{"as_of":"2026-08-11T13:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a4c8319447fa6c35a6e15c26c06b0cd02505a008af53215022b134e046063b8b","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T01:09:22.277718Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"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/2608.00465/citation-record","integrity":"/paper/2608.00465/integrity","json":"/paper/2608.00465/citation-record.json","paper":"/paper/2608.00465"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.921252Z","title":null,"venue":null,"work_id":"2bb631e8-7ffb-459a-8abf-2ec8e0c7bb5c","year":2003},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:18.425211Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:71ec12869d4e0371a22614a51989e3458d865f9a8cea05778971ca8ac892472b","observation_id":"7b7fced3-24f6-424d-9cae-280606703e3b","resolution":{"observed_at":"2026-08-07T01:09:26.924745Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.910674Z","title":"Bahouri, J.-Y","venue":null,"work_id":"6532af95-10d5-4abc-bad2-d7791cc33b04","year":2011},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:18.537025Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:399c40a09f11dc6addb646ddf4e9b18710dea9fa9a9bd6f18ca72d241c97550e","observation_id":"fb849c43-7c32-4827-8489-12be343dd68e","resolution":{"observed_at":"2026-08-07T01:09:26.914248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.900647Z","title":"Bedrossian, V","venue":null,"work_id":"ed72ddce-bf59-496b-affc-49562b08b343","year":2022},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:18.657968Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:0464dd8350f1a8da22a696bd0e267c02533eb5c7efb9cc3b759bb0df94a24413","observation_id":"416e82f4-013f-4510-9fa5-07b4e03bfb90","resolution":{"observed_at":"2026-08-07T01:09:26.903985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.891003Z","title":"Brandolese, Characterization of solutions to dissipative systems with sharp algebraic decay,SIAM J","venue":null,"work_id":"0793856c-e5e5-4e15-9920-752adcdf079a","year":2016},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:18.822544Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:aa52c03e9c7ae3a75522ef58be7b211c678b95d17c59073f5d7066904c9c3688","observation_id":"67477c5b-db4d-48c5-800d-68c809c9fb76","resolution":{"observed_at":"2026-08-07T01:09:26.894397Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.881970Z","title":null,"venue":null,"work_id":"89d5253e-6e52-4d95-a692-2a65e71d0042","year":2004},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:18.965965Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:2975024c383a1c694a56766097349ef9d7ad19af9d5494476955637a4d7cd5ad","observation_id":"664a9c1a-fa1f-4d86-866b-a06ffcf969b1","resolution":{"observed_at":"2026-08-07T01:09:26.885102Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.872349Z","title":null,"venue":null,"work_id":"0b32eed2-e931-4308-b7b5-3414778af431","year":2003},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:19.111550Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:c07c3c9179ee0446dd5e97f81cc4efffaf19bbb0366f7193db586aaa35f87794","observation_id":"1d229bb6-ea56-4ada-8fad-b0e260f6f670","resolution":{"observed_at":"2026-08-07T01:09:26.875969Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.862697Z","title":"Danchin, J","venue":null,"work_id":"e1fb3728-db68-4b8d-8dce-d39f2c62dcea","year":2017},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:19.254797Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:2a2785c52a399cf9e0c3a8b398a49b8ae6eadac4e994827ef80aaf49ba3f5181","observation_id":"fe166ace-740d-4f63-a02f-19cc7e126152","resolution":{"observed_at":"2026-08-07T01:09:26.866427Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.853336Z","title":"Deckelnick, Decay estimates for the compressible Navier–Stokes equations in unbounded domains, Math","venue":null,"work_id":"7862b841-4595-44e2-a7e1-101a66ad8091","year":1992},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:19.387086Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:cc04746b37d882621eacb4520997c593f7d70f485d2b41116bf1090d65f897ba","observation_id":"b0130dae-f949-4c76-9238-7fd9657d326b","resolution":{"observed_at":"2026-08-07T01:09:26.856642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.842493Z","title":"Deguchi, On the stability of stationary compressible Navier–Stokes flows in 