{"as_of":"2026-08-11T17:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:bdcdd7957e0e8f1430ccdd6e255d594bb6b8fe0792ac11cefabe204525b8b0e3","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-31T04:23:14.195880Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2607.25009/citation-record","integrity":"/paper/2607.25009/integrity","json":"/paper/2607.25009/citation-record.json","paper":"/paper/2607.25009"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.072787Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.072787Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:3804e2cf0bf6ac23ad624519bfcd60bed436cf63cf3814f3304d4e23d802ecd6","observation_id":"6586b83c-506d-483f-a6bf-cd53a4d7057b","resolution":{"observed_at":"2026-07-31T04:23:14.072787Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.079463Z","title":"Bahouri, J.-Y","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.079463Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:99f6ee4c52a66e9e30bc83da500dd0c98e29a12c85b752c7b76e712aa41ef48a","observation_id":"e49300c6-fd5b-4c6d-83fa-3a3b1751d224","resolution":{"observed_at":"2026-07-31T04:23:14.079463Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.084760Z","title":"Barbu and S","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.084760Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:0c697952aa78cc4ccb8c7343772c57492f1f99c32196b3457b277d849ca10e87","observation_id":"a23029d0-51bd-4206-aef8-8038ce376f0b","resolution":{"observed_at":"2026-07-31T04:23:14.084760Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.090158Z","title":"Bony,Calcul symbolique et propagation des singularit´ es pour les ´ equations aux d´ eriv´ ees partielles non lin´ eaires, Ann","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.090158Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:41007fafdb44b0b76902a27c2c473b7b27b404774d12f82ef78bde75d60b346b","observation_id":"ffc1575a-e3b0-40d4-b8da-ec06cf1ab21c","resolution":{"observed_at":"2026-07-31T04:23:14.090158Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.096269Z","title":"Bourgain and N","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.096269Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:24d50c7936aa1b6f71c3dd76d9589352059df87fb42885f306887be015dac79c","observation_id":"b6822089-1863-499d-ad26-25eb19ff1c07","resolution":{"observed_at":"2026-07-31T04:23:14.096269Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.102931Z","title":"Cannone,A generalization of a theorem by Kato on Navier-Stokes equations, Rev","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.102931Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:43067db28ea0c5daa8015c7f1c9c45e9720e85e94a9a46610cebbde3639b9ed0","observation_id":"beb400df-8592-4ce3-a882-1c930b49d17f","resolution":{"observed_at":"2026-07-31T04:23:14.102931Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.108578Z","title":"Cheskidov and R","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.108578Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:cdb4d2a9d23b6090c1dd9cbb1c87abb93079c2f542164ad170a96ec33055f260","observation_id":"acb70156-5728-453e-bd9d-7897b93a8982","resolution":{"observed_at":"2026-07-31T04:23:14.108578Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.113494Z","title":"Christ, J","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.113494Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:7afe5841869c31194878fca60fbf50f3b4ddd888113ec6c51bde81bc8b45e4f1","observation_id":"c5ef647a-3ddb-4eeb-b801-862b775f214a","resolution":{"observed_at":"2026-07-31T04:23:14.113494Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.118522Z","title":"de Andrade and A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.118522Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:37862e9b209221f9b3681506c1981c1064ce43458414087888d894725a102b85","observation_id":"34d672d6-d017-4d69-a3cd-edd35bef10fd","resolution":{"observed_at":"2026-07-31T04:23:14.118522Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.124563Z","title":"de Andrade, C","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.124563Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:7501aa54430db54cd29e9542989e188d88fe79f427e5bc80ce7af8ddd98ee14b","observation_id":"98728e0a-5eb1-40b8-b4fa-a12d8d39014f","resolution":{"observed_at":"2026-07-31T04:23:14.124563Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.129745Z","title":"de Andrade, C","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.129745Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:71f295a811a4dc6acadac90aaebd1205f348e63db61d6f519135e6a9875f948e","observation_id":"39268732-b205-4c97-92ce-cb46aee7c526","resolution":{"observed_at":"2026-07-31T04:23:14.129745Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.17430","last_updated":"2026-07-19T22:36:48Z","snapshot_observed_at":"2026-08-01T18:06:57.881721Z","submitted_at":"2026-07-19T22:36:48Z","title":"Critical thresholds and instantaneous norm inflation for super-diffusive integro-differential equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.17430","snapshot_observed_at":"2026-07-31T04:23:14.135457Z","title":"de Andrade,Critical thresholds and instantaneous norm inflation for super-diffusive integro- differential