{"as_of":"2026-08-13T11:22:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7d14e5b7b457a0441abff174e84945e72e1ba8500bb46021fa5b66bcac451ed4","coverage":[{"denominator":51,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":51,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T15:19:24.842143Z","state":"measured"},{"denominator":51,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":51,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2411.14561/citation-record","integrity":"/paper/2411.14561/integrity","json":"/paper/2411.14561/citation-record.json","paper":"/paper/2411.14561"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:24.391713Z","title":"MFEM: a modular finite element methods library","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.391713Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:2c2fa0012bc972e39162197567336dbeedb7ce33dbb54e0307e622ef8684641b","observation_id":"b3fe9de1-ff09-4a5e-b2c3-c99f0d4b7a02","resolution":{"observed_at":"2026-08-12T15:19:24.391713Z","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":"2026-08-12T15:19:24.406660Z","title":"High-performance finite elements with MFEM","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.406660Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:6f44774c745981364a9d09d589462e5ea2af031a43e42d34773fc2edc19eb574","observation_id":"5a85c178-4069-450a-bd41-e75982a0eed5","resolution":{"observed_at":"2026-08-12T15:19:24.406660Z","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":"2026-08-12T15:19:24.424155Z","title":"Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.424155Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:6bb0bbeeca543d59748e28866d13a32ab296acdc388fb5ea364f17e811e693d3","observation_id":"05f2e915-3dc9-4572-9903-49ee86b29bae","resolution":{"observed_at":"2026-08-12T15:19:24.424155Z","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/s10915-010-9390-1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.758845Z","title":"A class of domain decompositio n preconditioners forhp-discontinuous Galerkin finite element methods","venue":null,"work_id":"8fb0173b-a168-4dfe-b993-6fc8f63119a1","year":2010},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.429448Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:189fc42ffcfb8464103b07bc86db97081b3a9caa61944e360f921266a2785cbd","observation_id":"71f83da5-3645-45a1-8e51-9a7461cb8a59","resolution":{"observed_at":"2026-08-12T15:19:25.769489Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/18m1204383","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.735406Z","title":"Algebraic multigrid schemes for hig h-order nodal discontinuous Galerkin methods","venue":null,"work_id":"943cd548-d8d0-4837-bed7-cf19b35ef107","year":2020},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.438458Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:c51042b35ce51f3e92c6149d3009b9c8e96a39707861ac945e49cebb371dc135","observation_id":"fbeacf84-d994-4ed7-aae8-64cb23cdd110","resolution":{"observed_at":"2026-08-12T15:19:25.741668Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.447532Z","title":"A uniform additive Schwarz preconditione r for high-order discontinuous Galerkin approximations of elliptic problems","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.447532Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:cd19e606da93f5d1de7c9953dfc3dbc5b7267ee4768dbf9e88dd25bd80565d92","observation_id":"1976e44d-55b1-42b0-9349-6ad1b9d14d19","resolution":{"observed_at":"2026-08-12T15:19:24.447532Z","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":"2026-08-12T15:19:24.456662Z","title":"An interior penalty finite element method with discon tinuous elements","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.456662Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:f79cf54bf39436c0dd9f7c811a4b673e2566fcdc9142145803a21b37d2e7fae9","observation_id":"4db88b47-fd30-4519-933f-206f505733d8","resolution":{"observed_at":"2026-08-12T15:19:24.456662Z","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":"2026-08-12T15:19:24.462947Z","title":"Quadrilateral H(div) Finite Elements","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.462947Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:8b110e4a7239f7e2829043e94594ec84a48fa25b98ce13fb402d4870e4994f77","observation_id":"f1d0ce5c-842c-4233-ab1d-6f812b6a0bf6","resolution":{"observed_at":"2026-08-12T15:19:24.462947Z","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":"2026-08-12T15:19:24.475103Z","title":"Unified analysis of discontinuous Galerkin metho ds for elliptic