{"as_of":"2026-08-11T16:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1f1d6372fd4305d0959c40b92cd99925272881de47d2488c180f9e2f135b437d","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T00:18:53.989122Z","state":"measured"},{"denominator":50,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":50,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.00843/citation-record","integrity":"/paper/2608.00843/integrity","json":"/paper/2608.00843/citation-record.json","paper":"/paper/2608.00843"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:19:01.202346Z","title":"A stable finite element for the stokes equations.Calcolo, 21(4):337–344, 1984","venue":null,"work_id":"4d58cb70-5284-4ef7-bcf6-7a7a320afcc5","year":1984},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:49.419540Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:2ce6dca519b1feef67359b5ab9d8f83a284d0fb5a284c667459ecdc15a75e68e","observation_id":"0aa008cd-9393-4a7d-bb01-d106aa2ef26d","resolution":{"observed_at":"2026-08-05T00:19:01.278978Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:19:01.046713Z","title":"The finite element method with lagrangian multipliers.Numerische Mathematik, 20(3):179–192, 1973","venue":null,"work_id":"6aedc53a-f5b2-4b41-9cff-afd2ad7d05bf","year":1973},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:49.497950Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:d0e348ebba023c930aace7e710636fb5e382947454702c5df3f99a8f7ab017ec","observation_id":"93bfc5ca-08fd-467d-8a44-e15e34388d8e","resolution":{"observed_at":"2026-08-05T00:19:01.116228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:19:00.865688Z","title":null,"venue":null,"work_id":"9f085db4-b1cf-4f6b-a537-083544892f98","year":1993},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:49.628283Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:648e59c03a636a61a3d002836a212f2d47084dd296e5ddafdec4357c690c2808","observation_id":"9f7f43d5-5d10-4dd1-86e3-a74705958dbf","resolution":{"observed_at":"2026-08-05T00:19:00.969142Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:19:00.691818Z","title":null,"venue":null,"work_id":"4f0d9114-cfc1-48fd-a851-8a61c321eaaf","year":2007},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:49.737959Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:0236353352fabddd4b7262f22b1f9b3da21f56c9164019740fdab07258014628","observation_id":"41d963e2-9a97-4909-a446-c3f301330640","resolution":{"observed_at":"2026-08-05T00:19:00.766377Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:49.841698Z","title":"Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method.SIAM Journal on Numerical Analysis, 43(6): 2544–2566, 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:49.841698Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:1472aaf01e6decc3517e7130d0d69d4723cfdeb1552c444b6b332fcc28ae7e83","observation_id":"ec138e8f-bce6-4bec-bd09-dcf0bb0d1397","resolution":{"observed_at":"2026-08-05T00:18:49.841698Z","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":"2026-08-05T00:19:00.530028Z","title":"On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers.Publications mathématiques et informatique de Rennes, S4:1–26, 1974","venue":null,"work_id":"2469eebc-c354-41f3-b2b7-7e020b5e3fba","year":1974},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:49.937193Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:1cf335842a7c3efa1a367701c3ca200b4e161280c71df247f6888f036c8a9a2b","observation_id":"99cd6d02-a9e9-4f54-955d-6f742f3380cd","resolution":{"observed_at":"2026-08-05T00:19:00.610179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:19:00.375500Z","title":"Springer Science & Business Media, 2012","venue":null,"work_id":"833b756a-b13f-45df-a96a-8dd53f59de56","year":2012},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.037815Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:3299b551d0b81754a757b9dae1118cbd75572859cf21ffd6814b1fc6c1d1f63e","observation_id":"c6ff938d-3cd1-4f62-b92d-6c4c1cffeaee","resolution":{"observed_at":"2026-08-05T00:19:00.460679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:19:00.199106Z","title":"Choosing bubbles for advection-diffusion problems.Math- ematical Models and Methods in Applied Sciences, 4(4):571–587, 