{"as_of":"2026-08-11T11:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:079558f9d4ab25dbb184304018e393c5be2d973d5aa9aeb796a3f77bf4473e10","coverage":[{"denominator":57,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":57,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T03:21:08.843779Z","state":"measured"},{"denominator":58,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":58,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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":"2026-08-02T20:39:52.425525Z","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":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2602.08639","snapshot_observed_at":"2026-08-02T20:39:52.425525Z","title":"DOI arXiv:2602.08639v2","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2602.22861","last_updated":"2026-07-13T13:33:03Z","snapshot_observed_at":"2026-08-11T09:33:57.611104Z","submitted_at":"2026-02-26T10:55:43Z","title":"On $hp$-adaptive Structure-Preservion for the Cahn--Hilliard--Navier--Stokes Equations with Degenerate Mobility","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T20:39:52.425525Z"},"links":{"cited_paper":"/paper/2602.08639","citing_paper":"/paper/2602.22861"},"observation_digest":"sha256:99ce7b4db02434b7a4d8a82366854dd531050100a88879630e94e8dee2446a88","observation_id":"6910000a-a0d4-498f-9040-bad76db4c15c","resolution":{"observed_at":"2026-08-02T20:39:52.425525Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2602.08639/citation-record","integrity":"/paper/2602.08639/integrity","json":"/paper/2602.08639/citation-record.json","paper":"/paper/2602.08639"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.602997Z","title":null,"venue":null,"work_id":null,"year":1958},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.602997Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:2349d1a2e8caab289e95016e60b655ef7f37eba9a87896217467291eabd698f0","observation_id":"eaef4094-8574-419e-a400-d5edf3fb63e1","resolution":{"observed_at":"2026-08-03T03:21:08.602997Z","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":"10.1063/1.2009527","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Physics of Fluids","work_id":"9003bbd0-3c4e-4951-9a28-9c8cf630bc01","year":2005},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.608532Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:92fd67853411388fde5ca51100528f07c91b2e10a53faffc48b0b5d4e80158f3","observation_id":"a5f90b8d-91f6-46cb-939a-73241fa3070d","resolution":{"observed_at":"2026-08-03T03:23:36.935453Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.compfluid.2008.11.007","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Nikolopoulos, K.-S","venue":"Computers & Fluids","work_id":"24e31271-ef02-4050-bdd0-f09f15a5fba8","year":2009},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.612852Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:a584c2ce9a92ece01720d7c3c13505a4985d116fce685af5a9270f83cba3b6f3","observation_id":"b90f88c7-a72b-4ca6-b1b8-baa95d1887a6","resolution":{"observed_at":"2026-08-03T03:23:36.629782Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.617737Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.617737Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:d188d7f03aa6e708521c1a368ba35a6d53a8cab897a3a68a537382c5167da928","observation_id":"ee53ad2e-e39f-4ab8-9d61-d3b4c9d0a5d5","resolution":{"observed_at":"2026-08-03T03:21:08.617737Z","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":"2026-08-03T03:21:08.622298Z","title":"Lee, J.-Y","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.622298Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:e40f2c719ae8f19c59ab35607893a4385ccbfa88524b6753d31ff1e3aa4b0673","observation_id":"f1e1a42e-1080-4917-8bd6-b7d04f119843","resolution":{"observed_at":"2026-08-03T03:21:08.622298Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s0218202523500069","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Mathematical Models and Methods in Applied