problems","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.475103Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:a19a5d79bf3c1c1c587daf7918639ad4213e0d6606053983a60e7cd178c4ee97","observation_id":"69857c2f-43ba-4400-bdd7-833d1b606c68","resolution":{"observed_at":"2026-08-12T15:19:24.475103Z","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":"2026-08-12T15:19:24.480887Z","title":"Matrix-free multigrid block-preconditioners f or higher order discontinuous Galerkin discretisations","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.480887Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:4ce4a27e472cc3bb19decb30670974e25dd6ff7adf47b14fd1bdfd9b3e331c28","observation_id":"2548dc40-7698-4c33-9fc7-c147d72963d1","resolution":{"observed_at":"2026-08-12T15:19:24.480887Z","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":"2026-08-12T15:19:24.488907Z","title":"Numerical solution of sadd le point problems","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.488907Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:d5dbfdbd8ee8f0477b11514c3c12dea05b5fe8e940db0b0ff88109af46e49a76","observation_id":"a571e660-8dc3-453f-9277-d594aeb06f46","resolution":{"observed_at":"2026-08-12T15:19:24.488907Z","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":"10.1016/0377-0427(92)90259-z","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.602379Z","title":"Polynomial interpolation results in S obolev spaces","venue":null,"work_id":"2884f6a1-15b4-4eec-b8f4-8f5498064684","year":1992},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.499307Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:77a8a76b640c355d579308ce68e8cf951f93127cc412b88ae1cb79dec891fb8e","observation_id":"7b0a179e-0f1f-4f36-bc78-024f81c32fed","resolution":{"observed_at":"2026-08-12T15:19:25.610508Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imanum/dru053","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.563707Z","title":"Multilevel preconditioning of discontinuous Galerkin spectral element methods. Part I: geometrically conforming meshes","venue":null,"work_id":"daf82832-a129-4302-acd0-66a155bd800d","year":2014},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.505778Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:bae82208c8ee4c9e7e64ad4c0be834391103d1b5654b9359b2b21c50a8a2153e","observation_id":"eff63a72-dfc8-46ad-bf94-acfb66bb2c11","resolution":{"observed_at":"2026-08-12T15:19:25.571069Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.517510Z","title":"Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.517510Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:1a3f63d1bcf0f8d14568fd873d9fa4d7d8476660846d4bbc2a1c7af90135313f","observation_id":"0ebd2d6a-316a-426d-b1cb-bac5d7ae1895","resolution":{"observed_at":"2026-08-12T15:19:24.517510Z","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/s10915-006-9107-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.522176Z","title":"A note on disc ontinuous Galerkin divergence-free solu- tions of the Navier–Stokes equations","venue":null,"work_id":"d4fd0889-7af4-4784-a0b3-97890e978091","year":2006},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.528956Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:c32a1e19c88911aa90eb49cecbc3b96c5b38298300baedf45fe75668bdf64b1e","observation_id":"bd043300-7ce0-4b3d-b9d9-2c5753bcef09","resolution":{"observed_at":"2026-08-12T15:19:25.528202Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.09497","last_updated":"2024-10-12T11:22:43Z","snapshot_observed_at":"2026-08-12T22:24:49.141260Z","submitted_at":"2024-10-12T11:22:43Z","title":"Multigrid methods for the Stokes problem on GPU systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.09497","snapshot_observed_at":"2026-08-12T15:19:24.537667Z","title":"Multigrid methods for the Stokes pro blem on GPU systems","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.537667Z"},"links":{"cited_paper":"/paper/2410.09497","citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:b0314825f0882e9127e36c9e42a7f346ea17f5e31e1690c1fc61be5bfb0a83bd","observation_id":"bff5cd45-4d5a-4a4b-ba8a-36d95fa96f74","resolution":{"observed_at":"2026-08-12T15:19:24.537667Z","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":"10.1002/nla.504","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-13T11:03:48.094449Z","title":"Two-level preconditioning of discontinuous Galerkin approximations of second- order elliptic equations","venue":"Numerical Linear Algebra with