1994","venue":null,"work_id":"79dd78ac-2fac-40e2-a94a-fc6ac94ad30c","year":1994},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.155565Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:2875f7e0e6c701f499a258d18442ef92b091beacc459eb8503fea2f8081be6dd","observation_id":"d75fb253-2e12-453b-b27f-0baf975e0896","resolution":{"observed_at":"2026-08-05T00:19:00.277394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:19:00.040809Z","title":null,"venue":null,"work_id":"d0cb7fc3-c37f-4818-968a-8e6f244decd4","year":1982},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.287629Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:038014d220bfbbdbea59d1679188ecccceb181e7b81936ea123afcbcf9718eb5","observation_id":"dffd673e-6e52-495a-8237-e9d01f6be04e","resolution":{"observed_at":"2026-08-05T00:19:00.113232Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.cma.2004.01.030","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Edge stabilization for Galerkin approximations of convection– diffusion–reaction problems.Computer Methods in Applied Mechanics and Engineering, 193(15– 16):1437–1453, 2004","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"b9b3b695-9b16-401b-9b08-678023cbfee9","year":2004},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.400339Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:ab75bb60d37c6a7690e5329b899deae8ebf1cd79cec6b798e978c19d74c3fc91","observation_id":"6975bfa3-e6e2-484d-be95-72fab80e88ff","resolution":{"observed_at":"2026-08-05T00:18:54.795448Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-07T00:08:14.092392+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-07T00:08:14.092392+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:50.475437Z","title":"John Wiley & Sons, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.475437Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:aa0db6e98f98d99862648734eb2c4eb24b08c32d1613cc3877052bb08083db62","observation_id":"a4e98fa5-964c-4cc5-9a33-3ded224cc6cf","resolution":{"observed_at":"2026-08-05T00:18:50.475437Z","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":"2026-08-05T00:18:59.848196Z","title":null,"venue":null,"work_id":"8f1fece8-1931-4fa9-9b1b-89a146798f45","year":1968},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.563302Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:483f8ed697d3e86fea652e19266185c2ba025167150c4e3d17aef68e0aa1e345","observation_id":"cb8440ba-f335-4337-aa42-0f5368befffc","resolution":{"observed_at":"2026-08-05T00:18:59.968961Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:50.649319Z","title":"Runge–Kutta discontinuous Galerkin methods for convection-dominated problems.Journal of Scientific Computing, 16(3):173–261, 2001","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.649319Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:38e9dfd494916530a9d5907d256e39365d9ba23e5aaab9fa8621027348ab2979","observation_id":"150c1875-961c-4700-8aba-a902bd2741cd","resolution":{"observed_at":"2026-08-05T00:18:50.649319Z","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":"2026-08-05T00:18:59.662699Z","title":"Comparison of some finite element methods for solving the diffusion-convection- reaction equation.Computer methods in applied mechanics and engineering, 156(1-4):185–210, 1998","venue":null,"work_id":"cf0499b4-98e4-4224-8777-5498da019fe9","year":1998},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.730063Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:36e486f38b86eebed407ed4e2568a5e446856d0e80d3826473cf2eb4339f4df4","observation_id":"b1db7ca8-92be-4a87-a081-5dc434d00fc6","resolution":{"observed_at":"2026-08-05T00:18:59.738403Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:59.443048Z","title":null,"venue":null,"work_id":"270b14c2-ac97-463a-bfb8-9167b86c24fe","year":2000},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.835679Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:b9dfa67483f4b8a6d143f84b59c64f9f127936f224b47c21c0e4142a7be6b841","observation_id":"5eab655a-fdab-4d0b-a24e-75e89569cafc","resolution":{"observed_at":"2026-08-05T00:18:59.543496Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:59.235489Z","title":null,"venue":null,"work_id":"03f5d672-d4d4-4183-92cc-4b44869a41e4","year":2002},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:50.951692Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:5e9c98136e0f4a9e9804717776d75b07a369e96a17ec96953be2f17724dbf89b","observation_id":"77235a6a-7208-418b-867f-ac464e167716","resolution":{"observed_at":"2026-08-05T00:18:59.327175Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:59.073080Z","title":"Conforming and nonconforming finite element methods for solving the stationary stokes equations i.Revue française d’automatique informatique recherche