{"as_of":"2026-08-08T09:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fdb4df09a749148e10d84c5f6bcd1f534e94c01c4022dca1350486b4a141cff6","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:57:38.350613Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"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/2506.07176/citation-record","integrity":"/paper/2506.07176/integrity","json":"/paper/2506.07176/citation-record.json","paper":"/paper/2506.07176"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:57:41.498145Z","title":"ESAIM: Control, Optimisation and Calculus of Variations 13(4), 735–749 (2007)","venue":null,"work_id":"bef5f72a-f01c-4d28-b3d7-bfa64eca0b78","year":2007},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:34.816770Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:5e47aecb6c16b7c1599db0bd21af556fa45a1e001a000a080ca8d97aa9954886","observation_id":"c22d332d-fa05-46b5-90ed-558625a87fe1","resolution":{"observed_at":"2026-08-07T05:57:41.502810Z","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":"2026-08-07T05:57:41.486661Z","title":"Kluwer Academic Pub- lishers, Dordrecht, Boston, London (1989)","venue":null,"work_id":"a8fdd575-2e43-4191-a28c-ce92fae21166","year":1989},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:34.883714Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:bd55bd106bdf8f5f381390bb2989f50b8f50e41a35a4cceef14b7cf2d09a85d2","observation_id":"5a92be85-b7d6-4ecf-ab9e-581c28d9165f","resolution":{"observed_at":"2026-08-07T05:57:41.490360Z","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":"2026-08-07T05:57:41.476783Z","title":null,"venue":null,"work_id":"8bdd64a7-de42-412d-9bd5-2bc5d1b2d830","year":1978},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:34.980070Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:583508446df391d18ce341fa25b1d449a58483a885dd425dda9348579e8e350b","observation_id":"d5b4b20d-91a8-47b5-a6a1-3540cf0ce4bd","resolution":{"observed_at":"2026-08-07T05:57:41.480135Z","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":"2026-08-07T05:57:41.466655Z","title":"Sh., Suslina, T","venue":null,"work_id":"f72d9bfe-ee84-4ead-8414-1b2b0c0a1823","year":2004},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:35.086600Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:fcc324b14a133fd69c4188dbde1d2f7cf9e926956efdad14ea376fd03cc64de7","observation_id":"74efaa10-7803-46d8-bf57-48e14dd4a203","resolution":{"observed_at":"2026-08-07T05:57:41.469979Z","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":"2026-08-07T05:57:41.396469Z","title":"Sh., Suslina T","venue":null,"work_id":"757e4970-1451-4c2e-845b-54f3270e6d41","year":2006},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:35.328276Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:14d97d16fb1316def7528b85ec29f000331f4748da4d8869563a171cb00e3e0c","observation_id":"d3641a05-1862-47e2-8be2-0f30d06787c5","resolution":{"observed_at":"2026-08-07T05:57:41.407708Z","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":"2026-08-07T05:57:41.383875Z","title":"Sh., Suslina, T","venue":null,"work_id":"b0dcfc1d-79e5-4e47-90b7-352ff61045ef","year":2007},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:35.432346Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:bb4dd37a6d6bc12c3146179dcd631485e31821cfe59b5305682baeacdbb5932a","observation_id":"09b51eec-6ef0-441d-aca4-ca6c2740e390","resolution":{"observed_at":"2026-08-07T05:57:41.386818Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:57:35.517157Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:35.517157Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:5adce729d59e9ae8d3b124af9ec483a867037decbc2d717cfa4b2f6e59580202","observation_id":"096a6a61-ec43-4557-baf6-7a0cef1e7706","resolution":{"observed_at":"2026-08-07T05:57:35.517157Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.08120","last_updated":"2024-09-12T15:10:09Z","snapshot_observed_at":"2026-07-06T19:14:21.092302Z","submitted_at":"2024-09-12T15:10:09Z","title":"Quantitative periodic homogenization for symmetric non-local stable-like