Applications","work_id":"7079279b-d380-4047-a51a-c7cc35b0d6fa","year":2006},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.547534Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:001c6b17cbc3ba38be96f4f3f48269c14abd4497d6d0b91d3c38277060c0239b","observation_id":"1e9d5e22-8bcf-4ac7-b6af-c592f463dab2","resolution":{"observed_at":"2026-08-12T15:19:25.503455Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.cma.2018.11.012","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.470381Z","title":"An explicit divergence-free DG method for incompressib le flow","venue":null,"work_id":"f947f443-c30f-47f9-a8b8-cf2511f02c43","year":2019},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.558056Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:c22e8874225e1fc9434c132bf6bc651a5db6e525141b53a82e9a5f9cf7730bfc","observation_id":"463deb69-526c-4dbc-b7ed-258e84b367f9","resolution":{"observed_at":"2026-08-12T15:19:25.477089Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s002110200392","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.448402Z","title":"A multilevel discontinuous Galerkin method","venue":null,"work_id":"4f2ae684-2abc-4109-8544-00f11fea58f6","year":2003},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.564089Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:75e85b263d60d67260fca4dad3ca1257f7d0ca0372a57e541e947ae60ee26f04","observation_id":"31aff26d-ae97-42c2-8508-7e0b18efdbaa","resolution":{"observed_at":"2026-08-12T15:19:25.456161Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2514/1.15497","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.430230Z","title":"Application of p-multigrid to discontinuous Galerkin formulations of the Poisson equation","venue":null,"work_id":"919d6a1d-67bc-4d37-8696-4265503b3769","year":2006},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.577162Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:166e1a28b1bd44cf617a97d0f66aac56308ac1c56341398b471376aa3614c5ed","observation_id":"cd84ead7-21ba-4b84-9afb-726aec22afa9","resolution":{"observed_at":"2026-08-12T15:19:25.435766Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.583476Z","title":"BoomerAMG: a parallel algebraic m ultigrid solver and preconditioner","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.583476Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:1dc6699335448c2cef24fc29d086684badde9946da0f8642f0d000a96b1d7c8c","observation_id":"c0190d76-0b77-48c9-8980-29f11190dfa2","resolution":{"observed_at":"2026-08-12T15:19:24.583476Z","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":"2026-08-12T15:19:24.602543Z","title":"On the divergence constraint in mixed finite elemen t methods for incompressible flows","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.602543Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:42cbf771b0f4da3812eec2f3eda05a51319780b85afddf4c5a9e2cd5946a2fc7","observation_id":"2f2602fc-ef43-43de-9608-950858f7af13","resolution":{"observed_at":"2026-08-12T15:19:24.602543Z","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/j.compstruc.2004.04.015","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.366978Z","title":"Multilevel methods for discontinuous Galerkin FE M on locally refined meshes","venue":null,"work_id":"034bddd9-7764-4526-8351-22aee7d74047","year":2004},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.615389Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:cd8d3fc601c872b4e3714a3a2efb53974149c3372fe2d60fdd687c3beab9c4b6","observation_id":"f9d6bd99-bb41-4617-8df5-772846548a12","resolution":{"observed_at":"2026-08-12T15:19:25.376215Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/jnma-2015-0005","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.346105Z","title":"Multigrid methods for H div-conforming discontinuous Galerkin methods for the Stokes equations","venue":null,"work_id":"c045eb03-5f09-4219-b218-701755b0c777","year":2015},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.621292Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:bd279ad6e99d09ed20ca2d13bb5bd73f9f99c828694c7693d61989b17013dfc7","observation_id":"4b161093-93fb-4e67-975e-b636f4ec668a","resolution":{"observed_at":"2026-08-12T15:19:25.353444Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/21m1403916","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.324075Z","title":"Conservative and accurate solution t ransfer between high-order and low- order refined finite element spaces","venue":null,"work_id":"0ec586eb-6a06-4640-a5c8-d5d47510bbe2","year":2022},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.633874Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:c5c2b5363b0c867aedbead740ddf202d55a8b40330e8c018dae2fce54e9368c1","observation_id":"c9266407-238c-4b30-b2f6-42795e6f9fcc","resolution":{"observed_at":"2026-08-12T15:19:25.330491Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.641377Z","title":"Fast