551cf986a9efe7585485db6eb5d83adf7f3dde54b1f104d","observation_id":"2986e70d-160e-4c64-95e0-6dc4c687293e","resolution":{"observed_at":"2026-08-07T05:31:37.506396Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.487201Z","title":null,"venue":null,"work_id":"4cac9d15-17f3-48a4-9948-bdbc09026136","year":1993},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.045695Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:c50b8a85c794063f783d2b797efc28c3fe1370c52b85cc9278c0d4fbe81800fe","observation_id":"a2740bcd-41e4-4a85-b0c7-f114dcf97fa4","resolution":{"observed_at":"2026-08-07T05:31:37.491843Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.472921Z","title":null,"venue":null,"work_id":"cb282b86-7b58-4ad6-b82f-6a605b93ebf3","year":2022},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.050440Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:298b6e5f77b59a32f7c6220ab7fcb7016440dc42ad9a068307136cc2752ddc6a","observation_id":"de8c8fb2-fe32-42e2-b717-02eb9b5cecfe","resolution":{"observed_at":"2026-08-07T05:31:37.477515Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.457751Z","title":"De Philippis, A","venue":null,"work_id":"93148abe-3d33-471e-9e7d-c17d16dfe732","year":2013},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.054843Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:040b1f87f089d721b959306cbe134da4417a11ed08d0c452829cb9988953686b","observation_id":"dd9711be-7b2e-4e12-8d66-217f174e7e4a","resolution":{"observed_at":"2026-08-07T05:31:37.462503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.442661Z","title":"De Philippis and A","venue":null,"work_id":"35f333c4-a109-4374-8a2d-1cf93fe2f222","year":2013},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.059891Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:4739b896f24958489b53128a35360a14dc2b8c0ef154b37532ced13704fd74b9","observation_id":"62a60d9d-192d-487c-868c-3468aee7fb79","resolution":{"observed_at":"2026-08-07T05:31:37.447496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.426963Z","title":"De Philippis and R","venue":null,"work_id":"826fffe0-2eb3-4928-bf3a-a77a325570ee","year":null},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.064351Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:8e8fe86efd400bfba1f7bc3de5be8cd36b17e6ec41b40eb820f3f364293f9392","observation_id":"a761f364-5b24-4f56-a9a3-c2f5202d0a25","resolution":{"observed_at":"2026-08-07T05:31:37.432253Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.411497Z","title":"Figalli, The Monge-Amp`ere equation and its applications, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Z¨urich, 2017","venue":null,"work_id":"2eb55599-7de1-481a-961a-23bf3698ee53","year":2017},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.068989Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:0fe58ac368ea74c891ad3d89d52debbdc9f2ab69a7eba9acf03f8b7407a532c5","observation_id":"f3747941-7c69-4605-8002-6cbb0a963387","resolution":{"observed_at":"2026-08-07T05:31:37.416493Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.395821Z","title":null,"venue":null,"work_id":"2f6af10e-adc5-48bd-9712-62feecdfc386","year":2015},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.073365Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:308c59339b9766d16c00e4eae5812d2c7264931b639d08b0619a7133b2b5afec","observation_id":"d9ee5378-17fd-4049-bbc5-7896447acf85","resolution":{"observed_at":"2026-08-07T05:31:37.400691Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.380204Z","title":null,"venue":null,"work_id":"eed7a4ee-c343-4e8f-bc20-af4930bd724b","year":2016},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.077975Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:a511ef5817339104fcc8b27d1fe5d0a1ce33dca114453d6b5cc3045f6c9636db","observation_id":"c77ef764-715c-4cf9-957d-2af906dc3e32","resolution":{"observed_at":"2026-08-07T05:31:37.385018Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.364839Z","title":"Huang, L","venue":null,"work_id":"33165f4b-6a2b-4bf6-9ef8-f04e67ac87a7","year":2024},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.082316Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:81163552537638ce7b94475863beea02e2647b17d5c78b8891e02a5f345c4b8e","observation_id":"03d5aa5c-a925-462d-a383-9a6d165c0bd0","resolution":{"observed_at":"2026-08-07T05:31:37.369591Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.349385Z","title":"Jian and X","venue":null,"work_id":"06b65d3f-3e88-4b22-8bda-60fafbf3a9b7","year":2025},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.087531Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:72f43d4b7d66751c875be4663131925bbba0212ccc85042bdfe2ba13bebb4bfd","observation_id":"e0a1ada4-2d4c-4230-9017-9773adb11efb","resolution":{"observed_at":"2026-08-07T05:31:37.354442Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.21253","last_updated":"2025-04-30T01:42:12Z","snapshot_observed_at":"2026-08-07T15:57:59.493791Z","submitted_at":"2025-04-30T01:42:12Z","title":"Regularity and classification of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"cited_work":{"arxiv_id":"2504.21253","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.21253","snapshot_observed_at":"2026-08-07T05:31:37.173455Z","title":"Regularity and classification of the free boundary for a Monge-Amp\\`ere obstacle problem","venue":"math.AP","work_id":"1fb9ad9e-efe0-48a9-88c8-a5a9897d38ab","year":2025},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.092140Z"},"links":{"cited_paper":"/paper/2504.21253","citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:0810a1b69645665b790887e4f8bccbd3d2a1644ed31ca102ac5d65862ce1e3a5","observation_id":"50c4def5-d066-4192-a4ad-83f2abaae753","resolution":{"observed_at":"2026-08-07T05:31:37.180861Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.333256Z","title":"Mooney, Partial