{"as_of":"2026-08-14T23:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:83a51a16cfd9cf145c733b05fc8c1f996edc935d5d1dd7a808a131420bd6e5b8","coverage":[{"denominator":58,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":58,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T11:02:51.149406Z","state":"measured"},{"denominator":59,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":59,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-16T18:44:24.058799Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-16T18:48:17.242454Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"cited_work":{"arxiv_id":"2411.18724","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.18724","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"e32b8fbe-d8cc-4b02-8dda-aeb6a2b29c48","year":2024},"citing_paper":{"arxiv_id":"2601.08854","last_updated":"2026-05-04T02:06:53Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-01-02T03:33:50Z","title":"On Geometric Evolution and Microlocal Regularity of the Navier-Stokes Equations","version":4},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-16T18:44:24.058799Z"},"links":{"cited_paper":"/paper/2411.18724","citing_paper":"/paper/2601.08854"},"observation_digest":"sha256:3fd38b97f9a2707c9a6513eddb21eb6789e27b470e906dc398fb51b9ae36599f","observation_id":"b7fd5700-ab35-4c94-84fd-f69962d96fb6","resolution":{"observed_at":"2026-05-16T18:48:17.244645Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.18724/citation-record","integrity":"/paper/2411.18724/integrity","json":"/paper/2411.18724/citation-record.json","paper":"/paper/2411.18724"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2407.14533","last_updated":"2026-05-10T06:04:41Z","snapshot_observed_at":"2026-08-03T06:48:22.490000Z","submitted_at":"2024-07-10T04:21:33Z","title":"A String-Graph Approach to Molecular Geometry","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.14533","snapshot_observed_at":"2026-08-12T11:02:50.888629Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.888629Z"},"links":{"cited_paper":"/paper/2407.14533","citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:f0bb9b299106a800dffcb59b97b13d1f94fdd162ce7e17643cedb14a7fb3520a","observation_id":"b50738f4-3d32-44f0-ae21-228c25de9804","resolution":{"observed_at":"2026-08-12T11:02:50.888629Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:02:52.102390Z","title":null,"venue":null,"work_id":"3a5d36d3-24ca-44a7-8326-52724b922595","year":2014},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.898902Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:75198220a87102ecbf3f51cb786cf534d31e52e162d13270118845604eb4d6ef","observation_id":"b723536a-a290-4de5-9c9f-5a5fe5306636","resolution":{"observed_at":"2026-08-12T11:02:52.106803Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:52.088599Z","title":null,"venue":null,"work_id":"c69c4c2a-6e86-445d-9d38-30113b78673e","year":2023},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.903701Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:6dcae4779cedd4268e31684592c28459c7550337f539a4d055e4597173e9abb5","observation_id":"921c21e6-a6dc-449e-9b02-d32661694eb9","resolution":{"observed_at":"2026-08-12T11:02:52.092863Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:52.075225Z","title":"Lovelock and H","venue":null,"work_id":"42dff2ff-6710-476e-96d4-ed8a552aed06","year":1975},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.908199Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:1ddc286020c32d3af5c8b2c3668931f33a13b433fb58220ba25f0ab5dac3289a","observation_id":"f1382aa7-5010-4347-9708-309513c1c198","resolution":{"observed_at":"2026-08-12T11:02:52.079394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0710.1604","last_updated":"2009-05-21T18:01:19Z","snapshot_observed_at":"2026-07-06T01:31:36.983196Z","submitted_at":"2007-10-08T17:58:11Z","title":"A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0710.1604","snapshot_observed_at":"2026-08-12T11:02:50.912693Z","title":"Tao, A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation, arXiv:0710.1604v5 [math.AP], 