matrix-free evaluation o f discontinuous Galerkin finite element operators","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.641377Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:de389e39d7f6fb564db2af68d981ebc3f50b8a59b89d53d6fde0e522d46571bd","observation_id":"01d02e50-2a03-4825-8157-8f2df93fb3de","resolution":{"observed_at":"2026-08-12T15:19:24.641377Z","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(00)00322-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.273393Z","title":"Fully discrete hp-finite elements: fast quadrature","venue":null,"work_id":"35f4015d-c91e-46c0-8297-74b4101aa4cc","year":2001},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.649308Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:e69eaf672e7ce28af11af16e80531dfb7efc0aa67364a9ffb53f82cfa074c21a","observation_id":"8f8f74b5-57c9-4b44-9da4-821aaf74d682","resolution":{"observed_at":"2026-08-12T15:19:25.281664Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:26.029716Z","title":"Decomposition and fictitious domains meth ods for elliptic boundary value prob- lems","venue":null,"work_id":"59849905-df6d-44cd-a2f1-88109e6a9ddc","year":1991},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.658631Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:c5136f52bf1bf9032736f90aaba983b8e5784732637200ee6580cca24dff7787","observation_id":"768d1e14-b1fc-4fa7-83e1-8dcf78e30916","resolution":{"observed_at":"2026-08-12T15:19:26.038796Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:25.994427Z","title":"Domain decomposition methods","venue":null,"work_id":"8164fd56-09c0-414c-89d7-9535446f41b0","year":2007},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.666657Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:e8d3b9d441f58e68ea5b727788f82547ecdc366d32c477b3fa05a77b719a39ed","observation_id":"6eb8cb34-70fe-4f26-bc42-c3a1bf9b05ae","resolution":{"observed_at":"2026-08-12T15:19:26.000394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.672208Z","title":"Spectral methods for problems in complex geom etries","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.672208Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:dc97b3b46dd64ab9ce110089a327d4f9f4bbc3a8cdbf571fcbb0bce0af1aa941","observation_id":"a5a5dfc9-b355-45b7-9f31-dcebd22a8260","resolution":{"observed_at":"2026-08-12T15:19:24.672208Z","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/bf02243847","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.228321Z","title":"On a BPX-preconditioner for P1 elements","venue":null,"work_id":"018e4536-b8b9-4959-b789-d60d423a6a8a","year":1993},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.684212Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:e288d3bca6a574e0acf609fd50aa93a2bbfcd41456ff6b9a26f819f36a072fee","observation_id":"e31c279e-494f-4aaa-84bd-6309d19a6dd6","resolution":{"observed_at":"2026-08-12T15:19:25.239720Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.693779Z","title":"Additive Schwarz methods for the p-version finite element method","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.693779Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:d3486fcbcdaf7c27360361d445ef0e463b0004237eb6290afa670e0b4514dfb6","observation_id":"879e79d3-baf4-4db0-9c93-d75f1d2b39f2","resolution":{"observed_at":"2026-08-12T15:19:24.693779Z","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":"2026-08-12T15:19:25.969153Z","title":"Domain decomposition algorithms for the p-version finite element method for elliptic problems","venue":null,"work_id":"5bb4a2c9-9e6c-48c2-bb64-76b3d29c20e5","year":1992},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.702846Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:3ff46e10d18c9a90e3dd0cdfaf02df095183c4b97610b86e09011c5b0f65070c","observation_id":"fed0a3c3-c13f-47b8-a050-dc0c6b0ef076","resolution":{"observed_at":"2026-08-12T15:19:25.976228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/19m1282052","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.180168Z","title":"Efficient low-order refined preconditioners for hig h-order matrix-free continuous and dis- continuous Galerkin methods","venue":null,"work_id":"2dc56560-2a5a-4e22-8ff3-54ee3bfe49b9","year":2020},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.709458Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:805aa31e519a1cfc7bf200afa5ebea19e6e54c0cfdf2ad444a08a0a4ee780656","observation_id":"37f2f6fd-856d-4cf4-b1c9-de9830ba02c0","resolution":{"observed_at":"2026-08-12T15:19:25.186365Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s42967-021-00136-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.153812Z","title":"Uniform