{"as_of":"2026-08-08T05:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:33ce75a34eebe4adc82006a3a47ece220ef03a1b92154e0567dc8cbd8a15933f","coverage":[{"denominator":49,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":49,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:08:29.314755Z","state":"measured"},{"denominator":49,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":49,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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/2505.22853/citation-record","integrity":"/paper/2505.22853/integrity","json":"/paper/2505.22853/citation-record.json","paper":"/paper/2505.22853"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:08:44.995511Z","title":null,"venue":null,"work_id":"024b5e04-9ffa-4a52-88de-019fcc0ed326","year":2017},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:24.484756Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:9f459708ec1a02d2ac21c350c3aac867b84bc6fde16e092000c07ca84ded547d","observation_id":"1766cf1a-f812-42d3-81ce-0088664a60b5","resolution":{"observed_at":"2026-08-07T13:08:45.116233Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:08:24.608204Z","title":"I., & Khesin, B","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:24.608204Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:600bb0933e0b192830539386bc9629499ee3228c72afa4c2c91d8f94fdaecace","observation_id":"2bd9e0ad-80fc-4eeb-8a46-1275b82aa423","resolution":{"observed_at":"2026-08-07T13:08:24.608204Z","resolver_source":null,"status":"malformed_identifier"},"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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:08:44.753854Z","title":null,"venue":null,"work_id":"423518df-3a73-4cbf-a756-fed749b0af11","year":1967},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:24.744741Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:c88a72aef0825aacf80fb03220229ab650470e7f599557f212d7aaac2cd28258","observation_id":"a56f02b6-daff-46cf-9974-88528b361049","resolution":{"observed_at":"2026-08-07T13:08:44.860980Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:44.529938Z","title":null,"venue":null,"work_id":"e7f6987c-2f8e-4c62-9903-b1d43c48f83e","year":2019},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:24.885281Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:60c670f90261ed7ba996cef74a14b20745dc6a250c6fa3b18ba6bd56da617c8e","observation_id":"71c8040e-45ca-4f3b-a140-bb6ef0e4917b","resolution":{"observed_at":"2026-08-07T13:08:44.655332Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:44.250449Z","title":null,"venue":null,"work_id":"dcb2ab80-b0fc-45e9-9231-21be09a9ec40","year":1982},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:25.088481Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:ae7cee482654b4f2f30c1dee64ddb1acf1f7e7d4e6c57b90d143c733ed1f9261","observation_id":"64736aa6-62fd-48e8-b8cc-3f2c1ee9b88c","resolution":{"observed_at":"2026-08-07T13:08:44.375267Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:44.030859Z","title":null,"venue":null,"work_id":"4c49c9bd-0aab-4eda-a0e4-3da8ec5b31a1","year":2007},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:25.308668Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:feeedc7abb87c560e7fd316fbfbf4e1d22a9b0b5c0b991c63fc53ac76d3a8c3c","observation_id":"e72b00a7-60df-4b64-b730-dbc3966069b8","resolution":{"observed_at":"2026-08-07T13:08:44.128871Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:43.768166Z","title":"Millennium Prize Problems","venue":null,"work_id":"4a996b92-c08d-4938-aca8-377012f51ef6","year":2000},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:25.447843Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:0b358215888003c80b65f8f0d21e7192a8e5b82a77fe134b37448cf56e626f0a","observation_id":"dbd69ebe-b635-4a55-8288-b88ee102a8d2","resolution":{"observed_at":"2026-08-07T13:08:43.918785Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:43.488584Z","title":"Geometry and Fluids Workshop","venue":null,"work_id":"866eff91-3ac6-4e43-aa5c-ae0cdc0cd662","year":2014},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:25.694869Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:d9ffd3b63df1998f5f2aadf677229e50dda1a104aae990484fd94d8d6aa31308","observation_id":"44f274ea-57bc-4e94-be28-c45fc5bf44c2","resolution":{"observed_at":"2026-08-07T13:08:43.616588Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:43.264948Z","title":null,"venue":null,"work_id":"35e3f3f1-c4bb-41b0-932e-2a05b388c0d7","year":2012},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:25.809754Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:fbeca5effadc01e30c2db45ba67e90a895f91ccae14b6bd410444e12f44d8b6e","observation_id