opérationnelle","venue":null,"work_id":"618abff1-e8f6-4d1e-97cf-0a43805b9057","year":1973},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.071027Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:af52708d929ca7eeb35e1ee69f3987e195b46db133f81959230cc2da5ae6401b","observation_id":"10bf3aa6-2878-4a6a-8ef2-bcd66d58832d","resolution":{"observed_at":"2026-08-05T00:18:59.154367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:51.162977Z","title":"John Wiley & Sons, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.162977Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:410956c7d141250756afafda903549a8fc2a5c14a0f5f7e8ebdec112865da887","observation_id":"9f4c8128-0774-4c46-8111-1e66abca78de","resolution":{"observed_at":"2026-08-05T00:18:51.162977Z","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":"10.1007/bfb0120591","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Interior penalty procedures for elliptic and parabolic Galerkin methods","venue":"Lecture notes in physics","work_id":"e8986ca8-7c12-447a-a7c9-475cf511e34c","year":1976},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.224192Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:fd603efae97c973a76e2cc77289d898898c16a4fcf8bbfb17ef80bf996878d47","observation_id":"d826f267-4eca-45ed-9c26-29116d61d9c6","resolution":{"observed_at":"2026-08-05T00:18:54.580881Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-07T00:08:14.705041+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-07T00:08:14.705041+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:58.895204Z","title":"An absolutely stabilized finite element method for the stokes problem.Mathematics of computation, 52(186):495–508, 1989","venue":null,"work_id":"4e33e9af-eafe-40d0-af70-2c59bc04dd2c","year":1989},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.304293Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:41847447e2679da2ed6901dd7b199437669d9f93d2141bbf0cf168362d3518bd","observation_id":"366f43c4-6559-42f9-ae2b-51005de05903","resolution":{"observed_at":"2026-08-05T00:18:58.978454Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:58.768639Z","title":"Cambridge University Press, 2001","venue":null,"work_id":"41cabc68-2bd5-4aba-8b77-fe23df0cbc21","year":2001},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.424643Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:6a3133730350775e2e0106a348762c8860fc854640448584ac4ad130f6a04e02","observation_id":"ae0a3779-b9b0-4bc4-a59a-41ee5ce84057","resolution":{"observed_at":"2026-08-05T00:18:58.833946Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:51.575437Z","title":"High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method.Journal of computational physics, 48(3):387–411, 1982","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.575437Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:b4d5c8fe87c113b94127ce172ed4ecb6cc5c19dd3e6b5fd5cf014a9c76dc5367","observation_id":"b655b1ea-c0c9-4146-94d1-2670e075c5af","resolution":{"observed_at":"2026-08-05T00:18:51.575437Z","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":"2026-08-05T00:18:58.595840Z","title":"A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows.Journal of Computational Physics, 30(1):76–95, 1979","venue":null,"work_id":"d0f2df6a-c298-4020-ae49-3a7ea88fbcb2","year":1979},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.709567Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:47ff68100fa126090ae2cbf30395904e78e6c6fed16e65844d765c95d2769085","observation_id":"08b69b62-47b1-4bad-979d-1d5c1e56f528","resolution":{"observed_at":"2026-08-05T00:18:58.671553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:58.426892Z","title":"An overview of projection methods for incom- pressible flows.Computer Methods in Applied Mechanics and Engineering, 195(44–47):6011–6045, 2006","venue":null,"work_id":"7c3e800b-fc85-4cb8-8850-ec6085b74298","year":2006},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.787767Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:10b43a45feb229a9e80cd8ea01761e9f1e5ed8ffb74e540e1da65cca1a2042a4","observation_id":"592c2ee1-5303-4743-a2ff-497489fee3b9","resolution":{"observed_at":"2026-08-05T00:18:58.493360Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:51.891786Z","title":"Heywood and Rolf