{"as_of":"2026-08-15T10:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:15095982e16b02d79ccceb4e765d4669d04c3b2137b308d5b1ee767ecd8eb7a1","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T14:09:11.722250Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.19866/citation-record","integrity":"/paper/2507.19866/integrity","json":"/paper/2507.19866/citation-record.json","paper":"/paper/2507.19866"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:12.045711Z","title":"A HN AND M","venue":null,"work_id":"8d6e8a2b-2519-4736-b13b-12abda0671a9","year":2023},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.127339Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:ecb1290da42b66dcafb8d82088915995c56b6af1c2122425f30c95e17b90b711","observation_id":"a98e01a7-8f75-4ee1-8fd6-3d19b7bf8e03","resolution":{"observed_at":"2026-08-06T14:09:12.048114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:12.038127Z","title":"B ELLOMO , A","venue":null,"work_id":"be89b5c6-0272-40b3-9efa-d073284c53dc","year":2010},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.178591Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:57fde6af8d899c399499cc4836a50fb1d140f9b53a7f6c86d332df7ce1930e16","observation_id":"dd6a3856-a016-425b-a94f-891f9e4a4e07","resolution":{"observed_at":"2026-08-06T14:09:12.040556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:12.030011Z","title":"B ELLOMO AND M","venue":null,"work_id":"8150a7ae-1d15-43d3-bdb7-80c39f32862f","year":2017},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.262019Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:87c72a8956e331c3a7a01e69832ba12423a351422ffa0eb59c6c2896d5e00efd","observation_id":"16adfb8c-a557-4b4d-acc2-c0821ae40f24","resolution":{"observed_at":"2026-08-06T14:09:12.032719Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:12.021872Z","title":null,"venue":null,"work_id":"c08c43b5-d3ac-4ad3-abaa-ed0c481f1501","year":2017},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.343198Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:a838e32c99402616b3e8e41b646cd82cfa7f675136219ef539c78d9adaccbdc6","observation_id":"ecd39edb-b1b5-4f9e-a9de-5f33868b9516","resolution":{"observed_at":"2026-08-06T14:09:12.024949Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:12.013018Z","title":"BILER , G","venue":null,"work_id":"68736d62-4780-41f4-b07a-a14133ecff89","year":2006},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.451806Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:89a8644022afe2b072b75b5ced93c46f4b0a82c3ded26c4e25c5a71cb44ee8e1","observation_id":"09e96eec-95a4-4dfb-9dbc-d321b24f3f7f","resolution":{"observed_at":"2026-08-06T14:09:12.016351Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:12.005228Z","title":"F UHRMANN , J","venue":null,"work_id":"f8f8005f-35e1-4a9d-a4e9-5fe1f89f1c0c","year":2022},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.540504Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:c9dc4994bf8ca418cf209687ce87864ddfc68d5c5162fc4013e87b87f0799f9d","observation_id":"62749508-7830-45a3-824a-34b55e0d4246","resolution":{"observed_at":"2026-08-06T14:09:12.007693Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.997059Z","title":"JÄGER AND S","venue":null,"work_id":"8037b59a-d4bd-4142-9e64-51d0218a198c","year":1992},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.630195Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:22d9e1fb5bd67c6920b2522202e9ec9f683d7daa4415b8f987b8c4fb9e11307f","observation_id":"8546687e-d16d-4ee4-9f72-aadc5c71d4d0","resolution":{"observed_at":"2026-08-06T14:09:11.999745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.988391Z","title":null,"venue":null,"work_id":"ebc904f0-13b3-4e2a-b9ad-513ecd349b08","year":2009},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.711876Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:aed0df8e8a1e56e0554cad1a4a3e37caaa202a311c4dd07023abd72f01bf4de7","observation_id":"664c0703-d222-4a62-8518-3091434255e6","resolution":{"observed_at":"2026-08-06T14:09:11.991246Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.979938Z","title":null,"venue":null,"work_id":"3664c665-4d9c-4dd1-a089-64f1c44cc7f4","year":1970},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.823843Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:060a4b61cdd8f3f83aaf58a84a0551bca140b047d620afe0c955a4c9823c5cb4","observation_id":"62c69068-d7f7-4009-9415-c03f20b4e2c4","resolution":{"observed_at":"2026-08-06T14:09:11.982885Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.971835Z","title":"K OHATSU , Finite-time blow-up of weak solutions to a chemotaxis