":"8cfca500-e65d-4def-95eb-af3851103fea","resolution":{"observed_at":"2026-08-07T13:08:43.394330Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:43.009703Z","title":null,"venue":null,"work_id":"e326c228-521d-4639-867a-8ba15a92a212","year":2003},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:25.924943Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:cad77753ee5c2d3bc4fd84f0a2e6ea93588d32aac11a64a00c2d54f754d1709b","observation_id":"c9902adc-a429-4444-95c5-888fd6a8abe0","resolution":{"observed_at":"2026-08-07T13:08:43.141515Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:42.784919Z","title":null,"venue":null,"work_id":"d08edd53-f1eb-4159-bc65-aea665dc936d","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:25.974423Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:45a617944a637c3ac24e1486778631c8023c6d5908a32e74ba2d2716166da50d","observation_id":"3c26d05d-35fe-4987-a7f6-fd3e98161e16","resolution":{"observed_at":"2026-08-07T13:08:42.880740Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:42.490209Z","title":null,"venue":null,"work_id":"fb406d19-42f9-4376-b816-adabe650f021","year":2006},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.074758Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:94d963073ea146f1f1cedcf4bd609e8905162e37cbbf47b7098d59bebf760709","observation_id":"8cc1dc77-68ff-46ac-a36c-d18fe7490119","resolution":{"observed_at":"2026-08-07T13:08:42.615114Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:42.241197Z","title":null,"venue":null,"work_id":"f2c91843-f07c-44a7-af8c-ddb5bf8c6138","year":1995},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.156546Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:ec5102e06092859a84dc4a1e5f2b4c8c8a74e0310e280cd2b8c8aa3b025515c5","observation_id":"633491b0-2d5e-46c4-8566-d272856b9a41","resolution":{"observed_at":"2026-08-07T13:08:42.369028Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:41.989669Z","title":"D., Holm, D","venue":null,"work_id":"77b982d5-e89f-4b65-bb48-bba24b7ee7c4","year":2006},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.294832Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:9465e2c5f3fa766ac4d29000031119090373968887af65cb31b0e14d72b66fe7","observation_id":"e9f51cd1-08a7-42a2-8b69-8d5304953091","resolution":{"observed_at":"2026-08-07T13:08:42.090066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:41.760494Z","title":null,"venue":null,"work_id":"2691ae9e-1a6a-45a5-b802-492360273a6f","year":2008},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.425835Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:df5a7cb12e52c1694a99cb790ec5158122e8fbf6191f89525139c4afe1b253e4","observation_id":"45547a1e-1690-4fdd-bbc7-b1bd81649f9a","resolution":{"observed_at":"2026-08-07T13:08:41.891813Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/jfm.2013.391","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:08:29.386764Z","title":null,"venue":null,"work_id":"dfc4c340-bf03-4a42-8aa1-b0c40fe8bd30","year":2013},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.505982Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:2dd3e684172971f0f1584a37f578133ab74ca46af6187d12e2a729004a1514c9","observation_id":"34685294-0777-430c-a801-d005911014a8","resolution":{"observed_at":"2026-08-07T13:08:29.437904Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:41.540219Z","title":null,"venue":null,"work_id":"9ae7010c-4ac8-42b2-b622-f771c6691572","year":1999},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.589655Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:f5d8ced564a6444e03ffef2ef9b22b6c2d07352a428d566d5b02027c9d840204","observation_id":"512a681a-7a83-410d-995a-f2740ffe054a","resolution":{"observed_at":"2026-08-07T13:08:41.641615Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:37.514144Z","title":"L., & Berkooz, G","venue":null,"work_id":"0fc34ff7-b4c0-4a85-a152-700965076d5d","year":1996},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.736602Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:c7dca0b09ce0de89ee712264c620e277be680141b32a261d3c92969f1bbd0ca9","observation_id":"f5933ebf-6407-4a28-9c7c-298956e0e577","resolution":{"observed_at":"2026-08-07T13:08:38.858259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:37.104120Z","title":null,"venue":null,"work_id":"8ced7bb9-3580-4def-a124-84065e0e5f6c","year":1951},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.835608Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:082108e32b214a2f70760632ca66562cb606be84d7cea0739b2281bad1cd7819","observation_id":"84f32157-d514-42b6-8f07-b9f170c2808d","resolution":{"observed_at":"2026-08-07T13:08:37.246834Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:36.