{"as_of":"2026-08-14T07:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8b2487ebe5cb473f347cbed87a43481c488b19dc1815b8b0a939cf8f3bd86a1c","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T21:03:46.417446Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2412.05082/citation-record","integrity":"/paper/2412.05082/integrity","json":"/paper/2412.05082/citation-record.json","paper":"/paper/2412.05082"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:03:46.839641Z","title":"The deal.II L ibrary, V ersion 9.5","venue":null,"work_id":"a6cb37bb-bbf5-436a-96a7-dcd85d32af2a","year":2023},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.317395Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:86a2f2499c409c4b26da7ecbb2f204a15872acfa8330f4a2e344f7d687977af7","observation_id":"71a3b4ae-ae2a-4ad9-8a17-9d7364cfac6d","resolution":{"observed_at":"2026-08-11T21:03:46.843765Z","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":"2026-08-11T21:03:46.829272Z","title":"Arnold, Richard S","venue":null,"work_id":"baf34c21-5787-4a2b-b1f2-159f335d5442","year":1997},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.321915Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:ac075450bba0cddb5c680d0c282cf97d7eb1924adcd6b0174ac76e49dfc4a713","observation_id":"a55fb7d9-b5e0-4123-baee-8f32041a0465","resolution":{"observed_at":"2026-08-11T21:03:46.832862Z","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":"2026-08-11T21:03:46.819859Z","title":null,"venue":null,"work_id":"beb51cba-79ae-4c97-8c43-656f2451e1be","year":1982},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.326151Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:23702a050d0e2e5be9e7fdd8386041fc63d497f9b458c68154e8b5dccaa39d2d","observation_id":"5f8e6fdd-ebd7-4510-a00d-1e0016d7af72","resolution":{"observed_at":"2026-08-11T21:03:46.822805Z","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":"2026-08-11T21:03:46.810450Z","title":"Brubeck and Patrick E","venue":null,"work_id":"26021f2b-ff19-481e-bec0-ff8dc2bcc593","year":2022},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.329804Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:d191017d1d90c9409f16e79692366cea2247f097c0f865ff606fcece0f0fa394","observation_id":"0b0cda90-e8f8-43ad-84d8-169669a91f73","resolution":{"observed_at":"2026-08-11T21:03:46.813529Z","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":"2026-08-11T21:03:46.799389Z","title":null,"venue":null,"work_id":"9c59bd30-8caa-498a-9bed-866c02fd06e7","year":2010},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.333968Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:5d2ab40d184370f879473f095566a53e475dcd021ebac659afab0c2b8e1f8a24","observation_id":"805f9d34-41cf-4230-b7cb-720aeee24640","resolution":{"observed_at":"2026-08-11T21:03:46.803813Z","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":"2026-08-11T21:03:46.788984Z","title":"Brenner and Li-Yeng Sung","venue":null,"work_id":"68593f7c-26bf-4121-88a4-fabc80854595","year":2005},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.338130Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:309758b4b4196e8a2cef090d7c5824a4399ab636ef1f6a029deab995dc7ce44b","observation_id":"df02228d-6605-44ad-9aac-7a5d11b27bf9","resolution":{"observed_at":"2026-08-11T21:03:46.792673Z","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":"2026-08-11T21:03:46.778257Z","title":"Brenner and Kening Wang","venue":null,"work_id":"80012acb-9627-4500-b2fb-fee52e42975b","year":2005},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.343014Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:ec0a66b8bbd1d0992496df467d8fd4881c3a477ab0c22718cacdccaeb42e9ac9","observation_id":"673bcf57-a282-4cab-83c7-67b095ad7d60","resolution":{"observed_at":"2026-08-11T21:03:46.782019Z","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":"2026-08-11T21:03:46.767812Z","title":"Brenner and Jie Zhao","venue":null,"work_id":"1351ee76-d6b4-42ea-9730-b9e2a016168f","year":2005},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.346491Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:0fe5a9f9156d8030aa4af05fc9234e533d4c94bae78dd9b91c4a398e0735deda","observation_id":"23702500-8f60-4331-8aff-10927ca396da","resolution":{"observed_at":"2026-08-11T21:03:46.771381Z","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":"2026-08-11T21:03:46.758404Z","title":"An implementation of tensor product patch smoothers on gpus","venue":null,"work_id":"1837e0ec-35fa-4c0f-b06d-6ad7a0ea1220","year":2025},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.349891Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:6eff05581769cd08888f4207c700b44b304d80590a68d0559cb7c438fcedcbba","observation_id":"ded2eb78-6ee0-41cc-aaa8-4e35543dbc41","resolution":{"observed_at":"2026-08-11T21:03:46.761402Z","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":"2410.09497","last_updated":"2024-10-12T11:22:43Z","snapshot_observed_at":"2026-08-13T19:33:20.567694Z","submitted_at":"2024-10-12T11:22:43Z","title":"Multigrid methods for the Stokes problem on GPU systems","version":1},"cited_work":{"arxiv_id":"2410.09497","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.09497","snapshot_observed_at":"2026-08-11T21:03:46.566443Z","title":"Multigrid