{"as_of":"2026-08-12T21:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5228c179b3a43e53f84e8c911ded40f9679803de7b571282af1e573837fe3a95","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T17:45:52.216913Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2512.08816/citation-record","integrity":"/paper/2512.08816/integrity","json":"/paper/2512.08816/citation-record.json","paper":"/paper/2512.08816"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T17:45:48.240909Z","title":"343, Springer, Heidelberg, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:48.240909Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:0349452ec4d90fd445a753a25c2be985fafa077c6a086915f46be1003bb80d9b","observation_id":"aadfbdef-e639-453c-a90e-3660f73de169","resolution":{"observed_at":"2026-08-03T17:45:48.240909Z","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":"2026-08-03T17:45:48.394201Z","title":"Math.201(2015), no","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:48.394201Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:fbcc376fb47e06307b268b3f33341cafaac3fb0a58447cb7856f9de7d7d30fda","observation_id":"6f1d50c3-a4e5-4d1f-b153-9df7b03c0740","resolution":{"observed_at":"2026-08-03T17:45:48.394201Z","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":"2026-08-03T17:45:48.576748Z","title":"Pure Appl","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:48.576748Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:63bcecd35ad7ab5ddb51793802f95b5393eab4c09dea0195719de174f336cb59","observation_id":"05e14c7f-1136-4f12-bc6d-9715dfb3bc3c","resolution":{"observed_at":"2026-08-03T17:45:48.576748Z","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":"2026-08-03T17:45:48.759026Z","title":"Caffarelli and Alexis Vasseur,Drift diffusion equations with frac- tional diffusion and the quasi-geostrophic equation, Ann","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:48.759026Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:93065bceaa134555008f0ee2a2b2ccc844ce44b2cd7b8c6b1745d32f2e04879e","observation_id":"b6246fd5-b170-4067-a3ac-3020be5512f4","resolution":{"observed_at":"2026-08-03T17:45:48.759026Z","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":"2026-08-03T17:45:48.908971Z","title":"Carrillo and Lucas C","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:48.908971Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:e615eae93c26cc0a42053c95d1fc263d574176ea54c85e57a36ba70cbd24d878","observation_id":"ff61459a-c6a2-400b-80ed-e046e7fa2c38","resolution":{"observed_at":"2026-08-03T17:45:48.908971Z","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":"2026-08-03T17:45:49.034575Z","title":"Dif- ferential Equations443(2025), Paper No","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:49.034575Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:52a2d34df67e51f68bad73dc541d50afa7ab92dac7597625abdfce53e5556e27","observation_id":"a1e38699-3ab4-4e0d-8f10-9299314d2ffb","resolution":{"observed_at":"2026-08-03T17:45:49.034575Z","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":"2026-08-03T17:45:49.156054Z","title":"PDE7 (2021), no","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:49.156054Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:432cc6f3ef6e4acc59a1db3b8c515a1bd417e44b35bb2f1924fb8caddf7b0b93","observation_id":"156888b6-aab6-46cf-9594-df3a2f1491b5","resolution":{"observed_at":"2026-08-03T17:45:49.156054Z","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":"2026-08-03T17:45:49.283598Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:49.283598Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:e01d5ec9c7dcb06c5a5c3a4503ed3512c99b8fb027045577a29d4cd3260679c6","observation_id":"82780fc0-3841-42ce-9130-b03e3d8297e6","resolution":{"observed_at":"2026-08-03T17:45:49.283598Z","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":"2026-08-03T17:45:49.433377Z","title":"Majda, and Esteban Tabak,Formation of strong fronts in the2-D quasigeostrophic thermal active scalar, Nonlinearity 