Rannacher","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.891786Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:e9c5796f4951bf912d3f4afe1a6b914a10cc00465a8d0ffba19571c8cc4736c5","observation_id":"da80f42e-52f3-44e5-a706-f040d030e6d4","resolution":{"observed_at":"2026-08-05T00:18:51.891786Z","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":"2026-08-05T00:18:58.270130Z","title":null,"venue":null,"work_id":"4e4417f8-4830-4fb2-82e3-972c8eaa35c7","year":1995},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:51.973752Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:a6d7ce5d5b12660260adc3d97c7a88ea32c27a55e72b20fd43e58b1e0728918a","observation_id":"429edea2-6051-4190-a819-162226f79223","resolution":{"observed_at":"2026-08-05T00:18:58.328258Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:58.079418Z","title":"A new finite element formulation for computational fluid dynamics: V","venue":null,"work_id":"572febd2-e0f5-4281-a978-85f54a903593","year":1986},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.044524Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:55c0733b9d5f1da1fe55588cf63d67defca6d5556bd2599084f5750a0373e23c","observation_id":"d5a5279f-578c-4b85-9c6b-ae28de0d8716","resolution":{"observed_at":"2026-08-05T00:18:58.181461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:57.907825Z","title":"A new finite element formu- lation for computational fluid dynamics: Viii","venue":null,"work_id":"7f1a30ea-ac2c-4c10-a879-6d12fedf8c48","year":1989},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.147738Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:877898fde1493a1b2a7b275e4b8b5ec468df9f0af8e81df525ebbdeb03db91a7","observation_id":"b52505d2-291a-4194-aefc-66c174316766","resolution":{"observed_at":"2026-08-05T00:18:57.968307Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:57.780159Z","title":"Large eddy simulation and the varia- tional multiscale method.Computing and visualization in science, 3(1):47–59, 2000","venue":null,"work_id":"d8e5bd3d-0cdd-445c-8c64-754cd0b6fe70","year":2000},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.231912Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:af31fc0c7feb66595562f42e251513901b890c3ecd05322cb94794d13a304382","observation_id":"21ffc710-ac22-4e98-b95b-502e8765e6e3","resolution":{"observed_at":"2026-08-05T00:18:57.827398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:57.618538Z","title":"Springer, 2016","venue":null,"work_id":"865dc40e-0dd6-4bdb-83df-c144f8f1b8f1","year":2016},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.297884Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:6c9621c32d4bb331d3464717b321f8aaffe6c1ee1ed5176662b39aa9a86b5098","observation_id":"ee033e50-31a1-4824-ad5e-2b432ed1ee98","resolution":{"observed_at":"2026-08-05T00:18:57.688642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:57.428101Z","title":"Afiniteelementvariationalmultiscalemethodforthenavier–stokes equations.SIAM Journal on Scientific Computing, 26(5):1485–1503, 2005","venue":null,"work_id":"49925401-99d3-4ade-877b-aac6f634a1fc","year":2005},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.372122Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:050ec18b8840d06fef7e1a24dba6ba51ab67c30afa1cffa85a3306d56e3096d0","observation_id":"351aaa20-f038-4a40-b89c-9d7148de9e1c","resolution":{"observed_at":"2026-08-05T00:18:57.536883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:57.272817Z","title":"Three dimensional flow around a circular cylinder confined in a plane channel.Physics of fluids, 23(6), 2011","venue":null,"work_id":"fa12be31-e5e9-476b-a54e-4edb60ab1665","year":2011},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.477776Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:dae9fe3fb52c0d8612db1d14488199a92468aa8c9f5dd8ccc68d0b265aab5e85","observation_id":"57745e21-987f-431b-9ce2-104d78254b45","resolution":{"observed_at":"2026-08-05T00:18:57.353133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:52.570039Z","title":"A semi-implicit variational multiscale formulation for the incompressible navier-stokes equations via exact adjoint linearization.arXiv preprint arXiv:2512.21773, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.570039Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:d02742273cc0ac913c1b719713e5ab61ebe518d158c7cc7f325119af088be25b","observation_id":"7a0e20aa-2ef3-41fd-9778-bfe6f7a28b24","resolution":{"observed_at":"2026-08-05T00:18:52.570039Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:52.651853Z","title":"Flux correction tools for finite elements.Journal of Compu- tational Physics, 175(2):525–558, 2002","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.651853Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:f3fd356d33022d83554561de244a70b0cb9d4ac79bdec6e535b772475d3e8093","observation_id":"ac1c92e2-4fc5-46ae-9c44-67b745e75c90","resolution":{"observed_at":"2026-08-05T00:18:52.651853Z","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":"1993.1162","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:54.941293Z","title":"Blair