{"as_of":"2026-08-16T09:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3a8a24deeb7422a871b94e6ed976badd080db7270d50c1cc8445f4929c4de8fb","coverage":[{"denominator":58,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":58,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T13:39:54.570241Z","state":"measured"},{"denominator":59,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":59,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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":"2026-08-14T13:03:36.395201Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-14T13:03:36.637420Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"cited_work":{"arxiv_id":"1908.04910","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.04910","snapshot_observed_at":"2026-08-14T13:03:36.637420Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","venue":"math.NA","work_id":"16aa3b42-bc80-44ff-99e9-8a6903a2b66e","year":2019},"citing_paper":{"arxiv_id":"1908.06124","last_updated":"2021-02-18T13:36:35Z","snapshot_observed_at":"2026-08-14T12:52:49.003602Z","submitted_at":"2019-08-16T18:29:09Z","title":"Convergence of a Robin boundary approximation for a Cahn--Hilliard system with dynamic boundary conditions","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T13:03:36.395201Z"},"links":{"cited_paper":"/paper/1908.04910","citing_paper":"/paper/1908.06124"},"observation_digest":"sha256:2b2726031f736593dcca87986625d9cf4ec095ee54abcb83ded1c5e80127485d","observation_id":"601297a0-3de2-4405-ad9a-359d2040d486","resolution":{"observed_at":"2026-08-14T13:03:36.696012Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1908.04910/citation-record","integrity":"/paper/1908.04910/integrity","json":"/paper/1908.04910/citation-record.json","paper":"/paper/1908.04910"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.358844Z","title":"Abels and M","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.358844Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:8c12e1fa85a13194363fc288c7291078f5b86d84c2d84f29fd73b5d888e5534d","observation_id":"6c6e4422-6b42-477e-bc83-ef2026d39662","resolution":{"observed_at":"2026-08-14T13:39:54.358844Z","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":"2026-08-14T13:39:55.308802Z","title":null,"venue":null,"work_id":"1886c739-7071-48ff-9de0-fd9e0fbdf6c0","year":2016},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.363238Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:26d982fe4e52c525e95ea933cf87782ff13d0a35a0f9a2c4a08c65f0d4c55700","observation_id":"855601ad-b9b5-44cd-b04a-d4c1b99c6e9d","resolution":{"observed_at":"2026-08-14T13:39:55.312321Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.367183Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.367183Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:93e458d364e33a262bb69eafdecc24941ac0a24d9f600653101c76a8a737506e","observation_id":"0b2cd947-2390-497b-a280-ab13c2762ce0","resolution":{"observed_at":"2026-08-14T13:39:54.367183Z","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":"10.1051/m2an:2001133","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.918814Z","title":null,"venue":null,"work_id":"28f974d4-ca46-4f62-9275-86654befd4d6","year":2001},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.371180Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:18767edd8ee8857908f25bd8e15b0da7026e2072485057b9508d34950ef4db8e","observation_id":"86fe785b-0e1b-4462-acee-775a361518a9","resolution":{"observed_at":"2026-08-14T13:39:54.922126Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/0153049","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.909654Z","title":null,"venue":null,"work_id":"b2ec38f3-8402-4d6d-9200-b677e83b3bfd","year":1993},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.375205Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:bf2cd6822dd1e62bb27fa2d73aa4d07a4c21bbb5c51df4faded71574568a1e32","observation_id":"61589595-23c4-42db-a852-ad8529b42aa2","resolution":{"observed_at":"2026-08-14T13:39:54.912691Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imanum/16.1.111","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.898143Z","title":null,"venue":null,"work_id":"984aaa3d-3895-440d-8679-0b93ea5b561c","year":1996},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.379061Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:887e767cfc2430d0be0ded8b620347d2683315bbd33bc11abe9b80658e2126a5","observation_id":"eb3cee68-8d21-4208-8429-b39ff21836f5","resolution":{"observed_at":"2026-08-14T13:39:54.902092Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.383021Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.383021Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:75bd9f7bdeb10b4372f9162ce451c1e3f24eeeca1765e7c95c24a7cf883579f6","observation_id":"0ab9d450-16f1-4c06-9539-44d730c9d110","resolution":{"observed_at":"2026-08-14T13:39:54.383021Z","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":"10.1017/s0956792500000759","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.880043Z","title":null,"venue":null,"work_id":"2c1c0f10-9f8d-4396-9dca-3ab2580064f1","year":1992},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.386631Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:2e7e3617912112efa6e4ce70e512be9c0484adf271ab62836e62dd65f25fd3db","observation_id":"b00f2237-5f5f-4737-94dc-59a66c810a21","resolution":{"observed_at":"2026-08-14T13:39:54.883790Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.298196Z","title":null,"venue":null,"work_id":"d51bb6bd-6cd3-4ec5-9f99-2540c9c9402c","year":2002},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.390246Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:031498b3ac4311c54e4c940b76727f897cee312ef426b39b3082a998d0436d6a","observation_id":"c5bf8ea6-4b61-4f9b-bbe5-84e4ec67543c","resolution":{"observed_at":"2026-08-14T13:39:55.301756Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.289122Z","title":"Brenner and L","venue":null,"work_id":"3c30a42e-27c8-4b65-81d7-b2408437ff01","year":2002},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.393763Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:5041ade7fce78f1547d583220a770c57f1ad863459e91f939e3b3679c1c381c3","observation_id":"efe9d723-cc01-451f-92be-48aa99c441a1","resolution":{"observed_at":"2026-08-14T13:39:55.292191Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/120861333","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.869688Z","title":"Campillo-Funollet, G","venue":null,"work_id":"46f19434-43dd-455d-9045-4e8e5af732ac","year":2012},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.397185Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:52e3fc13999fe2ab143864649a2e89113929db386e78e84ee40a11e4ef966f16","observation_id":"e212e523-10e4-4883-8a2a-04d5ce82d2c9","resolution":{"observed_at":"2026-08-14T13:39:54.873260Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2017.04.010","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.858311Z","title":"Cheng, X","venue":null,"work_id":"de8a8606-19a9-4a39-a0e2-4c57c91ee640","year":2017},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.401498Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:e2305cc68996caad0150f76b845e9c653c0994cfcce3baaba6ade816953ada1e","observation_id":"3af16990-0145-419b-9b65-79f64a23505b","resolution":{"observed_at":"2026-08-14T13:39:54.862411Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.277936Z","title":"Cherfils, A","venue":null,"work_id":"042171b4-0370-4372-a3ab-71f89c148a1e","year":2011},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.405601Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:243df864b42e6d0d96bf796ba3fb46df4b365c456dc96a41c6f545107a5884b0","observation_id":"d2110d6e-b809-4060-901f-2ce31a9724a0","resolution":{"observed_at":"2026-08-14T13:39:55.281477Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.409850Z","title":"Chill, E","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.409850Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:3506f233d860a27c8db2a40b2b8446dc132dd8733507a3446cad01d9164335a5","observation_id":"91c079a1-a198-4b3d-8d96-b854efa58a3d","resolution":{"observed_at":"2026-08-14T13:39:54.409850Z","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.jmaa.2015.04.057","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.839262Z","title":"Colli and T","venue":null,"work_id":"f9459648-958c-4c75-8576-49c3c28ccfb2","year":2015},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.413965Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:6f3e2580439df1cc775b729972fa4c2b86d83730beed3c92f5ea7ccefbf02e43","observation_id":"adc75e68-369f-4ab4-b387-1814c09c493c","resolution":{"observed_at":"2026-08-14T13:39:54.843930Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jmaa.2014.05.008","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.828708Z","title":"Colli, G","venue":null,"work_id":"a3330486-7086-483b-8e28-5f0dc342fdec","year":2014},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.417412Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:887736f37a46a9dc6dcd7db2f93528fffc1f5cd4fd59e159a9851c89cbe3afc1","observation_id":"3c67a1a1-238c-48e5-8a68-88a8da871208","resolution":{"observed_at":"2026-08-14T13:39:54.832359Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.265507Z","title":null,"venue":null,"work_id":"aa3c270b-26f1-4fef-896f-7b7f1d8dec21","year":1992},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.420771Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:5352fc3aa07167ee7a7da1e417ddae1fdcb76a23f9622cc0a442783cc65ad3f4","observation_id":"f32b13ce-1d79-4fa7-8c8a-d3d0a0720d80","resolution":{"observed_at":"2026-08-14T13:39:55.270148Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.255886Z","title":"Elliott