methods for the Stokes problem on GPU systems","venue":"math.NA","work_id":"2f97010c-d823-49ca-8418-e115adb7ed13","year":2024},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.353236Z"},"links":{"cited_paper":"/paper/2410.09497","citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:15cb53ca398111bc1ae5d326083124a77681d99af28d676127b2744df12d0e6f","observation_id":"9e50efa0-986f-43ba-ad02-684486395ab4","resolution":{"observed_at":"2026-08-11T21:03:46.570510Z","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":"2405.18982","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T21:03:46.546624Z","title":"Multilevel interior penalty methods on GPU s","venue":null,"work_id":"4342bc3a-d11e-48c1-8a5a-2799c512e42e","year":2024},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.357998Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:30ead9f6091f081473d52da88183019d97433f35c18b7e780c59e656308e1a6b","observation_id":"24fb5066-6587-4703-b12e-eee777e81e95","resolution":{"observed_at":"2026-08-11T21:03:46.555430Z","resolver_source":"raw_fallback","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":"2026-08-11T21:03:46.749426Z","title":null,"venue":null,"work_id":"660a4ddc-7e67-4f09-8b6d-129fcdcac3d2","year":2018},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.361497Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:9407e5c0317fe90e6d3fea30a7c2bbf849de11b92a3e70c615374d6cb393b571","observation_id":"7c65434a-d118-4479-b29c-375d75235121","resolution":{"observed_at":"2026-08-11T21:03:46.752421Z","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":"2026-08-11T21:03:46.739010Z","title":"Acceleration of T ensor- P roduct O perations with T ensor C ores","venue":null,"work_id":"948760a7-4860-4979-ba3f-2158452ea427","year":2024},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.365020Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:0b494203904f6ff1540aacc648d8c8e1e9625ffbc4ae8393e48eb212db273205","observation_id":"6968a333-331e-4ac8-aaf5-5d8394cf221d","resolution":{"observed_at":"2026-08-11T21:03:46.742950Z","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":"2026-08-11T21:03:46.727260Z","title":"Karakashian","venue":null,"work_id":"8be09adc-2c23-41ad-bb5e-8652da0e962e","year":2005},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.369245Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:a2cf38b1cc9966c84138ed7f1bab929ae65e351aaf84dcb2ba34d88569cd240d","observation_id":"8e1dbd36-259e-4074-a610-c7206140c509","resolution":{"observed_at":"2026-08-11T21:03:46.731606Z","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":"2026-08-11T21:03:46.715702Z","title":"Performance and accuracy of hardware-oriented native-, emulated-and mixed-precision solvers in FEM simulations","venue":null,"work_id":"ea209bd4-8da2-4619-8bdd-f52a197cd1d2","year":2007},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.372648Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:b334aa652c2a432a61f4682c947532cedea37b0c1b832139599f483466eeaf95","observation_id":"860cb3bb-03b1-45d1-aa78-25bdeccedf8e","resolution":{"observed_at":"2026-08-11T21:03:46.720231Z","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":"2026-08-11T21:03:46.705720Z","title":"Kronbichler and K","venue":null,"work_id":"0ecf9017-b42c-4d1b-9423-7c5d31254375","year":2012},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.376116Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:3137b3902dfcac9cefa301307b95ce579eeb6b9e663b1ae925a2d2b98bb03082","observation_id":"2c2d4565-667e-4642-9674-85d7835bef13","resolution":{"observed_at":"2026-08-11T21:03:46.709306Z","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":"2026-08-11T21:03:46.695330Z","title":"Fast matrix-free evaluation of discontinuous G alerkin finite element operators","venue":null,"work_id":"1cdaecb1-0e2a-4207-8871-eb3c00dd3b45","year":2019},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.379023Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:9393f3d6799b2376d090c011fb703a3e4f7fe5e8b1f481ebf9829e6c14255360","observation_id":"744670ca-bbcf-4c01-865b-db5679c6867c","resolution":{"observed_at":"2026-08-11T21:03:46.699038Z","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":"2026-08-11T21:03:46.685131Z","title":"Kanschat, R","venue":null,"work_id":"8f84ffd7-52b8-4f30-a5fe-958c4dc21c90","year":2017},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.382188Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:a759e27351818bb0713e728f81876309b831bcc04f977703b01b421ac1dad0f7","observation_id":"8ea08618-858c-4801-a0f1-bb6631365be3","resolution":{"observed_at":"2026-08-11T21:03:46.688671Z","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":"2026-08-11T21:03:46.675997Z","title":"Kanschat and Y","venue":null,"work_id":"dfd8c14e-228b-45c0-93fd-1fc75919ad3b","year":2015},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.385040Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:8bd87c7fdb8d3a3d7c9607a2f2b1547d258955c5f43ec0c8811af41ecb24239e","observation_id":"6728b78a-2488-4aef-b6b1-a8391cf8b89c","resolution":{"observed_at":"2026-08-11T21:03:46.679316Z","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":"2026-08-11T21:03:46.666640Z","title":"Divergence-conforming