Perot","venue":null,"work_id":"311d13ed-f828-4f5a-9f0a-2c7d0e997b14","year":1993},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.725462Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:eca4297ec0f7933b0a9736ad08dde3c722425e3398ee7cd72c21092016fe260b","observation_id":"fcb22c23-ba4c-4de7-870a-3f283467f7c2","resolution":{"observed_at":"2026-08-05T00:18:55.016390Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:52.824667Z","title":"Pope.Turbulent Flows","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.824667Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:bbb1f2ea13ea3e6c1bfb6964ee169ac3c784decb1038734df5911bad0bb277aa","observation_id":"56a625ab-5c2d-4a5e-aedb-aa53dab7f0ef","resolution":{"observed_at":"2026-08-05T00:18:52.824667Z","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":"10.1016/s0045-7825(99)00192-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Factorization methods for the nu- merical approximation of Navier–Stokes equations.Computer Methods in Applied Mechanics and Engineering, 188(1–3):505–526, 2000","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"2eaf8a77-0c4f-403d-ba4b-eb721fc1a5c7","year":2000},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.918575Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:fa90cfd58c44ddbb57721071efae95da57ff4cad2c56d8dc37ba4fd309bc9130","observation_id":"b44b5474-0758-401f-856b-e05a0941965f","resolution":{"observed_at":"2026-08-05T00:18:54.363053Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-07T00:08:15.795242+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-07T00:08:15.795242+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:57.056710Z","title":"Springer, 1996","venue":null,"work_id":"e80a90d0-7016-41d4-889d-cf5a56b0e3ee","year":1996},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:52.999580Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:451c3ae2f2f9205c591d8f753835298fef236edbed1007b548d93f3243164299","observation_id":"60df0c73-ef87-4ea1-bce9-7075e106b771","resolution":{"observed_at":"2026-08-05T00:18:57.165462Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:56.870921Z","title":"Ridgway Scott and Michael Vogelius","venue":null,"work_id":"450d3796-8550-4e1e-874b-8442a0721873","year":1985},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.076962Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:d78b75fb53d941758afa67cf213d19d91965fb247e34d0980666acfc7fe65ebb","observation_id":"52603154-2ef1-4dbf-8546-7a9666b74e76","resolution":{"observed_at":"2026-08-05T00:18:56.935421Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:56.687728Z","title":"A new finite element formulation for computational fluid dynamics: X","venue":null,"work_id":"d0b40004-fa6c-4c07-bc21-06de23a09173","year":1991},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.152474Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:1c8c39cd245c3abcdc0c3864c9038ed612f8acec29de3d899fa2e6c0354904d1","observation_id":"39178e60-a785-4d0c-b4b6-5078aaad993d","resolution":{"observed_at":"2026-08-05T00:18:56.774562Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:56.564702Z","title":"On error estimates of the projection methods for the navier-stokes equations: second- order schemes.Mathematics of computation, 65(215):1039–1065, 1996","venue":null,"work_id":"53cfcea0-860f-4763-a4b6-f4aa5147a55d","year":1996},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.230169Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:dc37e505b1ef84e7ea42f9289538fd1cbe625d1b9bf319eb7017a089ec4d4d70","observation_id":"fcf05663-3dfe-488f-8f6a-77de0d07f42d","resolution":{"observed_at":"2026-08-05T00:18:56.626571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:56.399535Z","title":"Flow past a circular cylinder between parallel walls at low reynolds numbers.Ocean Engineering, 37(8-9):757–769, 2010","venue":null,"work_id":"21a88243-2edc-4b57-a660-9d8a8535bcf0","year":2010},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.306559Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:d7e0d9d0c79d09bee982176ff82206fdeb4790a9c928fd868ab5355c7adfe908","observation_id":"0bc24eb1-4df9-4391-a5d2-03b93b23599f","resolution":{"observed_at":"2026-08-05T00:18:56.481231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:56.247837Z","title":"A numerical solution of the navier-stokes equations using the finite element technique.Computers & Fluids, 