system with gradient dependent chemotactic sensitivity, J","venue":null,"work_id":"0e0d72b8-fd28-4d01-be48-aef51cff38dc","year":2024},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:09.945487Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:4dc1fc85b08f786bb8541414f78f4857089f155df223a8f64e7743acf051d73c","observation_id":"e8b0ab33-7607-4aff-82bb-c6da7d9feb00","resolution":{"observed_at":"2026-08-06T14:09:11.974601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.963945Z","title":"K OHATSU AND T","venue":null,"work_id":"b99624c6-db03-4070-9336-880c4531e016","year":2025},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.026779Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:82f9780b53aa27245fac3d3633b75ad17ee26e051e8b7bbb6ee678d6d66612d1","observation_id":"8af68f78-9fd6-4af5-9497-4441b10458b4","resolution":{"observed_at":"2026-08-06T14:09:11.966576Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.955844Z","title":"K OHATSU AND T","venue":null,"work_id":"bc5d419f-6604-4b78-857c-09ebf9975e4a","year":2023},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.112842Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:24ee1268cd8f4c21a70ccce8db06dab9309789f3110b5c9738008da51f1d933c","observation_id":"89210ffe-c65f-4266-9878-2b78d3ab512c","resolution":{"observed_at":"2026-08-06T14:09:11.958451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.947518Z","title":"LI AND W","venue":null,"work_id":"4d22d38f-faed-443a-b2a6-379ed03a6ffa","year":2023},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.206896Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:e98e8a40f155b6fb44892e7f4aeb6caa07f1f4e4a2e0ec8c60698ceecaabc3e4","observation_id":"f03708a0-4675-416b-835e-712f64002566","resolution":{"observed_at":"2026-08-06T14:09:11.950298Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.939638Z","title":null,"venue":null,"work_id":"67929315-9fc9-4fe8-a34b-d6447c05c2ef","year":1987},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.297826Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:ef15d7353dee6d0182e6266dd6f272172a11395e64e44183f4dcdbc24fa38bd5","observation_id":"8471a01d-37e7-4f37-932a-6bb7dfd666d5","resolution":{"observed_at":"2026-08-06T14:09:11.942230Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.931219Z","title":"M AO AND Y","venue":null,"work_id":"624326e3-cf60-4fad-834f-3a4218c8e9e6","year":2024},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.366611Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:d7c127f6fd1253221afa1a3442044a66622cf7afab0c23186ab0fdde4b746ae1","observation_id":"db0a57c2-6012-408b-9ed0-d08908458841","resolution":{"observed_at":"2026-08-06T14:09:11.934380Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.06315","last_updated":"2026-05-06T06:07:25Z","snapshot_observed_at":"2026-07-06T18:12:30.614996Z","submitted_at":"2024-05-10T08:37:20Z","title":"A note on the $8\\pi$ problem of J\\\"ager-Luckhaus system","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.06315","snapshot_observed_at":"2026-08-06T14:09:10.438969Z","title":"arxiv:2405.06315, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.438969Z"},"links":{"cited_paper":"/paper/2405.06315","citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:34ad0ac885ef374f4398278e401a5c5e50087e7aa24590824298c9ef483a2b2b","observation_id":"5fca0d17-fdec-4a63-84c7-6a663b81933c","resolution":{"observed_at":"2026-08-06T14:09:10.438969Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.14278","last_updated":"2025-05-20T12:29:26Z","snapshot_observed_at":"2026-08-07T15:35:06.810426Z","submitted_at":"2025-05-20T12:29:26Z","title":"Critical mass for finite-time chemotactic collapse in the critical dimension via comparison","version":1},"cited_work":{"arxiv_id":"2505.14278","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.14278","snapshot_observed_at":"2026-08-06T14:09:11.748213Z","title":"Critical mass for finite-time chemotactic collapse in the critical dimension via comparison","venue":"math.AP","work_id":"af513f5e-ed74-4108-8e83-de3330fc22b1","year":2025},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.442564Z"},"links":{"cited_paper":"/paper/2505.14278","citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:37a5b9871cd56c853290fdfe1fc39c8347c7e333026ace8cf5d9a86872b3951b","observation_id":"6a9e5ffb-2fc5-446e-ba7f-a2f6546b1ef1","resolution":{"observed_at":"2026-08-06T14:09:11.753840Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.922907Z","title":"M ARRAS , S","venue":null,"work_id":"1509f519-e501-4a7a-aad5-33712777b096","year":2022},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.447874Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:728dc4cd8661d5d96539a121aaa3ebd489b1ddf1f18d8e5c5afc9ee8189f62f3","observation_id":"02ef4bb6-1350-4a1f-b0b2-9482e8983d3f","resolution":{"observed_at":"2026-08-06T14:09:11.925398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.915229Z","title":"NAGAI , Blow-up of radially symmetric solutions to a chemotaxis system , Adv","venue":null,"work_id":"5f318576-dad1-4c69-b9eb-b81341188d0d","year":1995},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.555421Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:2581ac38d5e0e7cbebcc88c1b108b691020d29b4d2dc93101c5864549c96c714","observation_id":"5c4e019b-9b4a-4d14-beda-f6ebbbb9bdf2","resolution":{"observed_at":"2026-08-06T14:09:11.917904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.906240Z","title":"NAGAI , T","venue":null,"work_id":"ca80f7a6-cbfa-43da-8b10-72db23683c1a","year":2000},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.697530Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:e1d66d48917aef5b0a7144609a2403e20e8c08c6a92d098a54673f84b063453e","observation_id":"b24063d9-1201-463d-a3a5-e9f05eb9a413","resolution":{"observed_at":"2026-08-06T14:09:11.909161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.897753Z","title":"N EGREANU AND J","venue":null,"work_id":"58556d6b-0b10-41bb-904f-72e8229e0870","year":2018},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.814656Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:fea8904d589f9f3f500ba0d1dcd7ffb72606eb84ef5335bb9e88b656d5e05d50","observation_id":"6c46b4b0-a1db-4404-a242-f50e9f3f973b","resolution":{"observed_at":"2026-08-06T14:09:11.900677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.890096Z","title":"P ERTHAME , N","venue":null,"work_id":"4cb55b4a-9eea-40cb-bb61-fbfda384e650","year":2020},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:10.959063Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:0ae67057c816b1c2f95b72d1875ffe53157a8cbe5e87abe893efe9b6b037085f","observation_id":"1f2a168f-10e9-489a-8b40-c8f78a4230fb","resolution":{"observed_at":"2026-08-06T14:09:11.892687Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.881936Z","title":null,"venue":null,"work_id":"d9090e8b-ed32-4067-963b-a1d87f508cf8","year":1993},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.041541Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:6c6fd5d24d952b424151a8901b2c3cbc4fd700913dc8954f6df6d95182f82f3c","observation_id":"aa0e1f7e-b999-40f1-b320-abd7e310cb80","resolution":{"observed_at":"2026-08-06T14:09:11.884691Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.873816Z","title":"SUZUKI , Exclusion of boundary blowup for 2D chemotaxis system provided with Dirichlet boundary condition for the Poisson part, J","venue":null,"work_id":"c8c04265-3a36-4255-82fe-e249dca0fee3","year":2013},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.114128Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:bdedc51216c6aa2de94a544ddc3fc301a9bc9df321675036e89addc7e5d66f33","observation_id":"4882504e-f9f9-4d5e-9388-7fa3d1c7bc32","resolution":{"observed_at":"2026-08-06T14:09:11.877117Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.865797Z","title":"TAO AND M","venue":null,"work_id":"f46a7990-c4a4-43be-ab54-555acf1c2ae6","year":2012},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.251970Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:047d1aaea8f061b544868862b9354352b1b18f4bda8b9fd2e580c2995b1025aa","observation_id":"e3448383-2c7e-4180-899d-ae89860b169a","resolution":{"observed_at":"2026-08-06T14:09:11.868563Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.857262Z","title":null,"venue":null,"work_id":"90f4b7f5-2f94-431e-b75d-6c91dfa5ed57","year":2017},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.401469Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:0db41e0f39315ec49fae1343d7897161d9ad3545fffc687703140ae58d3acff6","observation_id":"d5a01192-c3e6-40f5-ac7e-d37dd43c09b6","resolution":{"observed_at":"2026-08-06T14:09:11.859982Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.848543Z","title":"Differential Equations, 423 (2025), pp","venue":null,"work_id":"bc702398-822c-46fa-84d7-75d9abbc74a9","year":2025},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.595114Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:5e2d22cf786c28d9db4206129ae1e7cd89f7dc27ba868908d35a16862d85511a","observation_id":"fa2d2605-fa4c-4367-a990-6f1ab6f9cb8c","resolution":{"observed_at":"2026-08-06T14:09:11.851533Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.839402Z","title":null,"venue":null,"work_id":"1c10a554-5049-4c36-a283-c9fa2201da72","year":2022},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.653330Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:d41985fe7792ecd1a0c9e8b18f37091247e63bb12db604e988bac11ae6144cef","observation_id":"e36c25f1-d4ae-487f-b37a-38960f962e02","resolution":{"observed_at":"2026-08-06T14:09:11.842778Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.831217Z","title":"WANG