operators","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.08120","snapshot_observed_at":"2026-08-07T05:57:35.611948Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:35.611948Z"},"links":{"cited_paper":"/paper/2409.08120","citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:099c7f2f757afab6176818eba6aef0f17bccc9c8add6182eeb975705addaf49c","observation_id":"8fafbfbb-fc3f-40c2-b303-33261a7c90fc","resolution":{"observed_at":"2026-08-07T05:57:35.611948Z","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":"2026-08-07T05:57:41.374961Z","title":null,"venue":null,"work_id":"10673799-798c-4ac7-85cc-679f525d6d4e","year":2021},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:35.692576Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:b1ca10bf8802ef90e8a6dc86b121e5ccabfae0edf2c9861ae72d7e199ab36e7b","observation_id":"80463a67-ecee-48a3-bd99-ba1d640932d5","resolution":{"observed_at":"2026-08-07T05:57:41.377712Z","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":"2026-08-07T05:57:41.365614Z","title":"Multi scale problems and asymptotic analysis","venue":null,"work_id":"48fcb82c-19eb-4ac6-b507-863b6cb0d39e","year":2005},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:35.846137Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:8348326a5429be9f8eea2067143292a7c08b755281810b817816d70fd58dfd5e","observation_id":"11c65254-4645-4dab-97ef-5e952bcca8ca","resolution":{"observed_at":"2026-08-07T05:57:41.368575Z","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":"2026-08-07T05:57:41.355403Z","title":null,"venue":null,"work_id":"37711ea5-ec1d-420e-a3f8-45a1bf87e97d","year":1997},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:36.007651Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:516ffdb96647857b82427891dbef510e6e3f96caeab179df4098bfa5cc81c63c","observation_id":"6cc9bd51-6d9a-46be-a814-e3031fcb4de6","resolution":{"observed_at":"2026-08-07T05:57:41.358716Z","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":"2026-08-07T05:57:41.342232Z","title":"A.: Classes of Linear Operators","venue":null,"work_id":"532e94f8-fb12-46d3-bd85-8d62a5364178","year":1990},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:36.167501Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:fcf6235145c1e1bd85439312c703e998ef25f1371d1445ba4f304a169a2ce3ce","observation_id":"5bf70815-edc8-43fe-8541-fb4ceadedd86","resolution":{"observed_at":"2026-08-07T05:57:41.346307Z","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":"2026-08-07T05:57:41.324040Z","title":null,"venue":null,"work_id":"b0d1d4d1-0fee-403e-80e8-b1b4a2d8117d","year":2019},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:36.320770Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:8a11416cb263cb733b2576bcdc1048dd46e61a42756ce6acc76b0b9a242607e2","observation_id":"edc0af8c-c393-4e54-87cc-8ca57980ade0","resolution":{"observed_at":"2026-08-07T05:57:41.327690Z","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":"2026-08-07T05:57:41.313968Z","title":null,"venue":null,"work_id":"85d9b884-b1b3-4ffa-8c2d-a93338be40b5","year":1979},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:36.452751Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:51e846d0f92a56e765ce77cee48c4126a1e12fcdae530d722e2683713076f0a8","observation_id":"6c2277d0-2af4-48dd-9f5a-2498f49c2078","resolution":{"observed_at":"2026-08-07T05:57:41.317059Z","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":"2026-08-07T05:57:41.303626Z","title":null,"venue":null,"work_id":"1c191870-df1a-462b-bc7a-e4991fda3c1b","year":1979},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:36.646637Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:cbb5c435b83c95aa98e8d1b8f1f0a0745a4e3079a90d38705f50102e269cac3e","observation_id":"60468401-fec8-45c2-ad80-afabee2b5ec4","resolution":{"observed_at":"2026-08-07T05:57:41.306713Z","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":"2026-08-07T05:57:41.293191Z","title":"Springer-Verlag, Berlin (1980)","venue":null,"work_id":"6263ff94-fec7-4917-b7b5-db6d0ec9f1a6","year":1980},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:36.792369Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:aa88e8c6472ccf4886cb9f41bb7a427bd78cdee8632120e336112cc2dd0a30f1","observation_id":"9f7c9c7d-f776-4ed1-aacb-c41ea94c94c0","resolution":{"observed_at":"2026-08-07T05:57:41.296885Z","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":"2026-08-07T05:57:41.278235Z","title":"Studies in mathematics and