716360Z","title":null,"venue":null,"work_id":"4ac1ba91-b83e-4417-bcd1-66d6908bd57f","year":2016},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.883373Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:8242b0f34444608ca2828769fb70d74b5cfbd199e4a3adaead6ae5ba0dba7296","observation_id":"ad8aaa4c-4e37-4432-9f60-5b529f05defb","resolution":{"observed_at":"2026-08-07T13:08:36.885590Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:36.460042Z","title":null,"venue":null,"work_id":"9e9bfacf-7dd0-4b10-af09-a1e26a9554a4","year":1941},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:26.981748Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:4efb50c84ed96874fc90033ea70f43c037f5a804e19fd99652cbc98b1518d9dc","observation_id":"d285a9a8-1100-43a6-8949-f6c06053d7fb","resolution":{"observed_at":"2026-08-07T13:08:36.572463Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:36.350608Z","title":null,"venue":null,"work_id":"d3225330-510a-411b-bc5c-81827a52e3f5","year":1969},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.070885Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:58c8b03a218b25b9ad34a056130e0cb30a2614ff9329194557421610ebd913b6","observation_id":"a658bf1b-047f-4267-ad37-15e66a38b273","resolution":{"observed_at":"2026-08-07T13:08:36.403165Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:36.204256Z","title":null,"venue":null,"work_id":"b49241f3-7b93-456f-ac05-26e54e54a690","year":1934},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.136661Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:9b4f3f6e32ec1166d6cae7d5b8b4c2e7a41b261e6bf41e0f7149dbbd13fdfd30","observation_id":"4fe6319c-5ca6-4fad-b55f-1af19e96c42c","resolution":{"observed_at":"2026-08-07T13:08:36.277729Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:36.090021Z","title":null,"venue":null,"work_id":"afcf781d-0731-4cb5-968c-dd842889df5f","year":2002},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.187479Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:aa7281d642ef443b32abcf834f1b1a8a90d2adc08f77ef67fca376647594b33a","observation_id":"a8f902ee-0d5d-4a0a-bfdc-04913d7f7694","resolution":{"observed_at":"2026-08-07T13:08:36.142314Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:35.960856Z","title":"The Navier-Stokes problem in the 21st century","venue":null,"work_id":"b19b3bc8-b90b-4c03-9673-90119c89f9ff","year":2023},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.244757Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:d4a5609500f4b1c285bbca30b0343c75d857011a9d36bfc0f9303cf63733b1f4","observation_id":"5f10c385-22c5-41f5-b3f4-78de142b4b36","resolution":{"observed_at":"2026-08-07T13:08:36.024882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:35.799543Z","title":null,"venue":null,"work_id":"899736cb-79b4-448e-90ab-dcc044774497","year":1973},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.344762Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:12bd7159978ade6b6f2bfbd038d4597342b820584af949894319a99c5a037a41","observation_id":"861583eb-da60-429d-9608-ef3296220629","resolution":{"observed_at":"2026-08-07T13:08:35.904099Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:35.678125Z","title":"J., & Bertozzi, A","venue":null,"work_id":"ccfc6095-9862-436e-bc25-177e36bf5086","year":2001},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.454827Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:7b48b64142f45ef2829bbd5df1be3ed468b67d28ebc5f1fd01b436d65316883e","observation_id":"93d72681-8282-4176-829b-e8d8f4dbad5f","resolution":{"observed_at":"2026-08-07T13:08:35.735934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:35.402998Z","title":null,"venue":null,"work_id":"032fbb7a-03e3-4082-8fd8-9363a58081a3","year":2008},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.506963Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:83fef0382ab07091a5696dfb4a751208d957dbcff142e03bc5da177f57a60b54","observation_id":"5d5229fe-c96a-4dd4-a4af-4d3bf335cb5d","resolution":{"observed_at":"2026-08-07T13:08:35.544070Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:35.272244Z","title":null,"venue":null,"work_id":"9d999b46-2b4e-4b1d-8cae-3ddb4259728f","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.601638Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:34b4aa81df79ddcb0c4ae64690662ce1b5fe78321bcbc3645555337b28773404","observation_id":"a5521c0f-372a-4dc0-8644-f3444e36d926","resolution":{"observed_at":"2026-08-07T13:08:35.336182Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:34.315138Z","title":null,"venue":null,"work_id":"09eb4203-4afa-4d93-baf8-e1dd7bd2338a","year":1904},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.684841Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