and H","venue":null,"work_id":"51c662a5-00f3-4727-becf-66cc9f5ab743","year":1996},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.423923Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:b5b5f581d1b2972e71f666373aff35dda4777ff852038025f51d6c4ee008ec2e","observation_id":"1e283607-d39c-454c-923f-26f5110624e3","resolution":{"observed_at":"2026-08-14T13:39:55.259362Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.245704Z","title":null,"venue":null,"work_id":"c04e849e-4092-436a-8fd8-117ddcaa51f8","year":1993},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.426781Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:3b8f1b8f372d3d6f343c0975ed3d7e1bef1890f6a89d675541249fd24786a9bc","observation_id":"aecb77da-3d05-4263-b6d4-a50f6a5049fc","resolution":{"observed_at":"2026-08-14T13:39:55.248884Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.429796Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.429796Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:ce20a78d27292c54513c16e9df57f373bf5a1243d4f3f60f7ddeff736cf23045","observation_id":"09b042d3-dd8e-48eb-899d-8123a6c1f3a8","resolution":{"observed_at":"2026-08-14T13:39:54.429796Z","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":"10.1103/physrevlett.79.893","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.811911Z","title":null,"venue":null,"work_id":"966c80d7-486a-45ef-84b0-885fc7ababfc","year":1997},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.432804Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:864bf8db69c3d0691a8a7c19583bf5879315227aff61c241d8b09ad54a6abfce","observation_id":"8e1ea2cc-fb53-4484-8810-a856b8047ccb","resolution":{"observed_at":"2026-08-14T13:39:54.815451Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.235551Z","title":null,"venue":null,"work_id":"8246b181-1056-4201-ba12-7d1a8e8dae8d","year":1998},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.435678Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:4a9dbc31da67527add29eaabe809772c847692f9f06cf3b373194f77792e923e","observation_id":"ebdfd4a2-7066-4d37-8922-237022284564","resolution":{"observed_at":"2026-08-14T13:39:55.239034Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.438260Z","title":"Frank, A","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.438260Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:4f83871ae225bb8d81cd2bdacedf4ed28514ad1f082578b62f0f6b9a54dcf968","observation_id":"8ccf4fbd-1e8f-43db-b3f0-a54a71a1a213","resolution":{"observed_at":"2026-08-14T13:39:54.438260Z","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/mma.757","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.791496Z","title":null,"venue":null,"work_id":"9f4586c7-e27a-4223-9a48-e9c099e1ce8c","year":2006},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.441467Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:3fc89785159f3212acbab67c7debeb41596cfb6069e141eaead12472083b1b07","observation_id":"7d6afb44-5a1a-4b9e-92e6-a41628540a3a","resolution":{"observed_at":"2026-08-14T13:39:54.796292Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.apnum.2015.09.002","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.780521Z","title":"Garcke, M","venue":null,"work_id":"6d4e4bd0-223a-42b2-a841-ef5a9acb9927","year":2016},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.444177Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:d2670946fe43f10534090a16b83902e5355bf068f4398e3a7fb9b73d6be2192f","observation_id":"8e5a6dbe-b09a-4491-9d57-69f3279c288f","resolution":{"observed_at":"2026-08-14T13:39:54.784261Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/19m1258840","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.769087Z","title":"Garcke and