its applications","venue":null,"work_id":"9e9e3511-7e61-4d8c-bbaa-926450d85454","year":1992},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:36.934074Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:0730aa3acef8f8e22764ac0d90ee42340466e2fcb253e83612d2c636286dc402","observation_id":"e9201350-6341-42f1-b1b0-60f809294a4d","resolution":{"observed_at":"2026-08-07T05:57:41.283119Z","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":"2026-08-07T05:57:41.210722Z","title":"V.: On operator estimates in homogenization theory","venue":null,"work_id":"808c0001-05d6-4214-b470-5c6e3ffad987","year":2005},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.068509Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:2ed1a22960593724904e4c926407ad7bcee8ce91050c624f036a00127d277e2b","observation_id":"9a179009-78ef-4afc-9830-3f8288aadf79","resolution":{"observed_at":"2026-08-07T05:57:41.267847Z","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":"2026-08-07T05:57:40.995500Z","title":"V., Kozlov, S","venue":null,"work_id":"f18f97f2-14cd-404c-8f1b-3a87a8ca3122","year":1994},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.237252Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:b8fb2fe7bbb89f50827b9f40b8421e2c9d303929e77561e158a7155c80aaace0","observation_id":"295d7752-266d-4dbc-84ce-00894c9d6782","resolution":{"observed_at":"2026-08-07T05:57:41.118021Z","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":"2026-08-07T05:57:40.681731Z","title":"V., Pastukhova, S","venue":null,"work_id":"a55d2106-d164-4a5d-b657-7f8c481672c5","year":2005},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.346209Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:56134d7b16a402485bcfdedd12f0576720dde16fe486ef6d5fcf2b40823e68d8","observation_id":"39a2d1a9-b2da-4acc-b245-5c41633d3bd6","resolution":{"observed_at":"2026-08-07T05:57:40.870650Z","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":"2026-08-07T05:57:40.401165Z","title":"V., Pastukhova, S","venue":null,"work_id":"bc8a2625-393d-4be7-a109-6c031e6b8c3a","year":2016},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.455511Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:cde97e28dc6470f077335f68cb57796ef2f96410a2f001784267fea850417537","observation_id":"4f82ad48-f532-4069-a4de-ba11a5607ab0","resolution":{"observed_at":"2026-08-07T05:57:40.540282Z","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":"2026-08-07T05:57:40.101419Z","title":null,"venue":null,"work_id":"2d9f6cfe-e51e-48c0-acf5-1252c6704c35","year":2023},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.559765Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:7f90b271f4331ad5284f769d8c1197a4599c1e30240d14e82bac0492cf9f20c8","observation_id":"d96762f1-e825-4b01-9312-95fcb71e8b1e","resolution":{"observed_at":"2026-08-07T05:57:40.221448Z","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":"10.1134/s106192084010114","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:57:38.667527Z","title":null,"venue":null,"work_id":"01d22f44-f3ec-4e2e-9777-5eb197c954d7","year":2024},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.642380Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:2aef6de1296989132e3df3012671e308d9f6307b4bfec53aa822987c5487ab9e","observation_id":"024ffcfa-6c8c-44e6-843b-f371564442c0","resolution":{"observed_at":"2026-08-07T05:57:38.774334Z","resolver_source":"doi","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":{"arxiv_id":"2311.16574","last_updated":"2023-11-28T07:32:02Z","snapshot_observed_at":"2026-07-06T16:53:39.713988Z","submitted_at":"2023-11-28T07:32:02Z","title":"Homogenization of nonlocal convolution type operators: Approximation for the resolvent with corrector","version":1},"cited_work":{"arxiv_id":"2311.16574","doi":null,"metadata_source":"pith","pith_arxiv_id":"2311.16574","snapshot_observed_at":"2026-08-07T05:57:38.904935Z","title":"Homogenization of nonlocal convolution type operators: Approximation for the resolvent with