AND Y","venue":null,"work_id":"d20080d5-e0cd-4b9c-a712-e58be45ebe04","year":2019},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.656437Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:dfbc2ba3a602620572155f8decaf0c928bf173d9a56251dde1140788799c979d","observation_id":"15e5479e-0a68-4853-947f-a2c90e5ea758","resolution":{"observed_at":"2026-08-06T14:09:11.834101Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.823497Z","title":"WANG AND M","venue":null,"work_id":"dccd646b-4703-46fe-a76e-d4c12002e8a6","year":2023},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.706468Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:8724b9fd2a32f17fc77ff7f7a469a3bb22d7fab37d4794ffef1b6bd5809d157d","observation_id":"8f13d5c6-2646-40cb-9084-b1219d90f081","resolution":{"observed_at":"2026-08-06T14:09:11.826128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.814363Z","title":"W INKLER , A critical blow-up exponent in a chemotaxis system with nonlinear signal production, Nonlinearity, 31 (2018), pp","venue":null,"work_id":"bd3cc29b-571d-4660-9fcf-62569c92abc8","year":2018},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.709211Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:203b2f7006e2444f8f27ff2758c42f1f3772af41cd6dfbbafeb5b5ac3b126edc","observation_id":"184dd376-26da-4802-ab9a-faae388dc6c8","resolution":{"observed_at":"2026-08-06T14:09:11.817711Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.805269Z","title":"Ann., 373 (2019), pp","venue":null,"work_id":"3c84b674-8383-40c9-bfc2-f8b11bae3095","year":2019},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.711916Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:4bfaf045ab066a186738cff9d4d8700828213f2057b92967e9bc32a5b65f1f4f","observation_id":"dc6a32f9-c1fe-4f53-8dfa-f21d5056b2bf","resolution":{"observed_at":"2026-08-06T14:09:11.808131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.796476Z","title":null,"venue":null,"work_id":"f877e561-5e26-40c7-ba1b-1ab5d7eadb32","year":2022},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.714454Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:62b3611555025d3275d095832b7106830d9ee580479ca8e96733154e47f2461e","observation_id":"3e1f5147-dc7e-4d91-8ae3-22e6f3b5d692","resolution":{"observed_at":"2026-08-06T14:09:11.799406Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.787392Z","title":"Nachr., 295 (2022), pp","venue":null,"work_id":"b5c91bd4-0794-4043-a2f4-84343abb10c8","year":2022},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.716916Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:7ee292ff4c61311275eb258cc7bbd34ae9a916ba439bb744830c7a0c2e8ba66d","observation_id":"a33856df-0cab-4725-b6f6-627a6ffbedcd","resolution":{"observed_at":"2026-08-06T14:09:11.790480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.779048Z","title":"W INKLER , Effects of degeneracies in taxis-driven evolution, Math","venue":null,"work_id":"12b6d145-8d8f-4c34-8d70-440c1d398a3e","year":2025},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.719343Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:1657ad4ac7657aba21559c2dea4ad778bc72c29638b1c5a61464a2c3ed7bc62e","observation_id":"45f18fe7-6db7-458b-bcb6-21d26df1e614","resolution":{"observed_at":"2026-08-06T14:09:11.781945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T14:09:11.769939Z","title":"YAN AND Y","venue":null,"work_id":"bb3caa73-de48-4662-bb30-c255be421737","year":2020},"citing_paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T14:09:11.722250Z"},"links":{"citing_paper":"/paper/2507.19866"},"observation_digest":"sha256:5ecfd95862cd3a34c1628c02d9dfdd1308b427df7f5a35ced997f1343eeb601b","observation_id":"e751ce69-80df-431a-80e2-5c147eeb993a","resolution":{"observed_at":"2026-08-06T14:09:11.773136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.19866","last_updated":"2025-07-26T08:45:29Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-06T14:09:08.010494Z","submitted_at":"2025-07-26T08:45:29Z","title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":1,"verified_fuzzy":26},"total_outbound_references":36},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2507.19866."}