Sciences","work_id":"5c636d13-9636-48bd-a07f-0b74dbf3898c","year":2023},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.626869Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:709c01b244d92f8a0ee85b29b6d67112f8e0cf26a55fb1d15af941d209e2687a","observation_id":"baf189f3-73df-44c2-80df-157c9caf076b","resolution":{"observed_at":"2026-08-03T03:23:36.324726Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.631598Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.631598Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:c54754fe3d445c8c30b85468d5a969451c0896c54edbecb94bcdf992ad606760","observation_id":"ce1e6ada-6d40-431e-8dab-7db19e60e222","resolution":{"observed_at":"2026-08-03T03:21:08.631598Z","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":"2026-08-03T03:21:08.635779Z","title":"Abels, H","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.635779Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:688d9c99cb4a17cb153b85ae2d5290430fc581029caa8b7d3e5d1e418018162d","observation_id":"cc34787e-0aba-49c1-a9bd-431db28040f2","resolution":{"observed_at":"2026-08-03T03:21:08.635779Z","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":"2026-08-03T03:21:08.640096Z","title":"Boyer, A theoretical and numerical model for the study of incompressible mixture flows, Computers & Fluids 31 (1) (2002) 41–68.doi:10.1016/ S0045-7930(00)00031-1","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.640096Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:2b99e5c495082235ffec31b4148ae0ce40945e19b0f41138578ad4c28a0846c4","observation_id":"eac1875c-87e7-46e6-82a5-c39cbec9b169","resolution":{"observed_at":"2026-08-03T03:21:08.640096Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-03T03:21:08.644375Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.644375Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:7a97bbcc630807c05e335eeb852c9602bcbe641a3d23c41f5649efbfbfcf4f67","observation_id":"0c13a645-9021-40bb-a941-6fd3d18542ae","resolution":{"observed_at":"2026-08-03T03:21:08.644375Z","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":"2026-08-03T03:21:08.648539Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.648539Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:524bc3fe77cc6f54ac281a5c7766b2d9448da744a2fa67f59332118c1d269231","observation_id":"2fc685e0-25a5-479f-be07-bd90ded0226d","resolution":{"observed_at":"2026-08-03T03:21:08.648539Z","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":"2026-08-03T03:21:08.652883Z","title":"Acosta-Soba, F","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.652883Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:33a36d0c5a677bf6d01814cc65a5bf74f109784daba9571a55cede6abf07f915","observation_id":"ee8b768e-bbae-458c-9692-d4dc62afb222","resolution":{"observed_at":"2026-08-03T03:21:08.652883Z","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.apnum.2024.11","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:23:35.954947Z","title":"Acosta-Soba, F","venue":null,"work_id":"137f8545-b85b-44ff-bca5-3fecf810a200","year":2025},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.657043Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:df3a5a741011ff86e61875fe1bc972849afd5b3946dd126bc12309823a6b3d23","observation_id":"bb714a91-a8e6-4778-b501-a718c6666016","resolution":{"observed_at":"2026-08-03T03:23:36.059331Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.661189Z","title":"Guillén-González, G","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.661189Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:8f671d64496b5a5f27232e35263dff94a6b189743763055a7c7c3b3d5277b3af","observation_id":"711a205b-762e-4600-9ece-1da9da43e9bc","resolution":{"observed_at":"2026-08-03T03:21:08.661189Z","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":"10.1137/23m1587853","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"SIAM Journal on Scientific Computing","work_id":"d5e9939c-665e-4ad6-a973-3a8dd61cb8a4","year":2024},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.665190Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:cddf57e7c2adc27ff49e71194323e4c62fcbad270f7973df385baf04a2d36045","observation_id":"8314e283-cbde-48c1-8029-035af60fe092","resolution":{"observed_at":"2026-08-03T03:23:35.831777Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1038/s44172-025-00390-w","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Zhang, Z","venue":"Communications Engineering","work_id":"60d603be-cef2-43c3-8c20-3f2f562b1c76","year":2025},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.669269Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:d29fcfe3970ac2b709bddef5e6d017e0838114a81328076adab18e990eec40f5","observation_id":"06da0a69-aacf-44f3-9b17-ed3d3d5ba17d","resolution":{"observed_at":"2026-08-03T03:23:35.559466Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1361-6501/adf2c9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Measurement Science and