corrector","venue":"math.AP","work_id":"c64cd717-0fe4-4b46-9dc3-025ccdafc2c1","year":2023},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.772983Z"},"links":{"cited_paper":"/paper/2311.16574","citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:491e94c3ff521343296cc86bbb6de9f9c231d42736b499f98c2c63101c9d000c","observation_id":"63feb99f-a0d4-4432-b9f5-4b878aaf18ef","resolution":{"observed_at":"2026-08-07T05:57:38.984884Z","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":{"arxiv_id":"2412.20408","last_updated":"2024-12-29T09:16:58Z","snapshot_observed_at":"2026-07-06T20:14:17.514140Z","submitted_at":"2024-12-29T09:16:58Z","title":"Operator estimates in homogenization of L\\'evy-type operators with periodic coefficients","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.20408","snapshot_observed_at":"2026-08-07T05:57:37.883359Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.883359Z"},"links":{"cited_paper":"/paper/2412.20408","citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:4d48e4b9cb1dafc7fb7b85c51c3f1e72c6ab9aab16580d02dc3ebea96e9986e8","observation_id":"76a196cb-eda3-4e00-b75e-0b1c0b805761","resolution":{"observed_at":"2026-08-07T05:57:37.883359Z","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":"2026-08-07T05:57:39.710104Z","title":null,"venue":null,"work_id":"410cb780-2c2e-4a1b-b06f-6ca092c9e290","year":2017},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:37.957544Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:8a199594a757d87232f6cc46c23e6ae5d9a2c02b3813d3cf21411fad66f02ed1","observation_id":"9d3f7da6-ed91-420f-8b33-94b01b15be98","resolution":{"observed_at":"2026-08-07T05:57:39.930766Z","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":"2026-08-07T05:57:39.420199Z","title":"Asymptotic Anal","venue":null,"work_id":"105762da-6af5-4504-9af1-6901489ff8e7","year":2019},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:38.066448Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:fd111b2201ecfd102b282363c74af2c722dd3533e7aa64e3c5afdf57ab2f446b","observation_id":"686f4c88-1e2d-4d47-95c5-3b7a476c5eec","resolution":{"observed_at":"2026-08-07T05:57:39.587095Z","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":"10.61102/1024-2953-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:57:38.472473Z","title":"Markov Processes and Related Fields 29, 173–188 (2023)","venue":null,"work_id":"306c039e-a35a-42d3-81c6-d6c8978501e7","year":2023},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:38.141785Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:eebe52e5e25bfe77cfd9c892c4c0cc727080550c397cd3fe1929321456ef086e","observation_id":"5a16f00f-49b7-4476-8ce9-cc1f3cf621fb","resolution":{"observed_at":"2026-08-07T05:57:38.567768Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"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":"2026-08-07T05:57:39.181802Z","title":"M.: Geometric and arithmetic methods in the spectral theory of multidimensional periodic oper- ators","venue":null,"work_id":"c51d2075-1548-4d10-9b6d-103c01c8322c","year":1987},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:38.237903Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:ed867cd53d9ab7025edf470d8e2fc4702fa8943900870337d9a5886f65c078e6","observation_id":"e9f7bc0c-4b4a-43f5-acbe-1ad263f9f429","resolution":{"observed_at":"2026-08-07T05:57:39.263223Z","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":"2026-08-07T05:57:39.075590Z","title":"A.: Operator-theoretic approach to the homogenization of Schr¨ odinger-type equations with periodic coefficients","venue":null,"work_id":"7a3ed3dc-3eec-4d5c-82ea-3730f06e65de","year":2023},"citing_paper":{"arxiv_id":"2506.07176","last_updated":"2025-06-08T14:50:52Z","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T05:57:38.350613Z"},"links":{"citing_paper":"/paper/2506.07176"},"observation_digest":"sha256:3b15a44c3d4518fbcb20dba3ac8fb11d7956772d4c2d159cde9a4971ab2d2e27","observation_id":"49a1d9e7-95fe-4a98-9604-6be5ba2622e1","resolution":{"observed_at":"2026-08-07T05:57:39.136513Z","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":"2506.07176","last_updated":"2025-06-08T14:50:52Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-08-08T03:10:25.530411Z","submitted_at":"2025-06-08T14:50:52Z","title":"Homogenization of non-symmetric convolution type operators"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":2,"verified_fuzzy":16},"total_outbound_references":30},"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 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2506.07176."}