7(1994), no","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:49.433377Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:424ad803f23946b2e9d53df3be41d3558ad8f418101ea908c18fd0225b7a289e","observation_id":"dbdfabfe-9a52-4054-ba82-54fb79c81648","resolution":{"observed_at":"2026-08-03T17:45:49.433377Z","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":"2026-08-03T17:45:49.519537Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:49.519537Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:a80d605588e60c86a0c08138a7173cc8da8d5d5d6cc5388844a95e4a760394cc","observation_id":"5e18fb7a-8f5b-459a-9f15-7a29747a5bbe","resolution":{"observed_at":"2026-08-03T17:45:49.519537Z","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":"2026-08-03T17:45:49.684680Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:49.684680Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:4a71d3e49be5c1c1becb5de74b09f1dfa83cee3a4f8373cc8403d0fdd10f0539","observation_id":"76aeb45d-775b-4f07-9a2a-314f2604eee7","resolution":{"observed_at":"2026-08-03T17:45:49.684680Z","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":"2026-08-03T17:45:49.816301Z","title":"8, Paper No","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:49.816301Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:bb3a1f5256f24c525fbdf3ed4f60c5d1c66ebfd4467f2c8e49d842bec7612d4b","observation_id":"bd38c740-7009-4c1c-8d04-7e09b14c819e","resolution":{"observed_at":"2026-08-03T17:45:49.816301Z","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":"2026-08-03T17:45:49.956501Z","title":"Math.407(2022), Paper No","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:49.956501Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:ea86912d5c5ffa0016f62d2b5ad36636f8233907b88f1e54785eba7eacdd0f7f","observation_id":"a381e096-57cd-4e6d-b097-00f426b61b7b","resolution":{"observed_at":"2026-08-03T17:45:49.956501Z","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":"2026-08-03T17:45:50.083315Z","title":"PDE10(2024), no","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:50.083315Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:e154c46586615586075f8a954d922794334e8883c05afe998d0df3c05f07492d","observation_id":"bc844b63-a80d-41eb-9c07-52c9ebb581a7","resolution":{"observed_at":"2026-08-03T17:45:50.083315Z","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":"2026-08-03T17:45:50.210886Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:50.210886Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:29481ea3ca70c2933783b9861261e40f6b99f26fa87f422f128e867cf10f9e7f","observation_id":"07d0e792-cd39-4be3-9047-63976e316d10","resolution":{"observed_at":"2026-08-03T17:45:50.210886Z","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":"2026-08-03T17:45:50.376874Z","title":"O˙ za´ nski,Instanta- neous gap loss of Sobolev regularity for the 2D incompressible Euler equa- tions, Duke Math","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:50.376874Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:a64052673e23f14fee044b601197bc6d871966174c8b2e2a62118362555948e2","observation_id":"cc822eee-c789-400a-bb06-3bd195a6c9ff","resolution":{"observed_at":"2026-08-03T17:45:50.376874Z","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":"2026-08-03T17:45:50.508159Z","title":"Math.481(2025), Paper No","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:50.508159Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:f702f19fc0017e6b2885b5b37e94363d11364c4a531f61c3a25c026409bbf411","observation_id":"d985d4db-5bc3-4154-aa65-27850335eddc","resolution":{"observed_at":"2026-08-03T17:45:50.508159Z","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":"2026-08-03T17:45:50.692531Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:50.692531Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:702334073eeb4570624fa8ee73bd7934112739587e6412e9b0590935e29413b5","observation_id":"4b30be0e-63e7-4363-88cf-d83880b68c37","resolution":{"observed_at":"2026-08-03T17:45:50.692531Z","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":"2026-08-03T17:45:50.795600Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:50.795600Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:a0d89bd72c10d645f5f0374fc174006167e3823ced68b24669ac5f74633212ab","observation_id":"aa34e240-27c5-4abd-8fcf-5a8087177208","resolution":{"observed_at":"2026-08-03T17:45:50.795600Z","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":"2026-08-03T17:45:50.870674Z","title":"PDE7(2014), no","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:50.870674Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:f9be73eee0f00a7f764512c2880a30a9b2ab4a15a57cf2cd3df7de78ce3aaec4","observation_id":"5fb73db2-caa5-4dd0-bd20-8dd04cd7adc0","resolution":{"observed_at":"2026-08-03T17:45:50.870674Z","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":"2026-08-03T17:45:50.909619Z","title":"5, 