{"as_of":"2026-08-20T15:02:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7da31c4c4d95efa77efa8db17932be99af494ca927a850440cb9839f846dfac5","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T17:27:12.654277Z","state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T11:32:47.185654Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.13342","snapshot_observed_at":"2026-08-01T11:32:47.185654Z","title":"Nochetto and Mansur Shakipov","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.26664","last_updated":"2026-07-29T09:22:27Z","snapshot_observed_at":"2026-08-16T17:04:03.618117Z","submitted_at":"2026-07-29T09:22:27Z","title":"Stabilized Morley FEM for surface Stokes in stream-function formulation: Optimal convergence via a new geometric estimate","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T11:32:47.185654Z"},"links":{"cited_paper":"/paper/2508.13342","citing_paper":"/paper/2607.26664"},"observation_digest":"sha256:390f5b7dd1773b8b6f9864b012ab1fce82f07247a4da7775aedb07b97af66366","observation_id":"12c5ffbb-17ed-4b08-b66f-0741bb936bd6","resolution":{"observed_at":"2026-08-01T11:32:47.185654Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2508.13342/citation-record","integrity":"/paper/2508.13342/integrity","json":"/paper/2508.13342/citation-record.json","paper":"/paper/2508.13342"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T17:27:12.908417Z","title":"Relaxation dynamics of fluid membranes","venue":null,"work_id":"6aeb7307-d0d6-4206-b7af-337e71a740cd","year":2002},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.611279Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:dfc0c2d0c09c77e124ef8eeb6b1d0c5b2a484dc947180a8eb8f0bc2dcb3c978f","observation_id":"62e9511e-6fbb-4ea5-9bef-b50f351dd2a3","resolution":{"observed_at":"2026-08-15T17:27:12.911587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.899204Z","title":"A posteriori error estimates for the Laplace-Beltrami operator on parametric C 2 surfaces","venue":null,"work_id":"da4500ae-7d7b-4a8e-99d2-dc1ea5f525e2","year":2019},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.618646Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:24092804710884a79dcb7a1bb5f7786615ca20720963b6317aec5dc3020616bc","observation_id":"546472de-57ca-442f-a9b3-5a7b590f336f","resolution":{"observed_at":"2026-08-15T17:27:12.902718Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.632205Z","title":"Pointwise accuracy of a stable Petrov-Galerkin approximation to the Stokes prob- lem","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.632205Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:39a08e69680866be91288b1d1f9f6a7c27c23ed9ab601312e459c17b37172ff2","observation_id":"b69c72f6-b007-4ac8-92eb-6b8c620a8345","resolution":{"observed_at":"2026-08-15T17:27:12.632205Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.19470","last_updated":"2025-07-01T18:18:18Z","snapshot_observed_at":"2026-08-20T04:58:28.451382Z","submitted_at":"2024-10-25T11:01:33Z","title":"SFEM for the Lagrangian formulation of the surface Stokes problem","version":2},"cited_work":{"arxiv_id":"2410.19470","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.19470","snapshot_observed_at":"2026-08-15T17:27:12.681106Z","title":"SFEM for the Lagrangian formulation of the surface Stokes problem","venue":"math.NA","work_id":"7dfc1c9c-cbba-41ee-ba69-eac0a570fb2b","year":2024},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.639621Z"},"links":{"cited_paper":"/paper/2410.19470","citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:01554b4c79167c0b4477accdc0ac6e839e2264d9a25202b077ff8d97adf5c4e9","observation_id":"4016e63d-decd-451d-9524-622c91849ce5","resolution":{"observed_at":"2026-08-15T17:27:12.686558Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.869849Z","title":"Stabilized mixed methods for the Stokes problem","venue":null,"work_id":"84aec28a-f042-435a-8c0e-df5938affa55","year":1988},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":1984,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.628920Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:9be138084249982f9f4c00bd3c4b459254747d918e5551a1eb1fe88f7a9e2968","observation_id":"13c454cb-b77f-4290-8ed1-bd8af9889ed5","resolution":{"observed_at":"2026-08-15T17:27:12.873475Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.859328Z","title":"L2-estimates for the evolving surface finite element