2009","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.912693Z"},"links":{"cited_paper":"/paper/0710.1604","citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:b3091a119a451ffbcdd14725748dd153b418d81f066a8fcc283cf452040e0995","observation_id":"c6b773ad-502a-40af-829c-89fe7af98118","resolution":{"observed_at":"2026-08-12T11:02:50.912693Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:02:52.061675Z","title":null,"venue":null,"work_id":"06e4d651-fbaf-4322-a74d-4e4ffc67a275","year":1953},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.917418Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:dcbe885f08aa93165f09036d22091c2b336455c7db475dbdbe9a454e0e2838b8","observation_id":"1959331c-72c1-4591-9372-62428fe9561a","resolution":{"observed_at":"2026-08-12T11:02:52.066164Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:52.048686Z","title":null,"venue":null,"work_id":"462b4cc5-184a-4b9f-a2c5-6a743a81c4fb","year":2022},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.922132Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:332219e06b7cf8458ee9082cebfd433ff4b153b88efd1a819bb38a02c9f6e11e","observation_id":"38313c0e-bbc6-4d80-9c3b-2ce0bb901784","resolution":{"observed_at":"2026-08-12T11:02:52.052997Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/9809061","last_updated":"1998-09-21T22:05:47Z","snapshot_observed_at":"2026-07-07T03:29:29.245070Z","submitted_at":"1998-09-21T22:05:47Z","title":"A Second Poincare' Group","version":1},"cited_work":{"arxiv_id":"gr-qc/9809061","doi":null,"metadata_source":"pith","pith_arxiv_id":"gr-qc/9809061","snapshot_observed_at":"2026-08-12T11:02:51.266081Z","title":"A Second Poincare' Group","venue":"gr-qc","work_id":"1c9033f3-3097-4c19-8155-46a1a26d2e7c","year":1998},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.927547Z"},"links":{"cited_paper":"/paper/gr-qc/9809061","citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:33f00f20568e9a192f3cd35324fa1c0bc21c854c4cf150ef829f17f23f897c97","observation_id":"0b42199c-bcc1-4b6a-88d4-f956e8e30c39","resolution":{"observed_at":"2026-08-12T11:02:51.270760Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:52.034980Z","title":"Antoniadis, L","venue":null,"work_id":"b525e9cc-e221-4b3d-8a30-502c87ab1970","year":2011},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.932268Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:24b1a39dbdf403a9160eae8bcf15406f473fd66b7f8c5f08ffe097e6a864c996","observation_id":"03d6d8f9-e7fb-493c-9940-fdd2be56d314","resolution":{"observed_at":"2026-08-12T11:02:52.039579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:52.021170Z","title":null,"venue":null,"work_id":"3ee0a6c9-c158-49de-bda8-f62d1bd840c8","year":1969},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.937414Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:3488dd5e424c590bd1163db0babc71c94c87d0659fed361d260b2deab94c9dcb","observation_id":"cfe1520f-df70-46ac-a3f7-b99dc692d60b","resolution":{"observed_at":"2026-08-12T11:02:52.025386Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:52.007772Z","title":null,"venue":null,"work_id":"56291df3-19a2-4b39-a2c6-ffe6ddf05f95","year":2013},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.942212Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:543a3677085b488500c97cff8e008043e5e63b7b5e366e7390623e04b9808a93","observation_id":"947e182b-72fa-4266-a983-b90e12587140","resolution":{"observed_at":"2026-08-12T11:02:52.012221Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/9805120","last_updated":"1998-06-12T00:45:37Z","snapshot_observed_at":"2026-08-07T15:59:09.112528Z","submitted_at":"1998-05-27T05:09:30Z","title":"Real forms of quantum orthogonal groups, q-Lorentz groups in any dimension","version":2},"cited_work":{"arxiv_id":"math/9805120","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/9805120","snapshot_observed_at":"2026-08-12T11:02:51.245748Z","title":"Real forms of quantum orthogonal groups, q-Lorentz groups in any dimension","venue":"math.QA","work_id":"d72dfa25-1c7e-467c-a7e2-cc4193a9d420","year":1998},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.946699Z"},"links":{"cited_paper":"/paper/math/9805120","citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:059cca53fcbe9f6005f308965e58464b5b45244f321f2a9502cb7faf3e4ec648","observation_id":"f9bc9f09-5100-4e6f-a87d-5c45da15cf06","resolution":{"observed_at":"2026-08-12T11:02:51.250953Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.994204Z","title":"Bacry, P","venue":null,"work_id":"93639592-31ae-4140-8e2f-ab17f8f03012","year":1972},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.951354Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:bab5c2bd7d8cb91dd221fc02368368e559b95deb2865340fb0f7cbe71c3096a9","observation_id":"ebb45fb9-f762-4ff0-9bc8-07885a956232","resolution":{"observed_at":"2026-08-12T11:02:51.998556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.980309Z","title":null,"venue":null,"work_id":"c0ed89e9-0ffa-4c1a-8146-b470fe882529","year":2020},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.955689Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:140fcab9f8cd0aefd625a7e434ab07a7d9df5a7a7743a6b5f067f9c4b2bebd47","observation_id":"e625ba8f-2262-40f0-b4da-d49f00adc6c3","resolution":{"observed_at":"2026-08-12T11:02:51.984797Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.966171Z","title":"Banerjee, Null