Technology","work_id":"24b7e2ba-8d21-46e3-b1e9-c664fd4b61cf","year":2025},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.673633Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:e6f9c47394022211e087fea58209f0bfebf1fb35ae2a403d2773c14cf9c1ca5c","observation_id":"aa542c60-1c21-4c2d-91a6-a770bbff07a7","resolution":{"observed_at":"2026-08-03T03:23:35.256077Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10915-024-02721-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Dedner, A","venue":"Journal of Scientific Computing","work_id":"223454e7-d829-4207-82f6-d5540efcf521","year":2024},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.677603Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:6a026d9734b116d60b15085264391a0edc98b30a011c0f13147b119c4dd05423","observation_id":"6becde5a-8509-4c18-bb91-0a6d7711523f","resolution":{"observed_at":"2026-08-03T03:23:35.090241Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.682200Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.682200Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:40d50c6b7a5ed0bc2064201d72bdaa5fd6c6c3896f0b978c3d3d5867a1c7ca29","observation_id":"3d954b81-dca2-4ac2-b736-6eb8710d2535","resolution":{"observed_at":"2026-08-03T03:21:08.682200Z","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.cma.2005.06.020","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Grooss, J","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"9e0832df-0244-4c0d-861b-b15d81053e47","year":2005},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.686575Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:e93f8a3d2f78c98f3ba2039e88b7ea6b0404e419ec12d90a56c08ca53b956cef","observation_id":"a1b3aa23-0e3c-40a2-bdb9-a87c0ddbbbaf","resolution":{"observed_at":"2026-08-03T03:23:34.772707Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2006.03.010","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of Computational Physics","work_id":"c4b379d1-08dd-4c87-870c-f5665d221d6d","year":2006},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.690866Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:ad60447b4a5bd6af25be83bce8f05cd9ae70c125cfc3bb32272a7fb409e6c589","observation_id":"f8dc6cdb-4366-4ff9-a078-77843243ae3c","resolution":{"observed_at":"2026-08-03T03:23:34.559110Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.695176Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.695176Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:9e29ec402a24d969d6c707df2d65b1a3d003249b0b40d045f7f4de75f73a47b3","observation_id":"7ccb4ea4-8384-453f-a5c3-2cc46317f8f5","resolution":{"observed_at":"2026-08-03T03:21:08.695176Z","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/s10915-023-02380-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Huang, W","venue":"Journal of Scientific Computing","work_id":"d6a2da1a-2e91-4f9b-9429-b6b606f3e933","year":2023},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.699450Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:8f413b5ece8281687ad593bcdf999660cd62ee8cb27e043cb490370f6f372944","observation_id":"fcca3b13-500a-485c-b59b-a4c255203726","resolution":{"observed_at":"2026-08-03T03:23:34.432698Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.703652Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.703652Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:7b4892c0428038b7aca98fcf62351230fef6d09fc464dadbd52994344ee9f9ac","observation_id":"ef84b49c-8d4f-4d61-839b-29f9407fcb6a","resolution":{"observed_at":"2026-08-03T03:21:08.703652Z","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":"2026-08-03T03:21:08.707626Z","title":"Frank, A","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.707626Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:57803147490434bd668558afb8fc566154c88487980e6e1aa2ba9002fbb5258b","observation_id":"53705437-f587-47ba-9683-835129186146","resolution":{"observed_at":"2026-08-03T03:21:08.707626Z","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":"2026-08-03T03:21:08.711896Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.711896Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:e29a6e31f7040268720b8ad221ac7dd0528f1c576bcad7a50f0a4b0e5b180fea","observation_id":"24962d56-2e80-4bb3-9150-24e07e65c584","resolution":{"observed_at":"2026-08-03T03:21:08.711896Z","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":"2026-08-03T03:21:08.715936Z","title":"Dedner, R","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.715936Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:57484ff47d1ac863ded7dc2594577c44cd153d0a28931ccead9406f13e126dab","observation_id":"9e3f884d-f7c0-4988-a0ec-e73aa6de88a1","resolution":{"observed_at":"2026-08-03T03:21:08.715936Z","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.apm","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:23:34.131132Z","title":"Dedner