P","venue":null,"work_id":"83a21526-d7f3-4527-8fd0-8ea8caf27745","year":2020},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.447022Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:d2b0e174c8bf9220325ed8d5b301334574e50140f478e5a8a75801874ff14aee","observation_id":"bb1837f2-8c79-44f3-8374-bd0940e00335","resolution":{"observed_at":"2026-08-14T13:39:54.772241Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3934/cpaa.2009.8.881","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.758372Z","title":"Gilardi, A","venue":null,"work_id":"d2694278-28be-4cc1-bda7-21c71a0ae32f","year":2009},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.449730Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:e7f26fb829cd0f2fef66c0b6c3732cd07da8847994b68f8ee209ad42d4a468a1","observation_id":"93d73a9a-b334-4fa7-bdb9-0ae9a49dc4c4","resolution":{"observed_at":"2026-08-14T13:39:54.762335Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.453296Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.453296Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:fee38281577df93541fd8d1d47d26a475415ec8057541b3443fe07e5c9c9607c","observation_id":"e5bce21f-f94c-4c9f-b74c-f05d3901bd2a","resolution":{"observed_at":"2026-08-14T13:39:54.453296Z","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":"10.1017/s0308210500028079","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.738666Z","title":"Grinfeld and A","venue":null,"work_id":"3b87d1c6-ef30-4b22-b470-20d8f40c62b6","year":1995},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.456667Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:36f19745ff8e46873e1c702fb3b33eab41a442c6ad9973cde6e44909ab2919d1","observation_id":"aeea4a73-e79a-471c-897c-b6f0d78b3dfb","resolution":{"observed_at":"2026-08-14T13:39:54.743329Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/130908208","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.725396Z","title":"Grün, On convergent schemes for diﬀuse interface models for two-phase ﬂow of incompressible ﬂuids with general mass densities, SIAM J","venue":null,"work_id":"189d9cc9-0b41-4643-a043-fe606a845908","year":2013},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.460826Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:381fc7e1e245529b509fabef519e28949bfd9d68002adcb74d58b65e9c262588","observation_id":"ad0064eb-60d2-44fc-aebb-8aef6b696d86","resolution":{"observed_at":"2026-08-14T13:39:54.729699Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4208/cicp.scpde14.39s","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.713068Z","title":null,"venue":null,"work_id":"eb640141-91aa-4825-9a14-e1ed041624e4","year":2016},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.465341Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:d25b8d9eb0503044dc38bffc36b30b792ebb1f1d362e11bfbde445f726daa460","observation_id":"eaaecc47-b9da-4eac-9195-a4f40b5c93f0","resolution":{"observed_at":"2026-08-14T13:39:54.717778Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2013.10.028","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.700831Z","title":"Grün and F","venue":null,"work_id":"674fe107-64a6-49e7-9962-8dd749e876bb","year":2014},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.469907Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:b13569c02b5bd34af92e017eb8d4c655f3061921daa3b491f9209efef3031b38","observation_id":"bc769f5c-2027-4046-ab5c-a6eb8d704f97","resolution":{"observed_at":"2026-08-14T13:39:54.705037Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.225825Z","title":"Kenzler, F","venue":null,"work_id":"04524db1-447b-4d86-ae2b-43342da73aef","year":2001},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.473698Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:806824c582b082891ebb89b0952d562ebade36c502d567ba24534b34dbf53337","observation_id":"414667f0-1a8d-4d5d-8279-a25f6635d925","resolution":{"observed_at":"2026-08-14T13:39:55.229197Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.12983","last_updated":"2021-04-24T16:44:50Z","snapshot_observed_at":"2026-07-06T09:08:05.920582Z","submitted_at":"2020-03-29T09:31:26Z","title":"Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions","version":3},"cited_work":{"arxiv_id":"2003.12983","doi":null,"metadata_source":"pith","pith_arxiv_id":"2003.12983","snapshot_observed_at":"2026-08-14T13:39:55.124752Z","title":"Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions","venue":"math.AP","work_id":"20c8b810-f658-4da7-aaa7-c8064b2a4d28","year":2020},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.477750Z"},"links":{"cited_paper":"/paper/2003.12983","citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:118e26e86c368c42c4606664ea665fe4d2c877bec51f7afa36880cc14e60f820","observation_id":"5cdd063d-9b09-4be7-9abe-ec