{"as_of":"2026-08-20T15:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:54981c2a07f5648177f51ec871ad07b8004ba8caac9fb3ea7750ec38db2a0f30","coverage":[{"denominator":49,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":49,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T20:00:56.329180Z","state":"measured"},{"denominator":49,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":49,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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/2506.14631/citation-record","integrity":"/paper/2506.14631/integrity","json":"/paper/2506.14631/citation-record.json","paper":"/paper/2506.14631"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:00:57.175272Z","title":null,"venue":null,"work_id":"6df0aa5f-0760-45ad-8ac5-aa556fc318a3","year":2022},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.107483Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:40959dbc02ae31dc723f126ea9cfee41306026a4c777982228c2a68627ebf060","observation_id":"d4211b3c-7a20-43fb-bf3d-7964cc11d40a","resolution":{"observed_at":"2026-08-15T20:00:57.179883Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.160025Z","title":"J., and Rodr\\' guez-Mesa, L","venue":null,"work_id":"2a5aaa9a-e9d0-420f-b310-db2a7c8f9a00","year":2023},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.112864Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:76af6d53d60652872f878d128a4c3227f7a6557f65f77cfd9dffdfd8d28fea17","observation_id":"1ccd3bde-5509-40b1-b00c-e5b344207fc6","resolution":{"observed_at":"2026-08-15T20:00:57.164803Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.144503Z","title":"Variation bounds for spherical averages","venue":null,"work_id":"5cfb9946-7e92-4c89-9aad-48ef77cb768d","year":2022},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.117661Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:4eb7dc4700204e9bdb66cec72972a4ae179df5d2af70093d8b39029a14cf3f71","observation_id":"11ae808c-c867-43bd-8671-a2334d2b624a","resolution":{"observed_at":"2026-08-15T20:00:57.149491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.129488Z","title":"New abstract H ardy spaces","venue":null,"work_id":"cd32d6dc-a7ce-4fea-b812-a54dc9a6f12d","year":2008},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.122949Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:3d3cd108afbb069386dd4315588240f4eb72096def7c1c75f819367352bcffa1","observation_id":"e3691639-c0b8-440f-a245-c0c6b47964e2","resolution":{"observed_at":"2026-08-15T20:00:57.134039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.03540","last_updated":"2023-10-11T14:32:23Z","snapshot_observed_at":"2026-08-20T15:39:53.174436Z","submitted_at":"2023-10-05T13:47:56Z","title":"Variation operators associated with semigroups generated by Hardy operators involving fractional Laplacians in a half space","version":2},"cited_work":{"arxiv_id":"2310.03540","doi":null,"metadata_source":"pith","pith_arxiv_id":"2310.03540","snapshot_observed_at":"2026-08-15T20:00:56.495567Z","title":"Variation operators associated with semigroups generated by Hardy operators involving fractional Laplacians in a half space","venue":"math.AP","work_id":"c355eb97-ccc6-4c25-9a61-9b9b98cce6f1","year":2023},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.127604Z"},"links":{"cited_paper":"/paper/2310.03540","citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:69f9682f72b8c2b5e4b0f286a025a7551623ec519ac1a8f35416992cc5e4fc47","observation_id":"dba1e51c-ede0-4bd9-b0ba-3d58ccaff900","resolution":{"observed_at":"2026-08-15T20:00:56.500995Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.114348Z","title":"On the maximal ergodic theorem for certain subsets of the integers","venue":null,"work_id":"8f019ab9-45b4-480f-bb67-0872fe4a304d","year":1988},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.132689Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:ac59df3a57cbd293c821d2218afaab668294f6473829cf34e205941e2f78773c","observation_id":"4fb7efa7-1153-4d57-b4d3-44d75587c011","resolution":{"observed_at":"2026-08-15T20:00:57.119397Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.098984Z","title":"On the pointwise ergodic theorem on L^p for arithmetic