Infinity and Unitary Representation of the Poincare Group , J","venue":null,"work_id":"5af24c7f-a4c5-4822-be05-5b1c2cd3fa73","year":2019},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.960719Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:84f796c3ecca3d77c02771c379c864c717db55f97c7e79f1e99584c197c8f31f","observation_id":"a8fdbaaf-15bf-4659-9df0-d10694fd8f9a","resolution":{"observed_at":"2026-08-12T11:02:51.970963Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.952196Z","title":"Becker, M","venue":null,"work_id":"939b6937-20fb-4d75-9000-c414e3898bc7","year":2007},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.965212Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:fbeb1066e8ba9e7495e9ee7f801e58542bdd769224b3d9534453ab7c178ef847","observation_id":"86e7dcc4-763e-465d-8dd9-a7759c7f6a44","resolution":{"observed_at":"2026-08-12T11:02:51.956740Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.938458Z","title":null,"venue":null,"work_id":"e8b46139-e4df-498e-87b8-d8a192e4bf51","year":1987},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.969592Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:ad5e4f6fa9bb84c32ef732a25dd5d83badde0500dda7f50b9e29052f0d282706","observation_id":"610c0006-c0fa-4dea-beb2-f37deea9b0a5","resolution":{"observed_at":"2026-08-12T11:02:51.942773Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.924720Z","title":"Brink, A","venue":null,"work_id":"d428363d-6516-4f58-a0d3-7f2b900d73ec","year":2002},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.974258Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:50d7119eb63f00fd5e34c268ab13e09aa7e7ac4212305cb8b7f1b74c11e48b2a","observation_id":"153e904d-341a-4b70-bc9c-3d143bd94a8b","resolution":{"observed_at":"2026-08-12T11:02:51.929113Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.910477Z","title":null,"venue":null,"work_id":"7a4695ef-34e0-44ff-9218-8edcc331cc58","year":2014},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.978600Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:43d318099e04f631f614c5f68a16f79f5fb32c4f95b415ce52523c125875839a","observation_id":"fa28db96-b542-48ad-9fa3-9b1e8720fc28","resolution":{"observed_at":"2026-08-12T11:02:51.915060Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.896535Z","title":"Budini and C","venue":null,"work_id":"b694ec53-6caf-4f6b-aa1f-5aaad1e14c88","year":1965},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.982822Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:26784ba54a08c2a6f699136f9f1bb4134fb7f92b39099ac3a78295f5e252fa72","observation_id":"68d43dff-89b1-478a-a4df-f881b105e124","resolution":{"observed_at":"2026-08-12T11:02:51.901092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.882220Z","title":"Diestel, Graph Theory, Springer, 2017","venue":null,"work_id":"4b791326-a923-49ae-9b0c-1b66c464c82c","year":2017},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.987574Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:1b32dc51b713bdf2124bd8aefc7830732c85622a59f8457e1d32c4287b788d4b","observation_id":"681c9c93-3b59-4250-b38a-8c24964eb309","resolution":{"observed_at":"2026-08-12T11:02:51.886973Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.868243Z","title":"Einstein, The Foundation of the General Theory of Relativity, Annalen der Physik, 49, 769-822, 1916","venue":null,"work_id":"b6ab3364-190c-4cd0-aa08-84fd6e4e5e18","year":1916},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.992039Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:87f523e7c69069c1c1d9b488037a4c1a758e2b262d76db9ff20d30f4edcc5c4d","observation_id":"9ebf395d-a3b6-4714-b4ec-8641d62a778f","resolution":{"observed_at":"2026-08-12T11:02:51.872899Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.854182Z","title":"Frankel, The Geometry of Physics: An Introduction , Cambridge University Press, 