1066615148","resolution":{"observed_at":"2026-08-14T13:39:55.131101Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.215394Z","title":"Kufner, O","venue":null,"work_id":"20dc0101-df11-4ded-917e-dacd2024129a","year":1977},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.481844Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:3aa1e632f1446006213be5e61d430f3870951e035966077a7aa24479af8e0423","observation_id":"1bbed14c-ac37-4697-a34e-9ab31445a5b7","resolution":{"observed_at":"2026-08-14T13:39:55.219029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1905.08504","last_updated":"2019-05-21T08:56:48Z","snapshot_observed_at":"2026-08-14T16:29:13.034748Z","submitted_at":"2019-05-21T08:56:48Z","title":"On a SAV-MAC scheme for the Cahn-Hilliard-Navier-Stokes Phase Field Model","version":1},"cited_work":{"arxiv_id":"1905.08504","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.08504","snapshot_observed_at":"2026-08-14T13:39:55.108102Z","title":"On a SAV-MAC scheme for the Cahn-Hilliard-Navier-Stokes Phase Field Model","venue":"math.AP","work_id":"af578449-5858-4f74-9d32-953ec9f5b70a","year":2019},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.486381Z"},"links":{"cited_paper":"/paper/1905.08504","citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:8cb60cffe0c5d3ed8108767bbf9ec5eebbaea051751b8b2f83a228e4cec9da2d","observation_id":"bed91c1d-afc2-4302-bd54-4dee8305a510","resolution":{"observed_at":"2026-08-14T13:39:55.112697Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.203812Z","title":"Liero, Passing from bulk to bulk-surface evolution in the Allen–Cahn equation, Nonlinear Dif- ferential Equations and Applications NoDEA, 20 (2013), pp","venue":null,"work_id":"3b39b1ea-5c8d-4dcd-b7bf-2e315f89749b","year":2013},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.490031Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:133a4fe5aaf0dbcb401bdb1529a3ec6bdaf7afd6904e446c93330ddbed37f5e5","observation_id":"522df909-d7e8-4261-aa35-c7d36c584db2","resolution":{"observed_at":"2026-08-14T13:39:55.207786Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00205-019-01356-x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.689126Z","title":"Liu and H","venue":null,"work_id":"6ec11711-13bb-4cb8-bcdd-bd2dd92c845e","year":2019},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.494311Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:5b37fbd5dd259944a8b8ee146d8d069ad02b3e5906b73ccbc6ed9f727fb1bab5","observation_id":"764049b0-5c80-4825-9605-559c619990f9","resolution":{"observed_at":"2026-08-14T13:39:54.692632Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"an/2018042","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:55.091119Z","title":"Metzger, On convergent schemes for two-phase ﬂow of dilute polymeric solutions, ESAIM-MATH MODEL NUM, 52 (2018), pp","venue":null,"work_id":"6449082f-008c-4682-b88b-b715fa5a1bad","year":2018},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.498212Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:cd2b0071441f50d8d4e1ad24843e9ba3b82b0d1c024f1291ae16398ee41953a2","observation_id":"38b7406f-b383-447d-8f72-543875e622d4","resolution":{"observed_at":"2026-08-14T13:39:55.097520Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.191795Z","title":"Metzger , On stable, dissipation reducing splitting schemes for two-phase ﬂow of elec- trolyte solutions, Numerical Algorithms, 80 (2018), pp","venue":null,"work_id":"bb8236b8-25c6-4405-b46b-fc8a172c8848","year":2018},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.501932Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:fffc3f8cf5ddda6558dcf50e9df2fe1c159d6a564246d5ec716fdd23250bcacb","observation_id":"b770e0d1-3b05-43c1-b1fb-85e057e67d63","resolution":{"observed_at":"2026-08-14T13:39:55.195332Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jmaa.2016.12.071","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.678827Z","title":null,"venue":null,"work_id":"a2b80801-08a4-4c4a-b182-e8fdec1fea42","year":2017},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.505861Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:d2b9802d22de76bd6cbc1bc928eed422f753822501298e600f524fdb82f76bd8","observation_id":"15ce39ed-ff5e-4060-a5b3-a9427c02eac6","resolution":{"observed_at":"2026-08-14T13:39:54.682547Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.510065Z","title":"Miranville and