sets","venue":null,"work_id":"a9c8a6a3-8080-4cac-9769-2fc307effd10","year":1988},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.137713Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:1245bd006032ad48be70412ffe6534b5f17789bb5512c15e30346c0a875544f6","observation_id":"8adc072e-158f-4a86-a20f-f00df38c033a","resolution":{"observed_at":"2026-08-15T20:00:57.103761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.084405Z","title":"Pointwise ergodic theorems for arithmetic sets","venue":null,"work_id":"f7afe745-9727-4c8c-8739-5fcc4cf29d7e","year":1989},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.142447Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:ab054dcea0a149d584ca7c1930bf15f09eee0f13901d843eb4a3ec22aa01654f","observation_id":"09b3bbbb-f4e6-44b7-98dd-78e51719028b","resolution":{"observed_at":"2026-08-15T20:00:57.089170Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.069454Z","title":"M., and Wr\\' o bel, B","venue":null,"work_id":"ea4ad57c-6465-4eec-97f4-54faf5c2b189","year":2019},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.147039Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:77c00accd136a43f7b36541721d5b111fc0fd3a96a6e469880efc1845047c6c7","observation_id":"b2e3fb36-98aa-410f-9024-112bda658c00","resolution":{"observed_at":"2026-08-15T20:00:57.074137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.054892Z","title":"A., and D'Ancona, P","venue":null,"work_id":"9a333fe0-15c9-4ab1-a096-c8d1b7b14d98","year":2023},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.151804Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:12539f86db96c9e253bf30930e9a149f21a9c8bd94a5f19a32f496b6e2c15068","observation_id":"b9d798d4-b334-4b6f-8eab-821a5fdc6fc3","resolution":{"observed_at":"2026-08-15T20:00:57.059484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.156243Z","title":"A., Duong, X","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.156243Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:a6fddbc5515d3d9deb5714a1268be546b08db6ac45c7d12e5ad6b50572b7c465","observation_id":"98fd2d1c-4a72-417b-a292-8610dd4f1137","resolution":{"observed_at":"2026-08-15T20:00:56.156243Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2309.02928","last_updated":"2026-04-17T05:46:04Z","snapshot_observed_at":"2026-08-17T00:36:28.530986Z","submitted_at":"2023-09-06T11:41:49Z","title":"Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.02928","snapshot_observed_at":"2026-08-15T20:00:56.161179Z","title":"A., and Merz, K","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.161179Z"},"links":{"cited_paper":"/paper/2309.02928","citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:0ed8d7197a3ce8a3f125ab1ae33e7f6d217af0fd535d6d8ec03471ac330e3e34","observation_id":"0b306a62-8df0-4ad1-a1fd-0007afc0390a","resolution":{"observed_at":"2026-08-15T20:00:56.161179Z","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":"2026-08-15T20:00:57.039478Z","title":"T., Jones, R","venue":null,"work_id":"a4d89d10-4b0a-4e81-82df-ea141f503faa","year":2000},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.166047Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:91745ec0ce74449ce98239a7b7a4c17791ab78ace9e48062777c8196081c412e","observation_id":"d51e09cc-a03d-4fdd-9e09-9541cf72ee49","resolution":{"observed_at":"2026-08-15T20:00:57.044770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.023735Z","title":"T., Jones, R","venue":null,"work_id":"23b8dfa0-912d-4add-90af-84a466b782a1","year":2003},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.170494Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:000a2052f7a0de91f6fda4210cd81458c5b0fe9f9224a65a59a24bd89db7393a","observation_id":"1b87af40-23b0-4d83-af1e-3ebd9f02f959","resolution":{"observed_at":"2026-08-15T20:00:57.028792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:57.008482Z","title":"Variational inequalities for the O rnstein- U hlenbeck semigroup: the higher-dimensional case","venue":null,"work_id":"75718841-a60d-48f0-af64-8e5999ff2209","year":2025},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.175055Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:7578a99a02dbf1659e6ad6f04ee9efb36093186b27873ad5040dc8109947678e","observation_id":"36dd421c-37f5-4cbd-9b96-8111c0ad6e73","resolution":{"observed_at":"2026-08-15T20:00:57.013273Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.993712Z","title":"A., Men\\' a