, B","venue":null,"work_id":"a40a3be4-3275-4272-ba89-6669a9badc69","year":2019},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.720827Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:19476a99c36560cc9d1e3545bc0d31c3acb49518b68d2d80981cc077909642c9","observation_id":"e075dead-4db1-44b7-9164-a67a7bccd5c3","resolution":{"observed_at":"2026-08-03T03:23:34.223264Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.725294Z","title":"Magaletti, F","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.725294Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:4c60d0abd532663c3a52ce8869bd7f111fbdd2518a838ba8666ff92aa2011a45","observation_id":"86d34e84-e517-44ac-8ee1-7730a5caad2a","resolution":{"observed_at":"2026-08-03T03:21:08.725294Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-03T03:21:08.729386Z","title":"Girault, P.-A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.729386Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:807cc16edbfbaa4e5392e2fa2b90e47fd7e96297379f2898d11188172c256711","observation_id":"dacfcb2d-38e1-4505-8baf-1553ec6a7b0b","resolution":{"observed_at":"2026-08-03T03:21:08.729386Z","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":"2026-08-03T03:21:08.733714Z","title":"Piatkowski, S","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.733714Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:d0e41d30e1991897b2042ea2d3fa94d12913ccdf75062a3e698e125cfe0f9f09","observation_id":"8041ebe5-17ef-46e6-bcb7-5eeb8937cbcb","resolution":{"observed_at":"2026-08-03T03:21:08.733714Z","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":"2026-08-03T03:21:08.738246Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.738246Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:0f1d55f0872a34de5ba3f3ede8da937be0d459fd8922e2fef82d500b81f0e669","observation_id":"89042c8b-b38e-43f4-8a15-b1b7c85b6cf6","resolution":{"observed_at":"2026-08-03T03:21:08.738246Z","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":"2026-08-03T03:21:08.742447Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.742447Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:a8e7ed6ed4bf2f3ab736632183762b1563edea013f96dc11a0d292c94fb00d72","observation_id":"f34bc5cb-ecb4-4c79-8564-81d2fce5f378","resolution":{"observed_at":"2026-08-03T03:21:08.742447Z","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":"2026-08-03T03:21:08.746620Z","title":"ten Eikelder, D","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.746620Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:95cef99ece8b73166621d6941c03b745c51e3b6ee135c6d5ae1918a4e598e4c8","observation_id":"103b0ee9-6fc3-4c05-b505-3473da6f5673","resolution":{"observed_at":"2026-08-03T03:21:08.746620Z","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":"2026-08-03T03:21:08.750765Z","title":"Ainsworth, R","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.750765Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:2d9585b76513b12de8b8d8f978a51a60e4e7a9cf7e6b9c87b9b0ac2e060e9a59","observation_id":"e24cb79b-3cc2-47ca-8246-5cbe0cd7634d","resolution":{"observed_at":"2026-08-03T03:21:08.750765Z","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":"2026-08-03T03:21:08.755205Z","title":"Rivière, Discontinuous Galerkin methods for solving elliptic and parabolic equations: theory and implementation, SIAM, 2008.doi: 10.1137/1.9780898717440","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.755205Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:0b903ed7b1eab5e58e76ee97ff1213bd38928d00bcf0b910bcb833447cda29a7","observation_id":"26c2111d-4328-4e26-a371-5121b5b91480","resolution":{"observed_at":"2026-08-03T03:21:08.755205Z","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":"2026-08-03T03:21:08.759620Z","title":"Epshteyn, B","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.759620Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:19ec6755c024fb88d0b1ce0310e3551b55a8e9df92122d09f40fb89f3a5689fd","observation_id":"d00134b0-66f7-4786-8cd0-a4f75fdde198","resolution":{"observed_at":"2026-08-03T03:21:08.759620Z","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":"2026-08-03T03:21:08.763929Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.763929Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:0778a2771a0c47deefaab41fde70f686d1ba8cea29f89f5ecb295f85c351ebaf","observation_id":"f3aeed7e-bcb1-411c-9f0e-6bdfd47a789f","resolution":{"observed_at":"2026-08-03T03:21:08.763929Z","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":"2026-08-03T03:21:08.768351Z","title":"Acosta-Soba, F","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.768351Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:7cf8f7564d2ba71388879ae60c4e2499979f7691ca5bbb578f7c7149a3069aa5","observation_id":"ec66d010-c471-4551-b52e-127c3d0bcc8f","resolution":{"observed_at":"2026-08-03T03:21:08.768351Z","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/s11831-014-9112-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Tierra, G.