method","venue":null,"work_id":"5a64cf3a-f5f6-4e7a-8247-9631c65a1257","year":2013},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":1988,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.636158Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:7b39083c50a1865d715c5ccd2b1787d6cdd485721881ef7f7d132079e351dbcd","observation_id":"e8973b0a-5fe0-4a55-b274-a10285edc494","resolution":{"observed_at":"2026-08-15T17:27:12.862739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.849408Z","title":"Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds","venue":null,"work_id":"cbff0918-32f5-43c1-927c-80a4b23906d2","year":2018},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":2004,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.643294Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:6fa75b9d7360dfbcc3c0523a7e11f615574cc199cb82a6dbcbfeef058b4f50d7","observation_id":"bc2c16a3-80ff-4f7d-afaa-996abdbc3e98","resolution":{"observed_at":"2026-08-15T17:27:12.853069Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.830471Z","title":"Finite element interpolation of nonsmooth functions satisfying boundary conditions","venue":null,"work_id":"319bca16-da6c-46ef-9024-78fb769d2b03","year":1990},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":2009,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.649636Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:fb62ec946fd08436d045eeeb95eade5ae2a3bf51f79e769d027aa580d88b9e23","observation_id":"fd7fa71b-0c1b-491f-96c5-d794b8dd193a","resolution":{"observed_at":"2026-08-15T17:27:12.833811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.879766Z","title":"On the stabilization of finite element approximations of the Stokes equations","venue":null,"work_id":"771d7199-0179-4e4b-add9-fb3a2c54f57e","year":1984},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":2011,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.625552Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:0851f2c89adf905c32cb9b1fcbfef937ada56c0a9d148e40b252ed557ee78f49","observation_id":"ce91e55a-cd7f-4167-8a89-f14c1345eb62","resolution":{"observed_at":"2026-08-15T17:27:12.883192Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.820952Z","title":"Stokes flow of an evolving fluid film with arbitrary shape and topology","venue":null,"work_id":"743cd8ce-f5c0-4dc3-9fca-3bc717c07f05","year":2025},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.654277Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:da12a88f116b69455e8604a260e4fc828bff96e0eea1e16cded297fd23950aa2","observation_id":"e684a1e7-26eb-40b2-877d-2ed689262dc5","resolution":{"observed_at":"2026-08-15T17:27:12.824346Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.839841Z","title":"A finite element method for elliptic equations on surfaces","venue":null,"work_id":"78aeb60f-dcfb-4a5c-b14c-2c93c93ba106","year":2009},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.646326Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:a476633c425689380ded5553e66fee8ec409a588866236f65e2fcfe86c3171f6","observation_id":"f131bd42-b7a1-4d00-a9c3-0ea3531bbcda","resolution":{"observed_at":"2026-08-15T17:27:12.843327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.889202Z","title":"Finite element discretization methods for velocity- pressure and stream function formulations of surface Stokes equations","venue":null,"work_id":"2c7a74e1-ca21-448a-a7ef-2145064b4370","year":2022},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.621988Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:7ce49978f865a3000cbce41368c67c9a3df9e1daf10c1bf2058ae1c50d6c1cd1","observation_id":"360cacb4-e308-41fa-b3e9-004caeef5f7a","resolution":{"observed_at":"2026-08-15T17:27:12.892785Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T17:27:12.615107Z","title":"[BBF13] D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-15T17:27:12.615107Z"},"links":{"citing_paper":"/paper/2508.13342"},"observation_digest":"sha256:27f5ae35098d63b5aa19217a6f3a9a685f629e2fa12741a2efc94ebe21dd8d33","observation_id":"b881e19d-9ad9-48b4-beb8-1a1856ccd764","resolution":{"observed_at":"2026-08-15T17:27:12.615107Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2508.13342","last_updated":"2025-08-18T20:01:15Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-20T10:24:00.538055Z","submitted_at":"2025-08-18T20:01:15Z","title":"Surface Stokes Without Inf-Sup Condition"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":10},"total_outbound_references":13},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 1 inbound Pith citation observation for arXiv:2508.13342."}