rguez, T., Torrea, J","venue":null,"work_id":"0d230947-6589-4243-92d7-b2192e381c0a","year":2009},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.179710Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:21318309d81296f423ed3c4aace0265ff94098c08a6167509d4096136a58697d","observation_id":"b5aa9e9a-2acd-48b6-bc94-2caf180ff7ed","resolution":{"observed_at":"2026-08-15T20:00:56.998349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.978283Z","title":"Q., and Uraltsev, G","venue":null,"work_id":"a048b189-25d2-4ac4-b7dc-66ceeefb5e87","year":2018},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.184118Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:b7fdee02eebe2bed63d71ac7f7e6bd091468db24f2b0466c610d6097e9058498","observation_id":"f2cb227d-f528-497f-8d90-0c5e7ccae485","resolution":{"observed_at":"2026-08-15T20:00:56.983674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.963295Z","title":"Weighted bounds for variational F ourier series","venue":null,"work_id":"4cd651d8-20cd-4bfe-b4ae-168155ee7261","year":2012},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.188472Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:d587089e7bcc6b053b3e653e1b2b650fef7d63c10738c882265bc787afc0231e","observation_id":"6a85833a-6cae-47fa-bbf3-1f9384456792","resolution":{"observed_at":"2026-08-15T20:00:56.968080Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.948191Z","title":"L., Merz, K., and Siedentop, H","venue":null,"work_id":"932a6d10-5f90-4001-9c7c-d38b41f2acb8","year":2021},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.193078Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:dcf7d22d99f7b9da691bc50ab4662a5264600f5066c730bf5156f2a3f42a5506","observation_id":"9dd458bf-0db1-4f17-a8d1-961d18dbed7e","resolution":{"observed_at":"2026-08-15T20:00:56.953040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.933425Z","title":"A., and Torrea, J","venue":null,"work_id":"2ffd504d-6ffc-476f-98e6-7f07cd7bc543","year":2004},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.197998Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:22fe0d34f1861314036e7bc03f66e5bd8d4221e3f11168720dd09b1a23e48597","observation_id":"916a814c-8777-4d59-8f44-b191ba7aa44c","resolution":{"observed_at":"2026-08-15T20:00:56.938068Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.918949Z","title":"D., Magyar, A., Mirek, M., and Szarek, T","venue":null,"work_id":"106ef234-1cc3-43f7-835c-e426b86fe0e7","year":2023},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.202550Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:b14bb1111e0afeaf89fcca9d061604c86afb65188fd2b6251a59729afc74c2f1","observation_id":"7cfc2292-98d7-405a-871f-66e5ce577c50","resolution":{"observed_at":"2026-08-15T20:00:56.923580Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.904611Z","title":"L., Kaufman, R., Rosenblatt, J","venue":null,"work_id":"1f773d3b-6c2f-44b3-aa51-c6e9010011e4","year":1998},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.206879Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:ff763374aa1c1f272c673eed9427f1d96ddeaddd5e2fc8c52608df9107070ea6","observation_id":"a059d03b-dd9f-4238-bc83-92f4df0e96e7","resolution":{"observed_at":"2026-08-15T20:00:56.908964Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.890562Z","title":"L., and Reinhold, K","venue":null,"work_id":"77f1a2cd-8667-4f4b-bfe4-c175b9cba19f","year":2001},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.211180Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:dc2a31f130b9a9eb29409dd887da5723cf82c8682b08967d0466fbe20e25dfc9","observation_id":"7c61837c-b165-4e14-a3b2-c75067ca04f5","resolution":{"observed_at":"2026-08-15T20:00:56.895224Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.876306Z","title":"L., Seeger, A., and Wright, J","venue":null,"work_id":"bb1728c1-8913-4b60-a951-eff38994db68","year":2008},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.215754Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:f7b1c32677a85d47567d2283ce97237e68daef37fa7b6939032780d02016c04d","observation_id":"93324c71-75dd-4a9d-b4d3-8aa101eae086","resolution":{"observed_at":"2026-08-15T20:00:56.881003Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.861143Z","title":"L., and