3D,Math","venue":null,"work_id":"cebb7b7c-208b-49b2-abfe-1300f5fb2853","year":2024},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:19.538555Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:a7bb7b8bd21b5d0f9f27ead7c58b3067b2256e490b69979386655e4ea145ce29","observation_id":"edbef6cd-a12f-4da8-90a8-1d21d4b53e36","resolution":{"observed_at":"2026-08-07T01:09:26.846167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.832677Z","title":null,"venue":null,"work_id":"aab05b27-2db6-4bfd-8ab2-6606ef0a6e51","year":2007},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:19.683228Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:83a51e9845923fa93370d2acef3dc9cead955e4766e22c4bdc34bded7b69149a","observation_id":"40f15107-591f-402b-91e8-86f6a8e5a4b1","resolution":{"observed_at":"2026-08-07T01:09:26.835546Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.822511Z","title":null,"venue":null,"work_id":"002ac21f-abb7-41a5-a586-7c2f11c57f15","year":2007},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:19.833613Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:cc737f0826059b758768b3415cbd67966786fe82b08a0712210bff0888ee1587","observation_id":"b421062f-86b8-46c9-a677-1d95567626fc","resolution":{"observed_at":"2026-08-07T01:09:26.825852Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.761826Z","title":null,"venue":null,"work_id":"49437e31-3c37-4177-9be6-da7eb08b5d87","year":2023},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:19.984472Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:42f1a43c54106708af11b99840cb5a6b4192edd3bc9b05dce515b4ac7c19f81b","observation_id":"2ae2dba3-87e1-46b0-87d1-68466d458ce3","resolution":{"observed_at":"2026-08-07T01:09:26.785883Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.633056Z","title":null,"venue":null,"work_id":"3338e1ae-e465-45db-a6c1-2cfc366ff4a6","year":2012},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.117321Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:ffd5bff1901f2d4afdf5828c1e9deb002c5a21d664a52aec98796452ac79e6f2","observation_id":"785c9de0-417e-4eea-a617-b0f5ad17f74e","resolution":{"observed_at":"2026-08-07T01:09:26.640325Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.414169Z","title":null,"venue":null,"work_id":"9c294ac8-4d81-40f3-87d6-980d7fe5052c","year":2019},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.282740Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:5f7a7a088605afdaa8a3f623bcc0dce43a54a4b5a24d6983d0daf1aff96ea43c","observation_id":"cd610d1d-7608-4e48-9bc7-5f75b2d9a478","resolution":{"observed_at":"2026-08-07T01:09:26.509393Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.231002Z","title":null,"venue":null,"work_id":"382328b6-9368-4aee-ad9b-7def511a7e62","year":1995},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.358577Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:acdebe98094a0444c2292613b87180850ba843728fab08b2c52bde48ab08085a","observation_id":"a5bdb119-42c4-43ba-89df-9daf49ec9860","resolution":{"observed_at":"2026-08-07T01:09:26.333878Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:26.005279Z","title":null,"venue":null,"work_id":"7aa2e939-a851-40de-a919-1338568016ff","year":2020},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.429366Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:f044ada204039b7aba1343ee754aa1cc489651b917702496ced1cfa8af86c2b8","observation_id":"6a80c36d-0264-4d98-8b38-1f0a3eec38ff","resolution":{"observed_at":"2026-08-07T01:09:26.104028Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:25.754666Z","title":"Huang, J","venue":null,"work_id":"c5a0d602-28d4-4115-91e6-62631cb288ab","year":2012},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.535719Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:4dfdfda48997ca9880f70b9d17821bbb9e7ca566a10ef4af0c3a66039c629ef6","observation_id":"916ce923-d13a-4294-80ff-2a92c630c339","resolution":{"observed_at":"2026-08-07T01:09:25.893394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:25.530848Z","title":"Iwabuchi, D","venue":null,"work_id":"03224acb-fe57-45b0-805d-292909b6ca8e","year":2025},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.630031Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:8a2f445146e58444d3f6ab70e036eac94bd20fe83dba05d661f79499093ab3ab","observation_id":"6a9282a8-9d38-43aa-acbd-5e4e2d834a37","resolution":{"observed_at":"2026-08-07T01:09:25.637399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:25.260102Z","title":null,"venue":null,"work_id":"c95779ae-608b-4f09-93f5-cff8193ed196","year":1988},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.701535Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:d2636e210af814b05decefc9e3861a15ca9ce369fada022764352085289835c9","observation_id":"399ee803-f2c9-4dd0-a049-dc2479feabc9","resolution":{"observed_at":"2026-08-07T01:09:25.382118Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:25.070072Z","title":"Kawashima, A","venue":null,"work_id":"cfa090a2-3f42-44c0-a08e-67d04a71b5a1","year":1979},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.786500Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:3d235083987d4df3ddf9b73856774cf7bade85e7a298dff64754850e1b18db9d","observation_id":"87da9b82-e63e-4e07-ad56-57f7b849dc23","resolution":{"observed_at":"2026-08-07T01:09:25.181333Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:24.770330Z","title":null,"venue":null,"work_id":"7307faf9-aaeb-4019-968e-d58ac2071347","year":1993},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.857985Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:be001e80bde2baf3f1916cda95fb6257de6828ee737a18cfb98dde85cb80ba15","observation_id":"8b2518f5-0085-48d4-a9b6-2d1e7c25d9f0","resolution":{"observed_at":"2026-08-07T01:09:24.897568Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:24.612854Z","title":"Liu, W.