1525–1535","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:50.909619Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:a45fbc2d0b261b10bb0da213a2b97fbd925e5521fc352f1522026b3645f74187","observation_id":"c66b2ee6-528d-4697-b361-9ab8cbdcfc09","resolution":{"observed_at":"2026-08-03T17:45:50.909619Z","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":"2026-08-03T17:45:51.005056Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.005056Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:23da9cadc2167f62a1bc99f6d9c4c8e99b00a48ad845944b042c5c56ab3cfe05","observation_id":"f9571768-364a-49f2-9c62-645efe618bbd","resolution":{"observed_at":"2026-08-03T17:45:51.005056Z","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":"2026-08-03T17:45:51.086714Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.086714Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:5e8e0d6c7fd7b852e2dd080d01b1e5489552446269035cd9e1daa6e705cff612","observation_id":"382308db-1a5e-49b0-9851-9f4c3922d614","resolution":{"observed_at":"2026-08-03T17:45:51.086714Z","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":"2026-08-03T17:45:51.172492Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.172492Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:65b9f4f559da823073d6377fcd2a3ef3b75e55a44cfa645fcfbc73a07df51137","observation_id":"eb5b7382-f0f2-4c5d-8174-b4de0bdfd27b","resolution":{"observed_at":"2026-08-03T17:45:51.172492Z","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":"2026-08-03T17:45:51.224182Z","title":"Elgindi and Nader Masmoudi,L ∞ ill-posedness for a class of equations arising in hydrodynamics, Arch","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.224182Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:e381e6c91fde453c40e44eb39adb7466d348fe347a689d46cae7e2ce1a53149a","observation_id":"83118e5e-22e4-4bdb-b938-8d55cea54eca","resolution":{"observed_at":"2026-08-03T17:45:51.224182Z","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":"2026-08-03T17:45:51.321276Z","title":"PDE17(2024), no","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.321276Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:8d9ed4b2b80bae5a41e6e543ed1d6e7afbc48af093b4c0a586494eaf24c16767","observation_id":"8e8dac41-5de9-4906-84aa-424281bbc7f1","resolution":{"observed_at":"2026-08-03T17:45:51.321276Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.06333","last_updated":"2025-08-08T14:08:30Z","snapshot_observed_at":"2026-08-05T23:02:51.674080Z","submitted_at":"2025-08-08T14:08:30Z","title":"Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.06333","snapshot_observed_at":"2026-08-03T17:45:51.383038Z","title":"O˙ za´ nski,Instanta- neous continuous loss of Sobolev regularity for the 3D incompressible Euler equation, arXiv:2508.06333, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.383038Z"},"links":{"cited_paper":"/paper/2508.06333","citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:b98a424e4334d08ed28a482acfb0bf5aa8d3bae608c0d9f8ff5a8a618860bd0e","observation_id":"cadfd057-da75-4f20-958b-ed53e5e42abc","resolution":{"observed_at":"2026-08-03T17:45:51.383038Z","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":"2026-08-03T17:45:51.492839Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.492839Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:9460549fe9d9c930cd7419cce3322036ba45e0a8d2ef93dd002dfa1aa291d17a","observation_id":"c70bf4fe-2bcb-44d6-8ca5-10e5a1c6e75c","resolution":{"observed_at":"2026-08-03T17:45:51.492839Z","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":"2026-08-03T17:45:51.548848Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.548848Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:7054993c8ecf0963f885ae869ba17fc3e6a114e73cf7d94de6c6188ee555604a","observation_id":"7caafb64-ad2d-4302-9e59-aab8e8c2c21c","resolution":{"observed_at":"2026-08-03T17:45:51.548848Z","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":"2026-08-03T17:45:51.642646Z","title":"Kiselev, F","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.642646Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:e6f2592d7af6af7de317790bfd5bcfbfd70239e16e19aa08e35056259d97b864","observation_id":"94bd2f28-1d93-4bec-868f-fb2efef09055","resolution":{"observed_at":"2026-08-03T17:45:51.642646Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.07813","last_updated":"2024-05-27T01:12:09Z","snapshot_observed_at":"2026-08-03T00:07:52.270167Z","submitted_at":"2024-04-11T14:56:17Z","title":"Illposedness