Wang, G","venue":null,"work_id":"5c3d60c1-2668-4cd3-a962-90dccf1e1b83","year":2004},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.220272Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:1e2b790173dfd14881e8302a7ccb9280f14f6f13676a23f57ff77d5e0fb518b3","observation_id":"5c80b562-c21e-4e45-af25-8d186e41bd3f","resolution":{"observed_at":"2026-08-15T20:00:56.865818Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.845736Z","title":"Sobolev spaces adapted to the S chr\\\" o dinger operator with inverse-square potential","venue":null,"work_id":"df2b4bb7-bc2b-40bc-b3e1-6a164b76e1d2","year":2018},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.224529Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:477faf2cba690597e61609d5cd182c1e7ee0d4bd55da56e75b66f73ab8fee7d8","observation_id":"28fbce51-35c0-4889-a6e4-fe576995bc9b","resolution":{"observed_at":"2026-08-15T20:00:56.850998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.830811Z","title":"R., and Sem\\\" e nov, Y","venue":null,"work_id":"e0f7037e-4a22-42c2-8a7f-c6bdaf673561","year":2024},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.229064Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:02b54a33b124cfcb058bdb3fdf4a553f378a7ed23def014f13c4ca2763d8ddaa","observation_id":"c161135a-7e5d-4722-8997-3d021caac587","resolution":{"observed_at":"2026-08-15T20:00:56.835720Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.816100Z","title":null,"venue":null,"work_id":"01a16382-b10d-4213-ab94-67aec63f7904","year":2020},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.234895Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:f07c40372b0d2bcb5ce25b254d76908bd0b2f75843c62689d0e2b97ac305aaa6","observation_id":"fd04f28a-5757-4202-8f2c-9a78450e18bf","resolution":{"observed_at":"2026-08-15T20:00:56.820722Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.800817Z","title":null,"venue":null,"work_id":"82d3cbe4-bbd9-45b3-b01f-fcfa494eaeee","year":2023},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.239653Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:151f7123ffd13d38b5943132f1e02eabcc2f6d8aadd671e59bb86d9177119b45","observation_id":"5de6e38f-2be6-447e-b932-2531b6326c69","resolution":{"observed_at":"2026-08-15T20:00:56.805862Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.786203Z","title":"A., and Szczypkowski, K","venue":null,"work_id":"5bdc6206-34e1-408e-9382-26dd5aff2877","year":2021},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.244080Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:87fe6d9787ff4ad2a39b10584aad9d179d072c1d19ef9d8328e599578f1ad5d0","observation_id":"c7b21d03-92b7-4163-b68d-75fd6cdf7b70","resolution":{"observed_at":"2026-08-15T20:00:56.790743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.771351Z","title":"Pointwise ergodic theorems for non-conventional bilinear polynomial averages","venue":null,"work_id":"ecc856ea-579b-486b-9730-aaa41993a05d","year":2022},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.248574Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:f363f1af487b680d6ccb11ae2c1126259560a49da497db8bb75d28d52aafb92d","observation_id":"f307ccfa-bceb-4079-8449-ceef995ff823","resolution":{"observed_at":"2026-08-15T20:00:56.776269Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.756296Z","title":"Strong q -variation inequalities for analytic semigroups","venue":null,"work_id":"b390cd5e-115b-4815-8ca6-dc47767ae34c","year":2012},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.253069Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:e8259b6a7c81a94179f813f1fa8328dadeac36ed0105b3e7e5b596f00f2497a5","observation_id":"3dd24580-9220-44f8-9ee8-796f4d71af57","resolution":{"observed_at":"2026-08-15T20:00:56.761280Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.740378Z","title":"La variation d'ordre p des semi-martingales","venue":null,"work_id":"ac3a3c40-e1db-4fa9-b368-94048aac5db1","year":1976},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.257586Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:44f4216519435dcc653a7692d7d11fcf93ebb3daaae9d634937e933a0d92b62e","observation_id":"a73ce453-79ab-476d-b7ee-4298a27471ed","resolution":{"observed_at":"2026-08-15T20:00:56.745158Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.725071Z","title":"L., and