{"as_of":"2026-08-17T18:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:80708c22ca8d275b0c91d28b90f176f5b7a780724bda014a5d523bfc0ab904d6","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T17:59:27.711726Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+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/2507.20069/citation-record","integrity":"/paper/2507.20069/integrity","json":"/paper/2507.20069/citation-record.json","paper":"/paper/2507.20069"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:59:28.087360Z","title":null,"venue":null,"work_id":"32cf2397-0257-4662-9a54-fbafdf58d04b","year":1989},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.592067Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:eca910544173e819cd6dd7e0fa83dd1ff57383252c0f1264bfd5254056c1abac","observation_id":"17b45007-a68c-4d0f-a0fc-4a8c9e974f3b","resolution":{"observed_at":"2026-08-15T17:59:28.090755Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:28.076001Z","title":"Baernstein, A unified approach to symmetrization, Partial Differential equations of elliptic type, eds, Symposia matematica 35, Cambridge University Press 1995, 47-91","venue":null,"work_id":"e997be64-b138-41fa-9118-1297e770f2c8","year":1995},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.596277Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:6f1563071b07a7ccf199cfefefaac778029f396df48fdc94b7f91b2d87fe6551","observation_id":"9e3a6df4-5534-4c8c-a4c3-25683b540d74","resolution":{"observed_at":"2026-08-15T17:59:28.079870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:28.065092Z","title":null,"venue":null,"work_id":"cd9f484e-c8d1-4e18-8f53-94b816ad81dc","year":1988},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.600089Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:a0a86b8fc0db3018231512a420e4a96a1de2868830e918e49a605025612b8761","observation_id":"5e52e36f-399e-4bb6-923a-c8b506190843","resolution":{"observed_at":"2026-08-15T17:59:28.068864Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.10013","last_updated":"2025-01-24T15:05:55Z","snapshot_observed_at":"2026-08-17T14:02:31.854690Z","submitted_at":"2024-10-13T21:19:28Z","title":"A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N","version":2},"cited_work":{"arxiv_id":"2410.10013","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.10013","snapshot_observed_at":"2026-08-15T17:59:27.741705Z","title":"A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N","venue":"math.AP","work_id":"35509c9b-d588-45dc-bf88-719bd7dfb428","year":2024},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.603797Z"},"links":{"cited_paper":"/paper/2410.10013","citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:8b69bffe0406d5336518f8e8d251eeb69b388fcb4a69863da66dfb5c5c48735b","observation_id":"f431a184-2182-407a-b48b-05cb6e76cda4","resolution":{"observed_at":"2026-08-15T17:59:27.747782Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:28.054978Z","title":null,"venue":null,"work_id":"21900d6a-77ff-4661-aa07-0a408b305cd3","year":2023},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.608151Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:78d95b719f4ec664ac859dda6ac5af835cafafa50ae6b597877249f70a55178f","observation_id":"418b1a71-9014-4d7f-94e7-f968bcf557eb","resolution":{"observed_at":"2026-08-15T17:59:28.058330Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:28.044420Z","title":"Calanchi and B","venue":null,"work_id":"403ad025-44c4-47b7-9d2c-6fc4d391daee","year":2015},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.611884Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:839cd23f3715beeac2e010760fa0e4643643b8a3421d953d1caa4c71c2c13853","observation_id":"836f9fd8-3142-41a6-9803-53c4a44d6ff4","resolution":{"observed_at":"2026-08-15T17:59:28.048138Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:28.034603Z","title":"Calanchi and B","venue":null,"work_id":"7ceb41bd-e6d1-4c8b-bc7c-924499e0a122","year":2015},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.615657Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:d876f8e89782f673e33495f80fc15cda59c849d344b2eb2fe1643366cbb1e344","observation_id":"fcc9628a-96d5-4d1c-985a-d88efd808085","resolution":{"observed_at":"2026-08-15T17:59:28.038062Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:28.024449Z","title":"Caffarelli