:81219efbf29a95e2e79a8d24e000b40cd40a203d797cea133a83cf3b4dc234f6","observation_id":"3e5dff82-91fe-46e4-b1c3-2364ee4808f2","resolution":{"observed_at":"2026-08-07T13:08:35.203165Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:33.181401Z","title":null,"venue":null,"work_id":"3a9fe47d-83de-410b-98f3-c934cd3df8b6","year":1959},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.774757Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:f8929113edaa2ea478a8e731922bdd423d26bb49a3bc69ce5895cebb033fb6bd","observation_id":"9e698ec1-8758-4d2e-8d10-a659f63764e2","resolution":{"observed_at":"2026-08-07T13:08:33.336055Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:32.964229Z","title":null,"venue":null,"work_id":"b4b47e00-4f18-4197-a0ff-76d80bef373e","year":2008},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.851501Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:edaf1d43da0cc0f2eb7d9b215f6b5c852b613d8e50c394170dcfd6a7abe751bf","observation_id":"4e8189f9-658c-4445-897e-ce98bf59fde7","resolution":{"observed_at":"2026-08-07T13:08:33.080234Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:32.774062Z","title":null,"venue":null,"work_id":"af7c513b-c7d5-4643-afc6-299e0d5a9712","year":1922},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:27.904891Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:2e126314b52f555b6046b6a0dff07f4aa2a27a47d8aa66649bd8d07a262e73bf","observation_id":"9f7b46b1-9e73-4c15-84e6-3dbdcc071f35","resolution":{"observed_at":"2026-08-07T13:08:32.865925Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:32.579786Z","title":null,"venue":null,"work_id":"5ca2f0e9-a373-469a-976f-825d7daab8c0","year":1991},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.014831Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:71f064ecbd04b8886658b2f94d7fd01c8a2580cd38ab9a22dda343ca63841d39","observation_id":"a4e6bbc4-9fad-4dff-90b5-a05ab6cb6435","resolution":{"observed_at":"2026-08-07T13:08:32.676054Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:32.340565Z","title":null,"venue":null,"work_id":"482bf3ca-144f-4173-b862-068269c8a6c1","year":2001},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.094762Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:671692ca94211a520e85f70123a967e344283d36ca4abc0c3624bd54065e1e54","observation_id":"e8ad94b2-8bc8-47d7-aeec-ac5d33eaf4ed","resolution":{"observed_at":"2026-08-07T13:08:32.488531Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:32.050141Z","title":"J., & Henningson, D","venue":null,"work_id":"e936c2a5-48db-4dff-b162-499f4a1d0f76","year":2001},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.144756Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:6704818a7653ec350e8df70b6359745bb888779ece2c508321157a906a774198","observation_id":"03e50dbd-4385-4985-898e-75bb1088ad29","resolution":{"observed_at":"2026-08-07T13:08:32.193205Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:31.851404Z","title":null,"venue":null,"work_id":"097d0fe1-8ea6-47d3-b661-644022cc8ede","year":1963},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.215623Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:efd60987d936c98251f868dcea2e9b938cde61d0e5a8691b012722755bcfd823","observation_id":"254ca904-4b97-41d5-b7d3-c066c1124905","resolution":{"observed_at":"2026-08-07T13:08:31.952186Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:31.716941Z","title":null,"venue":null,"work_id":"2a0e5773-3b3f-429e-900e-0874464d27e1","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.284756Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:8930ee5839486bf2243d625e586200c27a4c438563025cf5b8a22f9aac707d89","observation_id":"1c9165f0-9d2b-4ba6-a302-6168e4683d0d","resolution":{"observed_at":"2026-08-07T13:08:31.760918Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:31.533444Z","title":null,"venue":null,"work_id":"56f9ce6a-9a58-4ec8-be36-9106a6c203ec","year":1988},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.353875Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:78aa28d6f68564dca68174ffae030c38a7bdd107bb74772224b564e33a9fbccf","observation_id":"5370316e-9c6a-4d65-b29e-acdaf4a69544","resolution":{"observed_at":"2026-08-07T13:08:31.632906Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:31.368945Z","title":null,"venue":null,"work_id":"e7101054-accb-4191-b324-0ecd4c80d68d","year":2000},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.446019Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:6d3227190c08cc07edd63f52d9fef75722454d38f957a699054b5ced19e59176","observation_id":"7de8626c-c77d-4d50-a357-4ed900c3cd2d","resolution":{"observed_at":"2026-08-07T13:08:31.452489Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