Xu, Q","venue":null,"work_id":"35b5d912-d0bd-4b2b-aed2-4fe9aeea8475","year":2015},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.262124Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:ab790d7313fdb0b54a43054577f2cce0af9bf3c78e53d5071b4240a8cba8faed","observation_id":"7544bed6-7db3-471c-8a07-34e2a68bb3cb","resolution":{"observed_at":"2026-08-15T20:00:56.729952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.710109Z","title":"L., and Xu, Q","venue":null,"work_id":"34e575c1-640c-4c26-ae6b-25e0cdea8305","year":2017},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.266613Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:387e26131eedfde501cc005ccd2406e2b25f0e418f6da9e46e19feff8d0f9c25","observation_id":"0183ffa5-801b-4468-838a-cb031d5df806","resolution":{"observed_at":"2026-08-15T20:00:56.715104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.695615Z","title":"Variation and oscillation for singular integrals with odd kernel on L ipschitz graphs","venue":null,"work_id":"61eef869-b48a-49de-aa79-dd4b57396cf0","year":2012},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.271158Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:450dcbbdae7504294e8bec88c1ded0d8cc25125498cdd0f37882b10bd498ab33","observation_id":"50990721-8b2b-47c4-ad67-1c80654b4821","resolution":{"observed_at":"2026-08-15T20:00:56.700345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.680633Z","title":"Oscillation and jump inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes","venue":null,"work_id":"4761d38f-bd39-485b-a93b-455cb594c582","year":2024},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.275516Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:ed933046482b4dae6a347164384a5cc062efc0a47f7718e13c598a51579de471","observation_id":"d2e309ee-0910-4677-84b4-a4cf626f9dd8","resolution":{"observed_at":"2026-08-15T20:00:56.685616Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.665645Z","title":"On scales of S obolev spaces associated to generalized H ardy operators","venue":null,"work_id":"8ccc60ae-c441-430f-8d66-c8d8683f54aa","year":2021},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.279741Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:8e5bdc2085173004fd3b82964a512ef84fada364ad59dd7f95615bc02121c50a","observation_id":"2ffa52de-f99a-4d93-a1d9-a2d5213b0dd0","resolution":{"observed_at":"2026-08-15T20:00:56.670544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.650427Z","title":null,"venue":null,"work_id":"05289b87-4b1c-4363-a75a-e0d2cee85d16","year":2023},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.284114Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:968223e248adab1edbaced726880957bbd1846d28887a34c55c87e6c04316422","observation_id":"4161ddad-0f17-4cf5-8f94-372f7f482dd3","resolution":{"observed_at":"2026-08-15T20:00:56.655166Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.635211Z","title":"M., and Trojan, B","venue":null,"work_id":"d29bf905-a298-453f-a772-aea628f17648","year":2017},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.288495Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:d68fabfe88cc157d427d4c1ee5d7e9108e022e852fd47b4ec055f9639a37ad9a","observation_id":"7856fc4b-3ad5-4723-b8eb-2fc8a9653654","resolution":{"observed_at":"2026-08-15T20:00:56.640111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.619701Z","title":"M., and Zorin-Kranich, P","venue":null,"work_id":"5385d21d-f4e7-490a-a53c-f499ffbe208f","year":2020},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.292992Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:2b7ee477e82638c543cd61f690ecd32f4f8eb41a8279fee077d56518101630e1","observation_id":"d21394be-51f7-4519-8962-c9fea99e36d5","resolution":{"observed_at":"2026-08-15T20:00:56.624702Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.604328Z","title":"Variational estimates for averages and truncated singular integrals along the prime numbers","venue":null,"work_id":"87fd326a-4d4b-454c-a957-4701ba42e3d4","year":2017},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.297276Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:3de827c3525d7c50c3560f59b11015e7944ffe529cec696e55e130f28fa13fd6","observation_id":"df2a26c2-3d81-4b9c-b879-0fb3cda158c1","resolution":{"observed_at":"2026-08-15T20:00:56.609389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.588956Z","title":"Variation and oscillation operators associated to