equations, arXiv:2607.17430, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.135457Z"},"links":{"cited_paper":"/paper/2607.17430","citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:4e0811d39b042e42cb0c954f476b38994a7446b549e9dcd1543d049094029492","observation_id":"6bc27b25-3c07-49bc-b1e5-d4c132298973","resolution":{"observed_at":"2026-07-31T04:23:14.135457Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.140814Z","title":"de Andrade and M","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.140814Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:7a541db4154a987e3b906a943e1fcc7e1b117dc097c4a34dcec8b8d8abfdf5aa","observation_id":"e067f2a9-038f-4ae2-86f8-b603483c63fd","resolution":{"observed_at":"2026-07-31T04:23:14.140814Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.145806Z","title":"Giusti, I","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.145806Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:7ca4c2d679264ee7107f39fa4d83f1895cc081aef3c5ee696ee0fa94302bc9f2","observation_id":"f8a17a0e-1336-4ad2-9aa7-103cb5263999","resolution":{"observed_at":"2026-07-31T04:23:14.145806Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.150845Z","title":"Grafakos,Classical Fourier Analysis, third ed., Graduate Texts in Math., vol","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.150845Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:4752500a3c2f31062f0eb38363a77d07c64b3a5aab7acd6c83e17d2122cc5186","observation_id":"f1629cbc-1d1e-44c7-a520-646a98a85558","resolution":{"observed_at":"2026-07-31T04:23:14.150845Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.155717Z","title":"Henry,Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.155717Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:6a928a508311a79d1c257c2de51b65bf68d816a10143b22f3f79f4eee55494eb","observation_id":"84dd8e82-ade4-4dd9-8416-2c2140cfcec6","resolution":{"observed_at":"2026-07-31T04:23:14.155717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.160476Z","title":"Jaishankar and G","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.160476Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:2b39737caaa2cdbfd1fcb2a3d8272e0aa90942bc1b09330b8490aff25bafea65","observation_id":"215b31d6-a30e-4550-a9c2-d37f3f68b32b","resolution":{"observed_at":"2026-07-31T04:23:14.160476Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.165517Z","title":"Kato,StrongL p-solutions of the Navier-Stokes equation inR m, with applications to weak solutions, Math","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.165517Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:9948f5ce33ad66d0e3cc5cf9f1e43a043e7c4501d5331912bf5a7aeaa64f372f","observation_id":"97bbe3a0-d8f7-4a87-8f39-a38e1ad7f288","resolution":{"observed_at":"2026-07-31T04:23:14.165517Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.170485Z","title":"Koch and D","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.170485Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:49115ce2771aae4bcc0b86cca45b4242eca389eae10effe323ec4c489346b743","observation_id":"36dfdd77-406e-41c0-89e9-55f83bffcb64","resolution":{"observed_at":"2026-07-31T04:23:14.170485Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.175850Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.175850Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:b465a22f810ae68c58670a600106e45e1cb62b4dfa498213636361a75d4438f1","observation_id":"9ce586b5-7f9c-4ea3-a3ab-29cd932ab2c9","resolution":{"observed_at":"2026-07-31T04:23:14.175850Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.180845Z","title":"Mainardi,Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, Imperial College Press, London, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.180845Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:a1271e02094e4379a9681543f6baed1c49b4213dda99d3d7f1270502746baec3","observation_id":"bfbd7df3-e19a-4b51-8244-075acda3e67f","resolution":{"observed_at":"2026-07-31T04:23:14.180845Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.185906Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.185906Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:ddf8d051b06f3c29b4d25873eff56364a6a59ee8be3b685cac5d730621d4e825","observation_id":"1c0fc168-b1a4-4e84-91e3-7660d60f41af","resolution":{"observed_at":"2026-07-31T04:23:14.185906Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.190870Z","title":"Sawano,Theory of Besov spaces, vol","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.190870Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:f232c022d6e3bc72fc04ea4ffc0f4bb6a36ca33fc22d0f8df47317bdbc6300ec","observation_id":"3048045d-de62-4619-a3b7-342d25291ff6","resolution":{"observed_at":"2026-07-31T04:23:14.190870Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-31T04:23:14.195880Z","title":null,"venue":null,"work_id":null,"year":1941},"citing_paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-31T04:23:14.195880Z"},"links":{"citing_paper":"/paper/2607.25009"},"observation_digest":"sha256:c9c3ef29491abd407aefaeddce0a79f6d1720651474cf17eb4b8d2739e4ccc92","observation_id":"171e0a21-490f-44ba-954a-0a127e15b1be","resolution":{"observed_at":"2026-07-31T04:23:14.195880Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.25009","last_updated":"2026-07-27T19:07:16Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-11T15:06:41.739921Z","submitted_at":"2026-07-27T19:07:16Z","title":"The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":24,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":24},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.25009."}