and L","venue":null,"work_id":"34713bf1-c245-49b9-bf9b-92beb97fb31e","year":2007},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.619303Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:d2150871aa71691106ef8732cd4a486f3282e031abfc89e4eb03c3956bac652a","observation_id":"f21dc359-2a49-42bb-83f7-dac702539756","resolution":{"observed_at":"2026-08-15T17:59:28.027992Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:28.014318Z","title":"Cingolani and T","venue":null,"work_id":"bf50f116-ccbf-44bb-92ae-de15ee1a23fc","year":2022},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.622766Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:3b598301d8c6feda01c086e68462ee44a3aa979e6763f5144ef92f4e9a05aabc","observation_id":"4dcd2b1a-d42f-4713-8baf-5a88a9afd08f","resolution":{"observed_at":"2026-08-15T17:59:28.017780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:28.003888Z","title":"Cingolani, T","venue":null,"work_id":"fb38e38d-0b21-4977-9aa2-aed5c33b5beb","year":2024},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.626253Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:5e98c067142b16fb31c7c5f3303347f0a18f8489be4ec1698d1ebfa90c692fa9","observation_id":"930694c0-db15-450c-9899-d5cc2201b084","resolution":{"observed_at":"2026-08-15T17:59:28.007611Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.992944Z","title":"Caglioti, P","venue":null,"work_id":"5ac25f7f-971f-41ca-bb1d-607b245c39d6","year":1995},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.629704Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:67be86061380f30be5ad79bb896f4141b64c65cd6fda5414b8dbb61077653b3b","observation_id":"38a2ce31-6172-446e-b4d4-a7434185edc3","resolution":{"observed_at":"2026-08-15T17:59:27.997167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.982750Z","title":null,"venue":null,"work_id":"ba12db02-092b-4793-992e-e5f2f029a194","year":2014},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.632923Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:5dfbbb92895425ee8c2a38004b5cf30e350c29af1108683c35ca5e9935de06c4","observation_id":"92dd663a-b71c-429a-884c-002585bb98b4","resolution":{"observed_at":"2026-08-15T17:59:27.986068Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.972751Z","title":null,"venue":null,"work_id":"152efb9a-6650-4541-a010-e7e6b9498b2d","year":2023},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.636575Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:72418c50ff1ef392b3374e81385b35d0f57156701d7f27ef3607d781ca327211","observation_id":"9cd86d84-2608-49df-8ca8-da0dd8c96da0","resolution":{"observed_at":"2026-08-15T17:59:27.976301Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.963289Z","title":null,"venue":null,"work_id":"7cdb8245-2cc1-4e89-a12e-a5e9a9688da6","year":2024},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.639855Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:4ab489edb049cf42757d83e1cc785741a2abdb655026fc2d49e13ba86fe17f97","observation_id":"88c90cbf-b1c6-4666-a903-a32bb9e0fbfe","resolution":{"observed_at":"2026-08-15T17:59:27.966840Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.954383Z","title":null,"venue":null,"work_id":"8f72867b-b237-4ee8-91ee-2bd1640f09b1","year":2025},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.644036Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:5d83de0011382ebc2a14cc9ec0b46aa5f565a8dfd8591ab20298966213118f9c","observation_id":"5d59e2c4-943a-4123-b389-c73d9db8e536","resolution":{"observed_at":"2026-08-15T17:59:27.957753Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.944744Z","title":"Dolbeault and B","venue":null,"work_id":"067d172f-fcce-4f15-bd96-51677e1217a2","year":2004},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.647452Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:cd8ad21b0adc8e848ee1ceaf137afc1ff549a6239d8cc750bfc640bf14a31446","observation_id":"35f519bc-f7ca-4e8e-a1d4-af6939eb7250","resolution":{"observed_at":"2026-08-15T17:59:27.948274Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.934196Z","title":"Di