subspace correction precon ditioners for discontinuous Galerkin methods with hp-refinement","venue":null,"work_id":"07e422de-f7c3-4277-86d1-90f12c9e6e18","year":2021},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.717796Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:c08c6e16b094ae6c96dce1985fce2091af20b69f51f8a061866135e0a01521fb","observation_id":"90d735c1-c8fc-4a21-8790-c1dad3d8291d","resolution":{"observed_at":"2026-08-12T15:19:25.160938Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/22m1486534","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.127263Z","title":"Low-order precon ditioning for the high-order finite element de Rham complex","venue":null,"work_id":"ed600a7a-2484-4da3-9f0b-2f7f8517e904","year":2023},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.738419Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:cc326b7ddfff904a4cde04d0a33f0f1873a798eee983c9b7b7465843c666684d","observation_id":"77418238-ab4a-40d0-a21d-b85007e21db4","resolution":{"observed_at":"2026-08-12T15:19:25.135702Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/23m1568806","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.102757Z","title":"Matrix-free high-p erformance saddle-point solvers for high-order problems in H(div)","venue":null,"work_id":"65f63370-63b6-48d3-9099-001b479b20c1","year":2024},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.748008Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:bde21470c2c0dd8fdeb553aac7376483f74d44911c605e185a40d0f62da8d23e","observation_id":"8d442da3-12b6-4f65-8055-fdfb0ee16e64","resolution":{"observed_at":"2026-08-12T15:19:25.113277Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.759322Z","title":"Approximate tensor-product preconditioners for very high order dis- continuous Galerkin methods","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.759322Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:ac2b0b6b10882282702dbf52317a4b0c9e61ca2e1c3a97b3a168cf9750e52405","observation_id":"f3565d28-f5ba-48de-9d16-0431adc56627","resolution":{"observed_at":"2026-08-12T15:19:24.759322Z","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":"2026-08-12T15:19:25.931650Z","title":"Algebraic Multigrid","venue":null,"work_id":"38cc10cb-741b-48af-ac0f-52c617c0e690","year":1987},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.765176Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:2b0b3b570f3ae707e7a6eb484cfb87d7aaafdf04df05a321a795064f66a5b4d5","observation_id":"fa9cdf22-ec00-43dd-be89-7914afd7c738","resolution":{"observed_at":"2026-08-12T15:19:25.941131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.776556Z","title":"An explicit expression for the penalty parameter of the interior penalty method","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.776556Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:4295b1d3756e59039974bdb341089ea8e44c152078c1b3751401c3b6b34dfe96","observation_id":"6572dc4a-276f-499c-965a-eb7fac00f74d","resolution":{"observed_at":"2026-08-12T15:19:24.776556Z","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":"2026-08-12T15:19:25.901275Z","title":"Comparison of multigrid alg orithms for high-order continuous finite element discretizations","venue":null,"work_id":"2705aab2-523f-4212-a968-fdcbe6ada73a","year":2015},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.781835Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:9d3410ce3fe2fe24b78a99546d3abf6bb76d99ef235e618c44623bdbc61e0782","observation_id":"a0f51b6b-2614-48a2-bd46-d38190e39720","resolution":{"observed_at":"2026-08-12T15:19:25.910765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2014.12.012","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:25.004165Z","title":"Short note on the mass matrix for Gauss–Lo batto grid points","venue":null,"work_id":"fee090bd-8f5e-4ffd-882b-8be223a13d07","year":2015},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.794725Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:6b99d47e440fc266fe65ade4efb9582e78d121feb9de0d731ed1d86173eb873b","observation_id":"2e5ec88e-e4ec-46ba-ada5-b6ddcb5e24e0","resolution":{"observed_at":"2026-08-12T15:19:25.009883Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.801387Z","title":"Toselli and O","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.801387Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:c26dc3f90e5e88030bbaa6748f94ad4044031a7fb48b7ad14714f0018528ecbd","observation_id":"afe7980c-c223-44db-a7da-258bede9d4bd","resolution":{"observed_at":"2026-08-12T15:19:24.801387Z","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":"2026-08-12T15:19:25.865074Z","title":"A