1(1):73–100, 1973","venue":null,"work_id":"350d15a8-bf33-40bf-b210-b0b0eefe8f2f","year":1973},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.419201Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:e941f380111a2ddc7098cd383fdc42d510ac255250ce1fc1434e6b6fef0e3259","observation_id":"3e2754bf-36ce-4cdd-b898-8dd3ef15bf5e","resolution":{"observed_at":"2026-08-05T00:18:56.314624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:56.076501Z","title":"Sur l’approximation de la solution des équations de navier–stokes par la méthode des pas fractionnaires.Archive for Rational Mechanics and Analysis, 32:135–153, 1969","venue":null,"work_id":"47cd5e64-6312-4d8c-a904-02af635b1b9b","year":1969},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.497448Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:4fae02c81a9087f9bb2c061ea5045df419fc5c89e9d305010d42beff4afa9c1d","observation_id":"bb3df3f4-516b-4e18-a3ee-e7a7f0828de7","resolution":{"observed_at":"2026-08-05T00:18:56.173157Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0045-7825(86)90003-4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Tezduyar and Yong J","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"35243190-1bb8-4b80-81e6-3280f01fb225","year":1986},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.569253Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:ac8b6d0b4a0f7cb01ad4643e3e4d11b20ac35d2374c914cbccdc3ce2bc64be5b","observation_id":"8ebd7bc5-920c-4996-884f-fc01df2e0f3e","resolution":{"observed_at":"2026-08-05T00:18:54.186460Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-07T00:08:16.224747+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-07T00:08:16.224747+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:55.904143Z","title":null,"venue":null,"work_id":"e59ce0db-1560-4134-88a6-5317e5b941fc","year":1992},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.648126Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:ac06b35e7055fdc790a9980702649b1a2d1d37ad5c09bb0c95a91272588b5cd4","observation_id":"4e64dac6-e2ab-4c5a-8581-4b951c5e9b37","resolution":{"observed_at":"2026-08-05T00:18:56.006456Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:55.739913Z","title":null,"venue":null,"work_id":"e30e5fc7-b7fa-4803-afc3-282cab9896cb","year":1996},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.727969Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:18be84a1b0def107baf066c252af82e45fbb2bec432d9eb0d539121044f492fa","observation_id":"47121b06-83c8-4661-bdf2-bc1bcc2b78f9","resolution":{"observed_at":"2026-08-05T00:18:55.825859Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:55.573644Z","title":null,"venue":null,"work_id":"2fed813a-1eb9-40eb-806d-d5ad59c30bb2","year":1986},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.806087Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:c0621b906c9f3dfb14864f2547ab78dcdf760a181f069230e0f7e4d5dd942452","observation_id":"726369ee-ffab-445d-9f77-64a3ed328879","resolution":{"observed_at":"2026-08-05T00:18:55.641574Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:55.391255Z","title":"High-order cfd methods: current status and perspective.International Journal for Numerical Methods in Fluids, 72(8):811–845, 2013","venue":null,"work_id":"7c2ddd41-299e-44ea-8395-e82160b6e775","year":2013},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.912478Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:0cc232f891050786485c7b7eb7e8ce7a430fda67613dd0f1d364b02a20a27d46","observation_id":"e8081b43-f175-4145-9567-5bf9c94edc14","resolution":{"observed_at":"2026-08-05T00:18:55.467624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T00:18:55.212016Z","title":"Flow about a circular cylinder between parallel walls","venue":null,"work_id":"a8c8b4be-8bf6-4a6b-b7a2-503b3298f2ae","year":2001},"citing_paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-05T00:18:53.989122Z"},"links":{"citing_paper":"/paper/2608.00843"},"observation_digest":"sha256:21dc8d59b031df75ccb415713fa845fb4161b54aa44c392c26c6a43e244bea87","observation_id":"381739ee-3518-418e-8781-5fa38544612c","resolution":{"observed_at":"2026-08-05T00:18:55.305388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.00843","last_updated":"2026-08-01T19:50:27Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-07T10:29:31.615152Z","submitted_at":"2026-08-01T19:50:27Z","title":"A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":19,"verified_exact":5,"verified_fuzzy":26},"total_outbound_references":50},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2608.00843."}