Nezza, G","venue":null,"work_id":"b0279197-3ce8-492a-9d8a-e91401981fa7","year":2012},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.650636Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:502494f811e58adea1ea177bcb360123b2744771caf3adb1ac2bcaf90f93b8a3","observation_id":"f6cbb4de-808c-44d4-b59a-f00073bb9ea3","resolution":{"observed_at":"2026-08-15T17:59:27.937736Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.923949Z","title":"Felmer, A","venue":null,"work_id":"f6603d67-ca2c-4db5-abf1-7fb6061cfd4f","year":2012},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.654016Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:d208dc725f73174e5976299986326f43ff739b42b0a4d6779729cd93fa7cb41a","observation_id":"d8a62a2c-7d69-4f41-87de-d08124f5c642","resolution":{"observed_at":"2026-08-15T17:59:27.927568Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.913738Z","title":null,"venue":null,"work_id":"0cffff62-aaf9-45d4-b574-fd76538b470f","year":1970},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.657435Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:2a4ee135bb665aa1486f69c2531e4093cb1fe8450e9f166b7d73d83ffb5dcf94","observation_id":"411eb984-4e65-4289-9055-737bf275f271","resolution":{"observed_at":"2026-08-15T17:59:27.917181Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.903094Z","title":"Hyder, Moser functions and fractional Moser-Trudinger type inequalities, Nonlinear Anal., 146 (2016) 185-210","venue":null,"work_id":"9008de58-4c8e-4276-b942-4085e6773f53","year":2016},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.660925Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:4dd40d2830c1a3bb5e63dd9c3298a93303e32795f09ab5841c572ca095fcd1c0","observation_id":"045f7d3a-2c3b-460f-8535-6010e7146ae3","resolution":{"observed_at":"2026-08-15T17:59:27.907029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.892264Z","title":null,"venue":null,"work_id":"a0df2ac9-291a-447c-9981-0b8b4b5a13c4","year":2016},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.664700Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:171439cfdc057ff13090c91b5c8fc158599cc21250edbf205cf1b028fe079589","observation_id":"2b16f320-8e29-410e-9fe6-03830d61edbf","resolution":{"observed_at":"2026-08-15T17:59:27.896368Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.882560Z","title":null,"venue":null,"work_id":"4f728f60-2b12-4e3a-abf7-11966fdf0ca2","year":2001},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.668265Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:9415b4bcc36441b4d50eb73cf1b8ecb5a13ed4b5b8f0651f226ca42e41951b98","observation_id":"b40d5d50-3acf-4aae-bf96-76d40e8232f6","resolution":{"observed_at":"2026-08-15T17:59:27.886371Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.873327Z","title":null,"venue":null,"work_id":"f62e00ad-2d27-4a2f-af56-49481dde4f6a","year":1985},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.671480Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:646732d81cfa753c30a18998edee61a1f0806039ebdaca4a1fb89555b7b0c21d","observation_id":"46d2e6c2-0dfb-4c25-a6aa-14b1c9090c77","resolution":{"observed_at":"2026-08-15T17:59:27.876549Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.863508Z","title":"Moser, A sharp form of an inequality by N","venue":null,"work_id":"2e797848-ddfb-4035-990c-1526857dc6a7","year":1970},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.674907Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:87a762de4e0698f9356f41edd8fa0770ad5da241dad7bb9defd60a4c14a32ee8","observation_id":"b940f773-b888-4383-b62b-02528cd5e329","resolution":{"observed_at":"2026-08-15T17:59:27.867090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.852730Z","title":null,"venue":null,"work_id":"5ad8a12f-2118-4b7d-913b-ca68bd7ae4ac","year":2019},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.679050Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:0358e521f7b9c98687a30c109267aeab4e5c76e0bcb35615e6492423a8fd95cf","observation_id":"f6484990-c13f-4b92-a679-d143882872d6","resolution":{"observed_at":"2026-08-15T17:59:27.856438Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.841922Z","title":"Polya and G","venue":null,"work_id":"fc5c5e90-59a6-4af2-9d11-a9f48c0d738d","year":1945},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.682635Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:78dcd4c489ba2b2b6cb1cc44e33b8b1ca519de41d5fa4efdeb5d945583eeb9bb","observation_id":"c50af1d4-1a55-40ae-ab95-8c386d1085e9","resolution":{"observed_at":"2026-08-15T17:59:27.845659Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.831249Z","title":"Polya