-K","venue":null,"work_id":"7956f0b3-7384-40fd-b314-e7c0bb05ca3b","year":1998},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:20.945221Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:b4b0e9797a2f7f4d5a00a3338d87f29cd2ce3c0f46c6764a058220ed1a9950bc","observation_id":"be878be9-77f1-4aaf-9b29-e904b5118cbe","resolution":{"observed_at":"2026-08-07T01:09:24.686574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:24.543352Z","title":null,"venue":null,"work_id":"6b9a68b8-39cb-4486-9597-5e37ccc3fd6c","year":2025},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.029643Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:dd7bad9d1729099acdb3476c19a636d8b85d18ced8de44bb300271a2298d2b64","observation_id":"c0190c3e-5a0a-481d-8961-2d7f097b594b","resolution":{"observed_at":"2026-08-07T01:09:24.605064Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:24.427686Z","title":"Matsumura, T","venue":null,"work_id":"9647f369-2282-4ea3-b238-4b9e0ed2b48b","year":1979},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.122142Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:fb75b32216b30d621e9035404d9ba923db30f223e7f0420b94950240958b4062","observation_id":"2f41e098-5e05-4e66-b8f2-20b9befcb4a9","resolution":{"observed_at":"2026-08-07T01:09:24.480056Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:24.261242Z","title":"Matsumura, T","venue":null,"work_id":"77a1db2f-c4fa-4143-8e5a-0c6287576c29","year":1980},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.199958Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:13531bfd2c87b1d5543665cc4986053c977ac1d9054750a1b2cac3e70bdfa4ec","observation_id":"f5e09ce3-6aa6-4af7-8b77-29d6559b3ff3","resolution":{"observed_at":"2026-08-07T01:09:24.323684Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:24.156254Z","title":"Matsumura, T","venue":null,"work_id":"972313b9-8f68-44ec-8ab4-6d8cee924bbb","year":1983},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.268938Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:7702070e2737859452ee0bd9c985a8b4a5780e22e17a90e7c75c1d85739f1914","observation_id":"17207b73-5cf9-401b-9941-495a55ddd68b","resolution":{"observed_at":"2026-08-07T01:09:24.193261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:24.044437Z","title":"Matsumura, M","venue":null,"work_id":"0f3c4d43-f127-4250-b87e-ce768f86ff2a","year":1992},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.343302Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:4448a3cb7c167e63248e3cc6733477b05c0a8d88758e2216d3b3b28a5fbd4643","observation_id":"1f3ea256-ac64-4c67-8b84-3cb73a31d16b","resolution":{"observed_at":"2026-08-07T01:09:24.104682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:23.932147Z","title":"Okita, On the convergence rates for the compressible Navier–Stokes equations with potential force, Kyushu J","venue":null,"work_id":"af7785e9-ac29-4dd4-8e6d-c97360f48fda","year":2014},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.407713Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:1efa08ddc82363fc7277aa24473bbbdec5430611afdddbb9680d668a05b2d1db","observation_id":"de1159d3-8ec5-43e4-be7f-bc00b3da6d12","resolution":{"observed_at":"2026-08-07T01:09:23.975735Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:23.819923Z","title":"Oliver, E","venue":null,"work_id":"3376f935-c226-4279-9400-f048d958f55b","year":2000},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.505285Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:6b5d915c45a08d8b9fee6da971b14ef3ee99d0a2ed3c96236fccee7a5a28a544","observation_id":"0dfbece7-5ec7-4d47-9ffe-e61dc3ccee2f","resolution":{"observed_at":"2026-08-07T01:09:23.868602Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:23.682844Z","title":"Ponce, Global existence of small solutions to a class of nonlinear evolution equations,Nonlinear