2012","venue":null,"work_id":"77fc328f-09e4-4ab4-8b9f-245c656a92f6","year":2012},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.996797Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:00c19740d2d86e142c8a30e6d268a8f57fea2adbdf1b8830d677ee9cbcb0adbf","observation_id":"612c9148-1467-441d-97f2-26f27cf6c852","resolution":{"observed_at":"2026-08-12T11:02:51.858636Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.840079Z","title":"Fushchych, R","venue":null,"work_id":"39df221d-9ad4-445d-8d02-b2d85e0b3f8d","year":1994},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.001307Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:f1169a581322085b83b8678f0d2c146eaddcc2e1296aa4b6b50a71ca70e13954","observation_id":"358decc5-ef9a-4760-8e4b-8f856f797bde","resolution":{"observed_at":"2026-08-12T11:02:51.844673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.825891Z","title":null,"venue":null,"work_id":"a0a48d66-e4dc-44b1-8260-ce4e3790cd5f","year":1992},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.005783Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:1b398e7639609bca20302e7b85e288c5d55fa376b5931cabf1940f2d5c22224c","observation_id":"507c7132-22ca-4dbb-a426-d6f39ae724ae","resolution":{"observed_at":"2026-08-12T11:02:51.830453Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.812375Z","title":null,"venue":null,"work_id":"0e76dca7-779c-4d8e-a90f-b53788970cff","year":1987},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.010503Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:5201d054947fe9a66769e4f4d35eae295e8a60bf9a29e52c398720efb4f8f246","observation_id":"9f858e27-b20f-4c50-81c1-7933e2e6b3c0","resolution":{"observed_at":"2026-08-12T11:02:51.816825Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.797903Z","title":null,"venue":null,"work_id":"e57fc15d-4dd7-4ba9-b9aa-4d45f2020b51","year":2008},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.015455Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:580fc7cf41970be32f489140a2089af7791a7f17a1caa893f1f46b50f1e16413","observation_id":"295872d2-0f15-49e2-8af7-a297d50c9e40","resolution":{"observed_at":"2026-08-12T11:02:51.802500Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.784575Z","title":null,"venue":null,"work_id":"daf9378a-83a8-449d-abbb-9c188ad1133f","year":2015},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.020081Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:3357406a6c0ee1770e15a8da5c84a2d130f528ae49ebbc65244e733d11b1d36b","observation_id":"bec137ee-3c94-4672-bfc9-8146e67cd504","resolution":{"observed_at":"2026-08-12T11:02:51.789011Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.770958Z","title":"Hess, Tensors for Physics , Springer, 2015","venue":null,"work_id":"f9dd8684-31be-4108-af7d-d325c07ed709","year":2015},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.024540Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:1e76ce193170089c076518626db9be64df215d5efb439e8b51ccc6cb7a0bc8c8","observation_id":"da32994c-e0a5-4607-914d-5b4027d2720e","resolution":{"observed_at":"2026-08-12T11:02:51.775449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.757092Z","title":null,"venue":null,"work_id":"b6b0542d-bb72-447a-9fa7-5140544c7519","year":2010},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.028879Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:f0a2b1422a835d234386007b039ec3aaa86c6d9bf038dba61548caff3aaf29c2","observation_id":"aba62006-47f2-4ee3-9016-0d433e00fe6a","resolution":{"observed_at":"2026-08-12T11:02:51.761428Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.742744Z","title":null,"venue":null,"work_id":"a47f29cc-3ea2-4408-8cc8-17e767e8806d","year":2000},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.033389Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:3a0324076b55433f709db9c3d840a73ecf6311b5d5d3ef569a36be00bc3dea63","observation_id":"76786426-1243-4638-af9c-ed9b510bb6d7","resolution":{"observed_at":"2026-08-12T11:02:51.747172Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.728810Z","title":null,"venue":null,"work_id":"25552249-a096-4ace-945b-0bfc44754323","year":2000},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.038110Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:68c7ddbb1052a40a392c64a0647d2d7e4804cd7fb98a6266b0af60154060e15a","observation_id":"7a02c798-737d-4003-aa76-78c17a81a464","resolution":{"observed_at":"2026-08-12T11:02:51.733438Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.714951Z","title":null,"venue":null,"work_id":"ffc2c039-81dc-4bee-af08-007cc5d095be","year":2009},