-G","venue":"Archives of Computational Methods in Engineering","work_id":"9137bed3-1968-4f84-abd1-c11b30befd0e","year":2014},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.772725Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:3f3e686b7738b8af8af611d342dbe105775475d5e699beb81d02a6d96f3a87d8","observation_id":"7f660598-7a6c-410b-8c1d-0a66086eca82","resolution":{"observed_at":"2026-08-03T03:23:33.931322Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.776914Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.776914Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:09fd2664eee408417372013c5cdc9e3174d3e418abbd66296b9c511162862784","observation_id":"c6723050-9bd9-450d-8de3-6ec9542159b1","resolution":{"observed_at":"2026-08-03T03:21:08.776914Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-03T03:21:08.781122Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.781122Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:445a84e7fe2dc1afc17eac02aed6d49c6b5a8e24f9e932def33743f83725f12f","observation_id":"763f3796-f025-4367-9899-79523757cd76","resolution":{"observed_at":"2026-08-03T03:21:08.781122Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-03T03:21:08.785444Z","title":"Zhang, C.-W","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.785444Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:45ee039adbb8b315a5409e50a33dd59c1b7094161bd8c90987f91f084920af7f","observation_id":"be3d8ea1-95f4-4258-94a3-c0a689ff31b6","resolution":{"observed_at":"2026-08-03T03:21:08.785444Z","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.jcp.2012.12.019","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Cheng, F","venue":"Journal of Computational Physics","work_id":"9d1b36e3-9537-4b89-9a24-c8d6212faad4","year":2013},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.789647Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:11e6708d6405d0c11ee46d8dce423da6ac97b09b294d8ab172ff252d31962e6a","observation_id":"f41d70bf-e280-4592-8cb5-29bf3e626dc0","resolution":{"observed_at":"2026-08-03T03:23:33.705866Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.793744Z","title":"Huang, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.793744Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:5c28a67e02429f4cc103bc5d5ba0e4cca7a4d9302e64807fc2bcada545d9948d","observation_id":"193df561-f73f-4517-b0d2-6d6d33029f88","resolution":{"observed_at":"2026-08-03T03:21:08.793744Z","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/fld.268","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Klöfkorn, D","venue":"International Journal for Numerical Methods in Fluids","work_id":"08d45276-4277-45aa-b8bf-b89dd8262be6","year":2002},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.797697Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:09ea479f8b2a746211ec3433493b3c6fe2eb920ec1c1223f2d5aa71ad6d68175","observation_id":"59bc5d38-2a68-40a7-ae76-a751eb37f0ef","resolution":{"observed_at":"2026-08-03T03:23:33.408509Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.cma.2005","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:23:33.040641Z","title":"Guermond, P","venue":null,"work_id":"f477fb1a-8258-48f0-8c6a-f720478d98bd","year":2006},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.801763Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:eb87fc8392c84ee414214ad0293ed79c32e6d83de1cbcfbb9bca5cb13679e3a8","observation_id":"7193d759-1c21-46cc-b99b-d14a0f998d34","resolution":{"observed_at":"2026-08-03T03:23:33.170691Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.805733Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.805733Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:1890a9c27910c5933388fa3c961dc4894ae5d3ecd87f2f0f7646339d6861f4ee","observation_id":"e663fa92-1794-4f04-b25d-39b33991823b","resolution":{"observed_at":"2026-08-03T03:21:08.805733Z","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":"2026-08-03T03:21:08.809642Z","title":"Bastian, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.809642Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:3afd5c61ed57cc2b6e816a7c8e080b880699a4b49806310a4d36b525a9f47c8b","observation_id":"2c912292-bc42-41c6-b5c0-ff1cf8ac8417","resolution