discontinuous G alerkin methods and C^0 interior penalty methods","venue":null,"work_id":"abdc66ca-d325-464e-9c57-937447a8fba8","year":2014},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.388359Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:8e640a2c6744ea538fd0a48e6852bd4d2c4942447e8779777795ee8e9bd1a599","observation_id":"62096e0d-8ef4-4590-aeca-487a2b79b276","resolution":{"observed_at":"2026-08-11T21:03:46.669814Z","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":"2026-08-11T21:03:46.655701Z","title":"Lynch, John R","venue":null,"work_id":"7da6f58a-c89a-4e69-84ba-b977db26d326","year":1964},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.391848Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:e1de57d7b2d4a433f682bdce96dbe8f3c869cf45f930bcd2f2912d0041943f68","observation_id":"75058fed-7309-4dae-be45-0960bfb12c58","resolution":{"observed_at":"2026-08-11T21:03:46.659284Z","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":"2026-08-11T21:03:46.644539Z","title":"Melenk, K","venue":null,"work_id":"dc645086-8a1f-42b7-bc26-0a25e4a0e4ee","year":2001},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.395476Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:c6bd5f20fbf0adee43409f250dc24715ae62d174f1cfb0b1936b1b3023aa744a","observation_id":"6f68dc1f-e8a9-4fa7-a79b-2192edbd6661","resolution":{"observed_at":"2026-08-11T21:03:46.648788Z","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":"2026-08-11T21:03:46.633331Z","title":"\\\"U ber ein V ariationsprinzip zur L ösung von D irichlet- P roblemen bei V erwendung von T eilräumen, die keinen R andbedingungen unterworfen sind","venue":null,"work_id":"c5547705-89f6-40dc-b404-1c8f15a5a829","year":1971},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.398969Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:bda36e244cb3ab2dd7bbf4b9331e62165c9bb85a19f1afcfe27960d54103c9ac","observation_id":"0cefbdbf-eb29-476a-9c17-923156d735c6","resolution":{"observed_at":"2026-08-11T21:03:46.637454Z","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":"2026-08-11T21:03:46.622891Z","title":"N sight C ompute, 2023","venue":null,"work_id":"cc8538c7-a555-44ba-b5ba-be59132782f1","year":2023},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.402498Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:f5b6e93f4bf7ca4605c679956f883cafa9c424d31ccc29c91592374d899cd518","observation_id":"7c2b9d91-2ffe-4a6b-b827-52ca2a1b9916","resolution":{"observed_at":"2026-08-11T21:03:46.626424Z","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":"2026-08-11T21:03:46.611071Z","title":"Fast tensor product schwarz smoothers for high-order discontinuous galerkin methods","venue":null,"work_id":"61637ebf-32a3-429f-86bd-a2ff91a4b8c2","year":2020},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.406221Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:d1dc15478f6a8eb6d8771da0d91ba951aec1e85a27eb987448eb91aa5edf0ff3","observation_id":"f08df84c-3912-44ce-8612-d0b666a7ecd2","resolution":{"observed_at":"2026-08-11T21:03:46.615252Z","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":"2026-08-11T21:03:46.599030Z","title":null,"venue":null,"work_id":"5c3555b4-dc44-4f15-a907-61141127a5fc","year":2022},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.409713Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:41d47d9fe99a7cb02f8918781bbcbb7b1e6fa4ff4a542c28079fdadd8adddefd","observation_id":"2c109ae9-6b01-435e-94eb-129157811aa8","resolution":{"observed_at":"2026-08-11T21:03:46.603007Z","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":"2026-08-11T21:03:46.588238Z","title":"An optimal order multigrid method for biharmonic, C^1 finite element equations","venue":null,"work_id":"497e187d-3049-4874-bacc-287e94b5f2b7","year":1989},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.413948Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:bfc13a2c1b441c3c19ce00a5b42a7b000ddedaeb1de4088d649e368a3e244eb9","observation_id":"2471711b-e1ac-4985-b3e9-a66e4401d596","resolution":{"observed_at":"2026-08-11T21:03:46.591852Z","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":"2026-08-11T21:03:46.577798Z","title":null,"venue":null,"work_id":"efe0c5bd-0dcb-4f5e-b793-5963d864ef02","year":2005},"citing_paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-11T21:03:46.417446Z"},"links":{"citing_paper":"/paper/2412.05082"},"observation_digest":"sha256:49cf7348c74ddd7e7bb90dc974883de529dc24e3e57bb52b89b53ad3a50b9ddb","observation_id":"650adc07-04fb-4c87-aa74-672a924c7e4c","resolution":{"observed_at":"2026-08-11T21:03:46.581463Z","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"}}],"paper":{"arxiv_id":"2412.05082","last_updated":"2025-05-09T14:26:44Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-13T21:44:39.144924Z","submitted_at":"2024-12-06T14:40:24Z","title":"Tensor-product vertex patch smoothers for biharmonic problems"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":2,"verified_fuzzy":21},"total_outbound_references":28},"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 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2412.05082."}