of incompressible fluids in supercritical Sobolev spaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.07813","snapshot_observed_at":"2026-08-03T17:45:51.710733Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.710733Z"},"links":{"cited_paper":"/paper/2404.07813","citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:1fbafb4175955bbf99d501f01c019b0acbb56ca7d74723c77ec0662820cabb91","observation_id":"0d2a9f8a-391e-450c-aa88-68147b124348","resolution":{"observed_at":"2026-08-03T17:45:51.710733Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.08288","last_updated":"2025-04-11T06:44:31Z","snapshot_observed_at":"2026-08-07T16:06:38.012427Z","submitted_at":"2025-04-11T06:44:31Z","title":"Sharp norm inflation for 3D Navier-Stokes equations in supercritical spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.08288","snapshot_observed_at":"2026-08-03T17:45:51.765341Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.765341Z"},"links":{"cited_paper":"/paper/2504.08288","citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:e8b19e6fdccf8e84814518812b81651e6ac277823844b07c0e38f1ec37ea22ae","observation_id":"3b836bc7-d9cc-477f-85a5-5ccab8b309db","resolution":{"observed_at":"2026-08-03T17:45:51.765341Z","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":"2026-08-03T17:45:51.826459Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.826459Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:9f23d63eb78307fcb45950f9c676748d4cf9544b33f9fb8ebbb0d2070f75a727","observation_id":"3f31953e-ffb6-4a83-bf67-849e3d14c2ad","resolution":{"observed_at":"2026-08-03T17:45:51.826459Z","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":"2026-08-03T17:45:51.908669Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.908669Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:5004874a0bc565bdc00e4a814c6353905e696a06fef68f428b00d91943478631","observation_id":"2b3cdab8-259a-4779-acaa-b05fee33e40f","resolution":{"observed_at":"2026-08-03T17:45:51.908669Z","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":"2026-08-03T17:45:51.998435Z","title":"Resnick,Dynamical problems in non-linear advective partial differ- ential equations, ProQuest LLC, Ann Arbor, MI, 1995, Thesis (Ph.D.)–The University of Chicago","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:51.998435Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:85c25c7e3cbaa1cba3f49bb1efbd3ee624cefaebf86f52aedc8b51d4af087426","observation_id":"9642b2c7-0b0c-4e4c-95cc-e95ebcfd284a","resolution":{"observed_at":"2026-08-03T17:45:51.998435Z","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":"2026-08-03T17:45:52.083123Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:52.083123Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:bc9c2ed565f286a230f184efc58f0fd8ef67440154d9634f176bc895f79e7ee8","observation_id":"778a7741-9947-463d-a414-66116c68f09f","resolution":{"observed_at":"2026-08-03T17:45:52.083123Z","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":"2026-08-03T17:45:52.164067Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:52.164067Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:15281fd17cea823bbb6c625f388a58598abbcf674694c14b77c9a0ccc577ddaa","observation_id":"2fe37cd1-9f31-4c75-874c-09aacb5f8afb","resolution":{"observed_at":"2026-08-03T17:45:52.164067Z","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":"2026-08-03T17:45:52.216913Z","title":"Differential Equations 253(2012), no","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-03T17:45:52.216913Z"},"links":{"citing_paper":"/paper/2512.08816"},"observation_digest":"sha256:dca26b6d66ece9660ab685ffe5ed5050e8c030768bc60e4334d1c246dac299cb","observation_id":"67fe76be-ba09-4de0-96e2-5e5d56ec57bf","resolution":{"observed_at":"2026-08-03T17:45:52.216913Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.08816","last_updated":"2026-05-26T12:59:06Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-09T18:49:02.078622Z","submitted_at":"2025-12-09T17:09:40Z","title":"Norm Inflation For The Critical SQG Equation"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":38,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":38},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2512.08816."}