:31.224741Z","title":null,"venue":null,"work_id":"b4d8b885-67c0-45ab-86ec-45e84a1188f6","year":2007},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.581749Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:25bbb55e32e35fde331aac7ebdf11c5778682f57995c7b8ff5a6bbbf0b50cd6d","observation_id":"78ece879-6c2a-447d-9989-f1e9ed3dcfba","resolution":{"observed_at":"2026-08-07T13:08:31.299260Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:31.094961Z","title":null,"venue":null,"work_id":"5b2df436-807e-4e3c-8eda-3637a9e80e6f","year":2001},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.694756Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:e243e487ecceaaca8c378e0104a5bbec4e4c3fefde2d1d00d094a81e3e250055","observation_id":"401b7374-ff4e-4e7d-beeb-629b11b349fb","resolution":{"observed_at":"2026-08-07T13:08:31.146107Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:30.944876Z","title":null,"venue":null,"work_id":"e557b3cd-053b-4617-90be-eda725306233","year":2000},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.776914Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:d9991bd04f8576bbd74178474f0891942d8728398598283f81e4efd772747cc2","observation_id":"a8efc247-187d-446c-a9f5-16b0d5f6efd1","resolution":{"observed_at":"2026-08-07T13:08:30.997870Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:30.677831Z","title":null,"venue":null,"work_id":"f2845004-9759-4f82-911e-6c739089872f","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.832578Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:5dfe99613fc652ae028f77fc489acdb4c0fa59d4ba9adae23ea6299be4f642f6","observation_id":"c806552d-c71c-4d44-822f-3572335bb056","resolution":{"observed_at":"2026-08-07T13:08:30.786794Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:30.518639Z","title":null,"venue":null,"work_id":"66818d88-2abc-4b11-ad12-4c6325234ed4","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.897916Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:e16a19aa967b9e37662aaaf8f318d7d68234660d04c34d2ac71c2c9954929781","observation_id":"55a49a6f-bb53-4260-bde6-8d9ba89f6efc","resolution":{"observed_at":"2026-08-07T13:08:30.594896Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:30.264268Z","title":null,"venue":null,"work_id":"f61d5d3f-7d56-4fd3-9978-9ccec1bf3217","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:28.968907Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:8b7c7abd5833442c4e9970dcc429b536ad35088358e84c25a685203992885df9","observation_id":"010fe696-8161-4d0f-9d8b-b5d894a6550d","resolution":{"observed_at":"2026-08-07T13:08:30.395479Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:30.008521Z","title":null,"venue":null,"work_id":"6267a743-5b78-4562-88bf-a53a1863fbf3","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:29.124773Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:dcd5623143da60511c1d87aa6b1aa5a5e8c75c74961608ccacf4ee2f3205cd7a","observation_id":"f0bfd78b-bab8-4ef4-a751-af2b4c0f4ce3","resolution":{"observed_at":"2026-08-07T13:08:30.141922Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:29.692386Z","title":null,"venue":null,"work_id":"b0ce177c-184f-433b-9a4b-14d5c19670ad","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:29.234749Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:08d6e71c0baeef4ae50d638a97175013ee5b37a7f27fd8f9011de125828e5a01","observation_id":"26134203-b646-45fa-ac0c-039cad1bd1d3","resolution":{"observed_at":"2026-08-07T13:08:29.792618Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T13:08:29.514096Z","title":"This construction shows that the intermittency exponent bound is sharp and cannot be improved without additional assumptions on the flow structure","venue":null,"work_id":"1326e241-9820-486f-b3ce-eb75d4a76ae0","year":null},"citing_paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T13:08:29.314755Z"},"links":{"citing_paper":"/paper/2505.22853"},"observation_digest":"sha256:9d3ac6b21f51a3d43a0ed2344a7c955a2c67e6be0a91b8041bc0276d8ce531d8","observation_id":"7f872704-82a2-4cb8-8747-5cac31a6bdb9","resolution":{"observed_at":"2026-08-07T13:08:29.586842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.22853","last_updated":"2025-06-08T06:17:58Z","latest_version":3,"primary_category":"physics.flu-dyn","snapshot_observed_at":"2026-08-07T12:56:41.102323Z","submitted_at":"2025-05-28T20:37:33Z","title":"A unified quaternion-complex framework for Navier-Stokes equations: new insights and implications"},"reference_resolution":{"displayed":49,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":39,"verified_exact":1,"verified_fuzzy":8},"total_outbound_references":49},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2505.22853."}