semigroup generated by S chr\\\" o dinger operator with fractional power","venue":null,"work_id":"65935351-c350-4bf2-b145-d0345db53517","year":2023},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.301607Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:43cdbd5b37747cf9375f7d20791d626a501c987ad8454661917551c9881023fb","observation_id":"4301fe95-453e-4338-a3cd-6d22cbd8c223","resolution":{"observed_at":"2026-08-15T20:00:56.594134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.572608Z","title":"A variation norm C arleson theorem","venue":null,"work_id":"b73ef95f-3112-4131-85c3-d0e6578325cc","year":2012},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.306586Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:f34da1eb64031be9430d48c5891e44333f07de7ffbff571954215c8fe66113d8","observation_id":"e2438293-be7b-4a72-8ed2-38087125d2e8","resolution":{"observed_at":"2026-08-15T20:00:56.577787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.557647Z","title":null,"venue":null,"work_id":"dd653b2b-87b7-4e2d-8cb0-021802024072","year":1988},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.311576Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:0e61ae7dfe34f4e60c5be718f5c030604c61df738f9f89a35bffe587d8e15141","observation_id":"1eb4ab18-7ee0-4327-bbfd-d5168abcd449","resolution":{"observed_at":"2026-08-15T20:00:56.562322Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.542338Z","title":"The p -variation of partial sum processes and the empirical process","venue":null,"work_id":"34321a56-5f56-475a-b5ef-c263fe0980a6","year":1998},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.316285Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:e66d3e45bf8dbdb4e691384eb9fb364e7a97646536cec95305c5963d4fee1858","observation_id":"1293b464-9b33-4a45-b42b-78425c980d49","resolution":{"observed_at":"2026-08-15T20:00:56.547070Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.526888Z","title":null,"venue":null,"work_id":"e3e4aa3c-cb9b-46f0-82a3-00e47355e225","year":1970},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.320739Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:7017069570f195ecd977dda36cf4e13b1d1c60cde1833a39d76d95777ce2fa33","observation_id":"a79e7898-ec4c-4881-b941-18edcadb282a","resolution":{"observed_at":"2026-08-15T20:00:56.531633Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T20:00:56.511692Z","title":"Functional analysis , sixth ed., vol","venue":null,"work_id":"365786ac-a8c1-4ac2-8275-54ccd2c52967","year":1980},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.325020Z"},"links":{"citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:bc7d6843ea4a6d371051160d5d081dd9f8b941db4416ccf5e07dd2a03aac1cc3","observation_id":"f60a454c-3a2c-4e56-a49e-6bf1d4a031d9","resolution":{"observed_at":"2026-08-15T20:00:56.516558Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.04541","last_updated":"2020-09-09T19:56:02Z","snapshot_observed_at":"2026-08-13T09:18:54.921689Z","submitted_at":"2020-09-09T19:56:02Z","title":"Variational truncations of singular integrals on spaces of homogeneous type","version":1},"cited_work":{"arxiv_id":"2009.04541","doi":null,"metadata_source":"pith","pith_arxiv_id":"2009.04541","snapshot_observed_at":"2026-08-15T20:00:56.367346Z","title":"Variational truncations of singular integrals on spaces of homogeneous type","venue":"math.CA","work_id":"a2490819-8405-4410-8818-cb1b78f1a896","year":2020},"citing_paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-15T20:00:56.329180Z"},"links":{"cited_paper":"/paper/2009.04541","citing_paper":"/paper/2506.14631"},"observation_digest":"sha256:12cd2a92324da8c1ad0cc6d4f985fa99049027827bd3a7311dd37c9c87b6e003","observation_id":"0fce37b6-5814-4b75-b11c-0bf7e65fd0f0","resolution":{"observed_at":"2026-08-15T20:00:56.374672Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.14631","last_updated":"2025-06-17T15:26:04Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-19T00:40:58.955949Z","submitted_at":"2025-06-17T15:26:04Z","title":"Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators"},"reference_resolution":{"displayed":49,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":8,"verified_exact":1,"verified_fuzzy":39},"total_outbound_references":49},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2506.14631."}