robust numerical method for S tokes equations based on divergence- freehH(div) finite element methods","venue":null,"work_id":"1b143139-bbb4-4422-a2de-edfd1852669d","year":2009},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.809484Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:8a1438913090f520d400d50feff07472d8a4d4732f5d88b114dfd647bb3479bc","observation_id":"801c5d0e-c164-4983-83f4-a94a1820ee76","resolution":{"observed_at":"2026-08-12T15:19:25.880202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.822231Z","title":"The auxiliary space method and optimal multigrid precond itioning techniques for unstructured grids","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.822231Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:cd6e1521fa999cf97c713e2a79b36a0e541a3e5ab8365fe3627388b13ddb2074","observation_id":"0c99c016-21cc-4f96-a4f1-cde182722726","resolution":{"observed_at":"2026-08-12T15:19:24.822231Z","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":"2026-08-12T15:19:24.829942Z","title":"Iterative methods by space decomposition and subspa ce correction","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.829942Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:8ca4f01ef8430bc7acaa56e507f09e5aec94f31b320bdb98f1f4bf86ca665f09","observation_id":"c3a1d91c-23c0-48db-963e-f4074e1d0fac","resolution":{"observed_at":"2026-08-12T15:19:24.829942Z","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/s0377-0427(00)00518-5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:24.912684Z","title":"The method of subspace corrections","venue":null,"work_id":"6d74f61e-ac89-4368-9e24-bacaf9325e8c","year":2001},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.835998Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:c14b215d24854e60cc2140a6348cc03614f4d868ecaf808a7cc43928e24cf6e7","observation_id":"fd0b8285-a052-459a-867a-e1335bf9df84","resolution":{"observed_at":"2026-08-12T15:19:24.919950Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-12T15:19:24.842143Z","title":"The method of alternating projection s and the method of subspace corrections in Hilbert space","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.842143Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:4b060cfa5fabbc973128e5410c52f0699690bc33151b9ae21b1806e330b8d7b6","observation_id":"063c7874-3430-4eb4-9c4e-fc6f39075b0a","resolution":{"observed_at":"2026-08-12T15:19:24.842143Z","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":"2026-08-12T15:19:24.770893Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":130,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.770893Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:ab987e5a87ab5aefc02bfd0a1dd6a8c92294fa02c030911d6c62c4c18ac1e990","observation_id":"1ef9c8e3-546f-4157-8257-3cd679eac511","resolution":{"observed_at":"2026-08-12T15:19:24.770893Z","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":"2026-08-12T15:19:24.788626Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":680,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.788626Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:4cf6e9af1595a02df1508483f78abbdfa3a0045efd47a419fb06d3e4e87388b2","observation_id":"db7b9474-ffce-4049-916e-0c7834db53dc","resolution":{"observed_at":"2026-08-12T15:19:24.788626Z","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":"10.1137/080730044","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T15:19:24.970857Z","title":null,"venue":null,"work_id":"feb0a902-2b00-4389-b171-0a93e9d158ed","year":null},"citing_paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$","version":1},"reference_index":2802,"source":"pdf_text","source_observed_at":"2026-08-12T15:19:24.816387Z"},"links":{"citing_paper":"/paper/2411.14561"},"observation_digest":"sha256:6715f01433d182c41e3c99549223978375b1dd56682f6974bf09bb10bd0e9900","observation_id":"1b935126-d47d-4abe-9fae-d93d1a6c6bbc","resolution":{"observed_at":"2026-08-12T15:19:24.977283Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.14561","last_updated":"2024-11-21T20:18:34Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-13T09:48:31.287217Z","submitted_at":"2024-11-21T20:18:34Z","title":"Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in $H(\\mathrm{div})$"},"reference_resolution":{"displayed":51,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":24,"verified_exact":20,"verified_fuzzy":6},"total_outbound_references":51},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 0 inbound Pith citation observations for arXiv:2411.14561."}