":{"observed_at":"2026-08-03T03:21:08.809642Z","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":"2026-08-03T03:21:08.813843Z","title":"Dedner, R","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.813843Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:975ba80400557d6ad0909c1e430f6185bf45759e4526d2fa750a19c23ee73e55","observation_id":"f9a7a35b-ee43-458e-85cd-9e1a630f2d4b","resolution":{"observed_at":"2026-08-03T03:21:08.813843Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-03T03:21:08.817884Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.817884Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:3cdc0607539b7e436892f8609cc7687cc9fdf3bfee7c5b2af85a29fdabd7c61b","observation_id":"751a92d4-2890-462e-81bb-613703781356","resolution":{"observed_at":"2026-08-03T03:21:08.817884Z","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":"2026-08-03T03:21:08.822188Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.822188Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:a68963a3439e970f3f792409cd90610f932202230a09eff7a61d3fa66b4678ee","observation_id":"621b1e96-019c-4613-96aa-e176df9e6787","resolution":{"observed_at":"2026-08-03T03:21:08.822188Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.02111","last_updated":"2020-08-03T20:43:59Z","snapshot_observed_at":"2026-08-07T12:18:30.729216Z","submitted_at":"2020-08-03T20:43:59Z","title":"An adaptive central-upwind scheme on quadtree grids for variable density shallow water equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.02111","snapshot_observed_at":"2026-08-03T03:21:08.826298Z","title":"Blatt, P","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.826298Z"},"links":{"cited_paper":"/paper/2008.02111","citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:3417bca08b3d487e32b9f9a23411033fbf962817233ba1112a492d166d814c59","observation_id":"a665e868-0276-4279-b694-9db6da605cdc","resolution":{"observed_at":"2026-08-03T03:21:08.826298Z","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":"2026-08-03T03:21:08.830803Z","title":"Alkämper, A","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.830803Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:8001755193386164623ac3df5398d4f8fde9485a4c107d3aa183cc889b28220f","observation_id":"42eceef9-5720-4b33-9386-5392fe274c67","resolution":{"observed_at":"2026-08-03T03:21:08.830803Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/17m1156137","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Alkämper, F","venue":"SIAM Journal on Scientific Computing","work_id":"21bcc2a3-714b-45f4-8a5f-119259adcf18","year":2018},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.835156Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:96978353acbc53e8d302b1810683bc899408bdbf145cad3644b16fb34a851c94","observation_id":"ca0f1091-c2a9-4ef5-9262-1fb4a8d9b268","resolution":{"observed_at":"2026-08-03T03:23:32.887028Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/fld.2611","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Aland, A","venue":"International Journal for Numerical Methods in Fluids","work_id":"0b7cc92c-e842-4eea-946f-7e79b989f137","year":2012},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.839689Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:82dda873043f1f365709e3a1c55b4ecb28218a52c44465359f614c883ad42a17","observation_id":"10691f15-e710-4729-a2c8-5c4a33ba2800","resolution":{"observed_at":"2026-08-03T03:23:32.653798Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T03:21:08.843779Z","title":"psi_k \" ) dxL = dx ( m et ad ata = {","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement","version":4},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-03T03:21:08.843779Z"},"links":{"citing_paper":"/paper/2602.08639"},"observation_digest":"sha256:52d3aadb0d33b85e989a5dcb47254e0a7a73c273599d3260d2e88b4598f9c102","observation_id":"ec97f22a-0791-4590-a2e9-07212ef4497e","resolution":{"observed_at":"2026-08-03T03:21:08.843779Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2602.08639","last_updated":"2026-07-16T09:03:09Z","latest_version":4,"primary_category":"math.NA","snapshot_observed_at":"2026-08-09T19:03:12.748832Z","submitted_at":"2026-02-09T13:34:48Z","title":"Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement"},"reference_resolution":{"displayed":57,"state_counts":{"malformed_identifier":8,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":32,"verified_exact":17,"verified_fuzzy":0},"total_outbound_references":57},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 1 inbound Pith citation observation for arXiv:2602.08639."}