regularity for singular solutions to the Monge-Amp`ere equation, Comm","venue":null,"work_id":"94358c3c-2462-4ed5-adbe-dc08304409f9","year":2015},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.097184Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:279e37f71f7252abd416dd43a2afafa6a8e86d5a655e366ee620396770b0efcb","observation_id":"14138c52-a2e9-4cae-86b0-732ae0e8e640","resolution":{"observed_at":"2026-08-07T05:31:37.338580Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.318030Z","title":"Mooney, Some counterexamples to Sobolev regularity for degenerate Monge-Amp`ere equations, Anal","venue":null,"work_id":"2bedf801-1e58-4b5e-a05c-1a0ad3a23f6b","year":2016},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.101424Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:a5cc7ea125ddfe9f4f924415d1ff89c9950f06d7a573398a9bc175da5c063644","observation_id":"5f9b6fc9-f514-49fe-8459-a0462f278c16","resolution":{"observed_at":"2026-08-07T05:31:37.322830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.302577Z","title":"Mooney, Solutions to the Monge-Amp `ere equation with polyhedral and Y-shaped singularities , J","venue":null,"work_id":"c9ba9984-894f-42a8-862f-43918b7233d3","year":2021},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.106164Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:d0ab6c81ea303d4a4720758eef51c1a54fe8bbb598d3f56aaf1aa5c9e8a2089b","observation_id":"82cf9ff1-1c02-4843-9522-63c6946cf9a6","resolution":{"observed_at":"2026-08-07T05:31:37.307795Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.286807Z","title":"Mooney and A","venue":null,"work_id":"11900c95-c765-4eda-821d-6e18c940a781","year":2023},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.111125Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:79ea68040838abeeb95d706956fea9cac3b98cdcd30fb0f8cb6a91a5e2e484b7","observation_id":"cde64657-627e-4c75-b395-5a0e77244230","resolution":{"observed_at":"2026-08-07T05:31:37.291603Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.271014Z","title":"Savin, The obstacle problem for Monge Ampere equation, Calc","venue":null,"work_id":"39970c40-9ea1-49d9-ba7c-9fa24c666750","year":2005},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.115573Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:2abefb939d0f85dee3a0bb5e741df1f203f73afb765a1e3b349ddcb2491dff39","observation_id":"cfed6341-f3fe-4ba9-9f95-4109c93f41d0","resolution":{"observed_at":"2026-08-07T05:31:37.276285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.254934Z","title":"Savin, The Monge-Amp`ere equation, Geometric and analytic aspects of functional variational princi- ples, [2024] ©2024, pp","venue":null,"work_id":"f82f8d69-53c7-4b56-85b8-e233d125348e","year":2024},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.119811Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:2bdc38f09fb6ebed23f218903be9510d42485f1e326b714611193aefe0d6a351","observation_id":"1096a94d-8c61-4439-9757-26db0f0bb410","resolution":{"observed_at":"2026-08-07T05:31:37.259727Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.240083Z","title":"Schmidt, W2,1+ε estimates for the Monge-Amp `ere equation , Adv","venue":null,"work_id":"edf74a43-a913-46cb-a630-6e3a992a04b1","year":2013},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.124262Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:4c3145a1fb40d14ef83029bca3052f3cfbde726f5a5bde1b393a9f746150c01e","observation_id":"9590b293-f78b-4242-9865-48e9f8cbe41f","resolution":{"observed_at":"2026-08-07T05:31:37.244761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.224490Z","title":null,"venue":null,"work_id":"2b08b0e5-3df1-44b4-bb35-f9fc82b6bb53","year":2008},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.128781Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:d3b07ac6be83e940c5c1f9e9b5b3fcf06ebcf3a87d387da90bf86ab1137dfaf0","observation_id":"50a79f48-9c6e-4bfb-9b6d-d457ea79aead","resolution":{"observed_at":"2026-08-07T05:31:37.229610Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.207908Z","title":"Wang, Regularity for Monge-Amp`ere equation near the boundary, Analysis 16 (1996), no","venue":null,"work_id":"b87f03ff-e1cf-4335-8f60-a0e4e9c82f05","year":1996},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.132891Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:fa3d1d0e0797933655b1e219096d14c6c172fd86b2ce172e0d1cb3bb47f643ac","observation_id":"44491e69-d5bb-40e7-8f4d-0c4dda12a53d","resolution":{"observed_at":"2026-08-07T05:31:37.212877Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T05:31:37.192024Z","title":"Jin Department of Mathematics, The Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong Email: tianlingjin@ust.hk X","venue":null,"work_id":"372d1067-dc1c-4909-ba85-d8ab66c86b6e","year":null},"citing_paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem","version":1},"reference_index":107,"source":"pdf_text","source_observed_at":"2026-08-07T05:31:37.137202Z"},"links":{"citing_paper":"/paper/2506.08387"},"observation_digest":"sha256:3f2eafa2d276a83737872130a2c1bbec8e028b00ccd82b8b5137e40105f16c9d","observation_id":"19b757f0-c6f1-4f28-a899-4884355fad7f","resolution":{"observed_at":"2026-08-07T05:31:37.197378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.08387","last_updated":"2025-06-10T02:53:20Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-07T05:09:52.639331Z","submitted_at":"2025-06-10T02:53:20Z","title":"On the singular set of the free boundary for a Monge-Amp\\`ere obstacle problem"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":1,"verified_fuzzy":15},"total_outbound_references":24},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2506.08387."}