Anal","venue":null,"work_id":"443b86c4-9944-41a7-97a4-b570b7e06828","year":1985},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.589688Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:ae2e20090768753844f6f347fcf5cde67541088937b56bbe6ca66fd936fca8cb","observation_id":"b27b4143-d605-4355-a712-cb444dd116e0","resolution":{"observed_at":"2026-08-07T01:09:23.761255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:23.544514Z","title":null,"venue":null,"work_id":"cf4de3d2-d335-4a56-a534-a3fa4b84fd27","year":1991},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.664980Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:9a21dfdf1e8e80047c47bbebeb917cc1435b61a24f72a1f84f9c59cb7c215474","observation_id":"deaa6d78-393a-4248-bbef-5edfc58207b4","resolution":{"observed_at":"2026-08-07T01:09:23.610136Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:23.406560Z","title":"Shizuta, S","venue":null,"work_id":"819c15f2-0384-4558-ab6c-c51489ac2e6b","year":1985},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.741345Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:adb91106fa90527eb9aa4bd3671e742ae28876c30ed628c7d0aa630d78697a32","observation_id":"375434db-2e03-4b5c-9b13-19d29d2b1535","resolution":{"observed_at":"2026-08-07T01:09:23.486049Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:23.256900Z","title":"Shibata, K","venue":null,"work_id":"75d62c53-1fe9-4e61-9ec3-f0c5c01d4b14","year":2003},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.827417Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:cde6790deb3381066333cf52642f2268dd9b36d826086f8b870cb74cfb60fda4","observation_id":"f634c051-f4dd-47f2-990c-7cd01f184672","resolution":{"observed_at":"2026-08-07T01:09:23.324259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:23.130926Z","title":"Shibata, K","venue":null,"work_id":"3301b6c0-ec27-4ec4-9ed8-0e9228764007","year":2007},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.905549Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:91d59bbc64faa39dc7bcfd39f5a6a6c7ea67b7e2082e156e6fde738150b273ed","observation_id":"4ff616c2-4a62-4dbe-9eb6-a37ee868bf39","resolution":{"observed_at":"2026-08-07T01:09:23.194944Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:23.004903Z","title":null,"venue":null,"work_id":"ca270364-983f-4fae-8df6-dd32175e7580","year":2006},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:21.994467Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:baaaf531ffb69972cf6a277cfa46b1509d6b5475371aa477861f45dabbfce370","observation_id":"3915243c-c250-440a-b2be-10444233357b","resolution":{"observed_at":"2026-08-07T01:09:23.060430Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:22.855160Z","title":"Wang, Optimal convergence rates for the strong solutions to the compressible Navier–Stokes equations with potential force,Nonlinear Anal","venue":null,"work_id":"b8bc3ce2-bbb8-4084-917c-148d74d273ca","year":2017},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:22.052879Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:70e49c9d68981cce7ebda191e6766d67ed5e690a9f007db650519b9e470e3810","observation_id":"0384a2a3-9a30-42b4-bed5-998aa7a3bbc6","resolution":{"observed_at":"2026-08-07T01:09:22.924418Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:22.695591Z","title":null,"venue":null,"work_id":"cc3d1706-dfbb-4165-b4ae-2d02bca556ab","year":2021},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:22.149264Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:c3ea0c4ccc3c99d8af35b5456e1579faaf8b115819ee864f3382a6b56de28c34","observation_id":"79e00456-115d-43da-be00-7682d84ace03","resolution":{"observed_at":"2026-08-07T01:09:22.769790Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:22.532617Z","title":"Xu, A low-frequency assumption for optimal time-decay estimates to the compressible Navier–Stokes equations,Comm","venue":null,"work_id":"d3e1074a-9285-4fe7-9b69-fd91b487ced0","year":2019},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:22.212342Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:2ab3261d27ead53d7120a4c71a910a467291abe9cb3dbbbfbada7796199a4ae7","observation_id":"3bb69371-d521-497d-a14a-e6169d90f2cc","resolution":{"observed_at":"2026-08-07T01:09:22.607634Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:09:22.385941Z","title":null,"venue":null,"work_id":"a0e1770d-3052-4357-b842-3f82c8496b2e","year":2015},"citing_paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T01:09:22.277718Z"},"links":{"citing_paper":"/paper/2608.00465"},"observation_digest":"sha256:8531c09aef910f3985282bf0a9ed130e2604bf8d5e391a571a6afad2f7f97f4a","observation_id":"371085ab-8109-4206-803a-b70476a01083","resolution":{"observed_at":"2026-08-07T01:09:22.451750Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.00465","last_updated":"2026-08-06T05:10:42Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-11T13:11:03.386805Z","submitted_at":"2026-08-01T06:12:26Z","title":"Compressible Navier--Stokes equations with a potential force: global well-posedness and optimal time-decay rates for arbitrarily large $L^2$ initial data"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":0,"verified_fuzzy":22},"total_outbound_references":39},"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 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2608.00465."}