and G","venue":null,"work_id":"855899da-e582-4881-8165-bca034353cd2","year":1945},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.686274Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:587f6f55d41d2977fd7e307906ae2bf80bcc996b1be51ccd613e99e70d22935b","observation_id":"3137a801-f341-4cce-a2d5-14a50fe268ef","resolution":{"observed_at":"2026-08-15T17:59:27.834866Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.821153Z","title":null,"venue":null,"work_id":"2796d4a0-a3ef-40af-ab1c-ecbbd0bd5174","year":1965},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.689728Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:e9ed62707cf6ba3aa05943598296a2101b9c32d31bafc336d467a0ca0c6e9c9a","observation_id":"00729228-e89a-45f4-9e77-8fdeb1c4a180","resolution":{"observed_at":"2026-08-15T17:59:27.824540Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.810817Z","title":"Roy, Extremal function for Moser-Trudinger type inequality with logarithmic weight, Nonlinear Anal., 135 (2016), 194-204","venue":null,"work_id":"e189fe38-8bdd-4191-8f5b-5196bff3f133","year":2016},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.693412Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:542a7a3a91e52d283a2fc2f61a98eb22ca20b0f97d69e319e18fd71140c71479","observation_id":"4e752caa-1344-47fa-8dad-a31713ff8d52","resolution":{"observed_at":"2026-08-15T17:59:27.814581Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.799088Z","title":"Roy, On attainability of Moser-Trudinger inequality with logarithmic weights in higher dimensions, Discrete Contin","venue":null,"work_id":"0c232cfb-8941-4736-9091-91404b3efb7b","year":2019},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.697968Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:fd5ff8946c984ed765f63ec25cd01f83dc4dc925c26397ef0a85ff9e3bc21791","observation_id":"c5fe1237-da3f-4589-9074-8d3f5035f2e1","resolution":{"observed_at":"2026-08-15T17:59:27.803622Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.788465Z","title":null,"venue":null,"work_id":"cb33370d-e456-441a-810a-6a9961c87179","year":1967},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.701484Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:32a68de71e4ee4e458dce089b5f03a10ecfb367500fcf375de76721075441503","observation_id":"f394a5d3-edac-489f-8359-e7a0f52cd987","resolution":{"observed_at":"2026-08-15T17:59:27.792311Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.777409Z","title":"Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch","venue":null,"work_id":"a3923444-1968-40ac-a241-68ce7849189b","year":1992},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.704960Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:9f920c289f1567115ea5d75994c4643cd9f061c2aa68d1b4a124e2a57c649a24","observation_id":"21ea71af-eb67-449c-8538-435a55988d55","resolution":{"observed_at":"2026-08-15T17:59:27.781382Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.766529Z","title":null,"venue":null,"work_id":"cf940a2d-51e7-427a-8a11-c08b9252fe4e","year":2025},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.708358Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:bff82c6796ca80043f6b480689b9f62fd9028ceca2d0404166a6d8238b1293e9","observation_id":"17a8624d-5590-4cf9-99c5-b76b7f9ea4ed","resolution":{"observed_at":"2026-08-15T17:59:27.770129Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-15T17:59:27.755767Z","title":null,"venue":null,"work_id":"dd227ca2-e01f-4340-ad27-af8d19cf4da4","year":1961},"citing_paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T17:59:27.711726Z"},"links":{"citing_paper":"/paper/2507.20069"},"observation_digest":"sha256:c8bb153a60bd23d714704471a346a574001facbd2bfaf85cb9c7583e0a9d4efc","observation_id":"19ae0880-ee45-4cff-ad07-fd860208b767","resolution":{"observed_at":"2026-08-15T17:59:27.759468Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.20069","last_updated":"2025-07-26T21:51:32Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-15T17:48:09.781592Z","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":1,"verified_fuzzy":17},"total_outbound_references":34},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2507.20069."}