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.042357Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:17c54daf0de97da94638c66864cd7d677fa520ffc1ba721dc684f574d248913c","observation_id":"a43e02e0-651a-4369-aba9-5cf41247c658","resolution":{"observed_at":"2026-08-12T11:02:51.719527Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.700781Z","title":null,"venue":null,"work_id":"7f42c4a7-2347-4c1b-ace5-8b8e2a315ba8","year":2013},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.046947Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:a596d9801875561f3f78b6c8063d8a1a51f88059617ce5942ac6ec0b0f01ec9f","observation_id":"76b39aed-b93c-46d3-ab53-a27ff28d2e6c","resolution":{"observed_at":"2026-08-12T11:02:51.705302Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.686268Z","title":"Leinster, Galois Theory , University of Edinburgh, 2023","venue":null,"work_id":"74e2c38f-06d3-47de-91e7-0c50228cc2db","year":2023},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.052135Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:c39559dac60894c40b452aba28106f83801cd60dff683c91f685d4b6dad3e390","observation_id":"fff26515-a8fd-4c0c-96f5-0afdec374613","resolution":{"observed_at":"2026-08-12T11:02:51.690794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.672207Z","title":null,"venue":null,"work_id":"3666b81d-5949-4a77-9fba-db7c1be3e207","year":2002},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.057598Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:15b4ca7bde1297ffee3498dfd0399cb5b3b12b2d0e4cc0948d5c12627b12e0d1","observation_id":"bc6e487c-5a8e-45bd-811e-b7156708e94b","resolution":{"observed_at":"2026-08-12T11:02:51.676818Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.658393Z","title":null,"venue":null,"work_id":"928865bc-d6f8-4977-b432-19ea3c8b4ad2","year":1967},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.061846Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:920ae0b56e2a53660550558c6b8d8e6c2bf9cd53fe76bc3c04d2a805bbadb54a","observation_id":"b1822e53-b471-4a67-99c9-735ad353fd5a","resolution":{"observed_at":"2026-08-12T11:02:51.662931Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.643649Z","title":"Mucherino, C","venue":null,"work_id":"054b7d1f-da20-49b1-abc1-ba02bee8b483","year":2012},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.066173Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:848446728a34027f26ba8ecd2a0ea4c5bf46fbb1858314ce31b35d5c2c754cc2","observation_id":"f07e57ad-8755-445b-9c08-55de952f8dd3","resolution":{"observed_at":"2026-08-12T11:02:51.648676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.628287Z","title":null,"venue":null,"work_id":"22e963c3-95fc-4fa7-8ee6-6b4f8306f8b2","year":2000},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.070599Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:a22c963cad17ce200033ee23e77ce6ac57b88a1c9e2abe0e6bd5456894d6dc0c","observation_id":"b89b1891-c0f8-4090-9138-9e5da2bbd438","resolution":{"observed_at":"2026-08-12T11:02:51.633825Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.614279Z","title":"Nakahara, Geometry, Topology and Physics , CRC Press, 2003","venue":null,"work_id":"a7c474b5-235d-4057-a5ce-99ce4681bafc","year":2003},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.074748Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:5d5ed9ccb328f2e0587bc59c582bbddb072963eb10a41181ec38323cce0b48b4","observation_id":"fff8dbb2-28d3-4076-995c-85bb13d9136c","resolution":{"observed_at":"2026-08-12T11:02:51.618966Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.600372Z","title":null,"venue":null,"work_id":"87d99c84-fa38-41ce-a2ae-1c0d14acd502","year":2014},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.078914Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:3ebc475e12b15fb1e9589bb47c2fc7de8156a1943645476820ad464763cea625","observation_id":"19a3ee76-3419-48a0-a16f-3b28acb9eab1","resolution":{"observed_at":"2026-08-12T11:02:51.604699Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.586347Z","title":null,"venue":null,"work_id":"4de20713-d6c4-4054-9455-b1f0249d5e55","year":2011},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.083511Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:f394a9c02146a7022d4b4c4637862accc4ddff9bc3b882005b084215bcd473d2","observation_id":"55c79bcb-6ad7-455a-8f42-30c7c04752bb","resolution":{"observed_at":"2026-08-12T11:02:51.591005Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.469319Z","title":null,"venue":null,"work_id":"c6303f7f-6e8c-4f0d-b20f-5b09644ae9ea","year":1995},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.087952Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:62ba7e77049b1ad45a88dc0b4d6cae359cbdd89e65fa1cf0eb53992d53912635","observation_id":"243e63e3-d442-4e29-ab5a-1497d5f278d6","resolution":{"observed_at":"2026-08-12T11:02:51.473712Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.455785Z","title":"Podles and S","venue":null,"work_id":"c7eb53ca-980c-48f8-91a2-28d35e68a0f8","year":1990},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.092299Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:aea1c57cf7a59f47f64cb43bd2ddb572995c4161255fa8320967a984cee7f6fe","observation_id":"ed0016f2-e93f-4678-9daa-f88d2e9192a7","resolution":{"observed_at":"2026-08-12T11:02:51.460288Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.440645Z","title":"Polchinski, String Theory , Cambridge University Press, 1998","venue":null,"work_id":"40e558ea-0753-47ad-95de-727d5f66f3c5","year":1998},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.096734Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:c16de6f654de26a30eee25e2c106b81ce916c13cd86a98152f3649d5622a63f8","observation_id":"30a1a9bd-ba7e-4365-8c6f-28086820c698","resolution":{"observed_at":"2026-08-12T11:02:51.446200Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.101053Z","title":"Rosales Ortega and C","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.101053Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:63166183f00c6a3285121a0d2073d52f5dcfa83ac0447c8a8da4e8061e60fd04","observation_id":"75c4c2a6-b5d4-4caf-97ea-d7adf6ce877b","resolution":{"observed_at":"2026-08-12T11:02:51.101053Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:02:51.426736Z","title":"Rovelli, Loop Quantum Gravity , Living Rev","venue":null,"work_id":"e086c6df-33a9-4be3-a9fa-452c75ce9754","year":2008},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.105348Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:92f1f79be75cc4a86e98497e495a208fbbff7c61f13a5e5227642a8eaa174b9d","observation_id":"c61ff0ec-07f0-46f0-a0bb-8895eace64c3","resolution":{"observed_at":"2026-08-12T11:02:51.431374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.413186Z","title":null,"venue":null,"work_id":"9a752405-150e-474b-9ca9-7a27b1ecf330","year":1974},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.109869Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:63e3d059be1f7464732fb0ab47752d231c90aa0c9b65debe04732ebec8d6a8ac","observation_id":"f3d1a80d-65e8-4a9a-a60a-cb817f34d6e5","resolution":{"observed_at":"2026-08-12T11:02:51.417592Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.398544Z","title":"Spivak, Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus , Addison- Wesley Publishing Company, 1965","venue":null,"work_id":"b1de120e-b52e-4dc3-8876-3290900aa692","year":1965},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.114042Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:4e3ec554dd0f57c61d30da823b335703cab5efbf195dff5a51b6188041c7d248","observation_id":"54c12dbd-eebd-4ffc-893c-e34792cf753c","resolution":{"observed_at":"2026-08-12T11:02:51.403235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.384579Z","title":null,"venue":null,"work_id":"6bb65599-4c45-40da-b428-b7f00f19dce3","year":2012},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.118384Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:427dfb4b32efa03673aaa00610bef4c8882fdc21328b0a43954b663512a49251","observation_id":"971e43a8-4811-4c4d-9d0c-c17b72027eee","resolution":{"observed_at":"2026-08-12T11:02:51.389063Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.369328Z","title":"Szabo and N","venue":null,"work_id":"fcfda809-b0b0-4f05-8084-4f6a56c13754","year":1996},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.122953Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:ef79a2515f09fde45885dbe5a82c7d6c97740b76dfc3619a0d0a08ae4feeb047","observation_id":"f112aa6a-bf3f-4557-b521-4e8dcacb404b","resolution":{"observed_at":"2026-08-12T11:02:51.374460Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.354032Z","title":"Thiemann, Modern Canonical Quantum General Rel- ativity, Cambridge University Press, 2007","venue":null,"work_id":"78e8858a-a9be-4c7e-8fbd-59b965391e52","year":2007},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.127376Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:397a15243599137195ea8c7ff30e2f43960765f939bcd68aab15560c4816d89f","observation_id":"081ea0cc-2117-4b8d-823d-ef168aef942f","resolution":{"observed_at":"2026-08-12T11:02:51.358738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/9310026","last_updated":"2009-03-20T21:49:19Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"1993-10-19T14:17:10Z","title":"Dimensional Reduction in Quantum Gravity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"gr-qc/9310026","snapshot_observed_at":"2026-08-12T11:02:51.131701Z","title":"t’Hooft, Dimensional Reduction in Quantum Gravity , arXiv:gr-qc/9310026, 1993","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.131701Z"},"links":{"cited_paper":"/paper/gr-qc/9310026","citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:e9b4e9d3a406758d4bad77676f517fffaec1e9c011aeb5f0285cdc0d2186f446","observation_id":"8a3d92bc-a691-4784-85aa-413da315f605","resolution":{"observed_at":"2026-08-12T11:02:51.131701Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:02:51.339845Z","title":null,"venue":null,"work_id":"0a8bf893-8aa1-4308-97bc-2dc7bf14a593","year":2014},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.136700Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:cd2378cce7f2800e2cefd5f8c7d2b27f4b50c1ce879cee12300b99db23c34101","observation_id":"6da32a03-9231-4d6b-9582-82a983c188ae","resolution":{"observed_at":"2026-08-12T11:02:51.344343Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.325183Z","title":"Weinberg, The Quantum Theory of Fields , Cambridge University Press, 1995","venue":null,"work_id":"a39acba3-a994-4f0e-ae5f-811d8f9e46f0","year":1995},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.141049Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:5df79bd790386080879cc8e6b11abec89496d04bcea446d59af9c9b87bb3c015","observation_id":"e7cf2494-5a2a-4672-aca2-5657123ebf58","resolution":{"observed_at":"2026-08-12T11:02:51.329947Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.310512Z","title":null,"venue":null,"work_id":"83aa6258-a595-4943-a23d-fb5b20e9fd94","year":1934},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.145089Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:df01df4c1b095af1cf3c65367f9d251aca5da08fa728dd58a3d99b8fe1fd7f03","observation_id":"e2b347eb-32b7-47df-985a-9658961a91b7","resolution":{"observed_at":"2026-08-12T11:02:51.315432Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T11:02:51.295719Z","title":"Zwiebach, A First Course in String Theory , Cam- bridge University Press, 2009","venue":null,"work_id":"c0f5b3c5-b2e3-4b79-9442-722bd03cc92f","year":2009},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:51.149406Z"},"links":{"citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:5e2fc0c2ab32793357cff8d1d3618b9b8c65d245d599257616bf0e11f285a869","observation_id":"fa38a1da-6cc5-488c-ab27-6277211528ce","resolution":{"observed_at":"2026-08-12T11:02:51.300771Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.14533","last_updated":"2026-05-10T06:04:41Z","snapshot_observed_at":"2026-08-03T06:48:22.490000Z","submitted_at":"2024-07-10T04:21:33Z","title":"A String-Graph Approach to Molecular Geometry","version":4},"cited_work":{"arxiv_id":"2407.14533","doi":"10.48550/arxiv.2407.14533","metadata_source":"pith","pith_arxiv_id":"2407.14533","snapshot_observed_at":"2026-08-12T12:16:16.734455Z","title":"A String-Graph Approach to Molecular Geometry","venue":"physics.gen-ph","work_id":"b5755d5f-a9b5-4a4d-8edc-c49cda8624cf","year":2024},"citing_paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations","version":2},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-12T11:02:50.894178Z"},"links":{"cited_paper":"/paper/2407.14533","citing_paper":"/paper/2411.18724"},"observation_digest":"sha256:5ee41244633c26dc9423ddb1532dc9a1ed96c281eab6d6c595e5f5e3ae239c5c","observation_id":"ee86356c-5a0a-420c-a035-8c3960be3b8c","resolution":{"observed_at":"2026-08-12T11:02:51.215227Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.18724","last_updated":"2024-12-04T02:58:39Z","latest_version":2,"primary_category":"physics.flu-dyn","snapshot_observed_at":"2026-08-14T02:06:13.843122Z","submitted_at":"2024-11-27T19:54:45Z","title":"A Geometric Approach to the Navier-Stokes Equations"},"reference_resolution":{"displayed":58,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":32,"verified_exact":3,"verified_fuzzy":23},"total_outbound_references":58},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 1 inbound Pith citation observation for arXiv:2411.18724."}