S","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.510065Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:c45d266df26a8d19e056aa601541790b4439c299a0958b1ac61303c6d94828db","observation_id":"f42b6f30-4c70-48c3-a313-fcbf5abb2274","resolution":{"observed_at":"2026-08-14T13:39:54.510065Z","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":"10.3934/math.2018.2.263","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.658698Z","title":"Motoda, Time periodic solutions of Cahn–Hilliard systems with dynamic boundaryconditions, AIMS Mathematics, 3 (2018), pp","venue":null,"work_id":"21adc40a-6ad2-41eb-803e-f8be386c7e64","year":2018},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.513283Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:db537d4839fc7d2715329158a8cee5c52f50dc5a4661b447ee3c11ada11a783a","observation_id":"dc43bdd2-794f-45b5-99db-25f4cf661a2c","resolution":{"observed_at":"2026-08-14T13:39:54.662980Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.516434Z","title":"Nečas, Direct Methods in the Theory of Elliptic Equations, Springer Berlin Heidelberg, 2012, https://doi.org/10.1007/978-3-642-10455-8","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.516434Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:00977098216195a100108d6ebe0843c0117db3070b1279f32cf9ca0c4fa4bf92","observation_id":"037b6632-37d3-479b-8d1a-014d046c9b5d","resolution":{"observed_at":"2026-08-14T13:39:54.516434Z","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":"2026-08-14T13:39:54.519326Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.519326Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:e42581102a7f7c27d1d332d749a2fe84bcd0b1317bb7824ad6c91637ebbdaf86","observation_id":"507dc871-f0f2-4024-a171-270d4a052e6e","resolution":{"observed_at":"2026-08-14T13:39:54.519326Z","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":"2026-08-14T13:39:54.522364Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.522364Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:37aec5f4ddb620f446022b1ac478cb541f2822d64c6fb3a7cab6f41b11fc10fd","observation_id":"2cdbd9ef-7998-4945-b0fa-cb905f77d78d","resolution":{"observed_at":"2026-08-14T13:39:54.522364Z","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":"2026-08-14T13:39:55.182447Z","title":null,"venue":null,"work_id":"d7eb1913-7a6b-4fd5-84b7-f0b41865a23f","year":2006},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.525250Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:dd8c9fd09ee24a79d7b3c284a4a37cebf89ff425a38390f59433b3efa3aa4019","observation_id":"1be497ae-5f09-46ca-803b-d4c9cf65babf","resolution":{"observed_at":"2026-08-14T13:39:55.185453Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.173505Z","title":"Racke and S","venue":null,"work_id":"581d7db9-d360-468e-974f-8bed6b747948","year":2003},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.529230Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:e6af20fa787f04fd9a6c4c98a72e0f00b83c463637bb12a431bc030101f3fdac","observation_id":"778910bd-4bcb-4c47-9e8c-b881accec0f6","resolution":{"observed_at":"2026-08-14T13:39:55.176233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.162612Z","title":"Rybka and K.-H","venue":null,"work_id":"4a10f304-05f5-46e9-946d-1c65305a2d62","year":1999},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.533413Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:d8b9a4f6cb39f042ec79e6f666916f7d8e593cf5a94afdbc84e9aac587f144fe","observation_id":"a1582cd0-53d4-43ac-802a-b53c2a8212c3","resolution":{"observed_at":"2026-08-14T13:39:55.166418Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.537847Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.537847Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:e589d39eb66bf5d20c9ef0c7a2750b3cf86a563198ea445be18e13fa25d72276","observation_id":"eda4f00e-0d90-4859-a422-193be0b2506a","resolution":{"observed_at":"2026-08-14T13:39:54.537847Z","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":"2026-08-14T13:39:54.542187Z","title":"Shen and X","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.542187Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:6c4f5d0177dabcbb2a435577c99fe3f6647009f18d9d654fd4422a6f8936a4ce","observation_id":"f8d16009-3850-4ee1-beca-a1c1981fba9e","resolution":{"observed_at":"2026-08-14T13:39:54.542187Z","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":"2026-08-14T13:39:55.151077Z","title":null,"venue":null,"work_id":"c4a19028-df64-4d1c-9b06-9ed1d5cf9a08","year":1989},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.546435Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:e92d0f2201e3bdd5c8742d32cc1f51df31ddbfca94d391624352c4846f840434","observation_id":"eb456965-237b-4908-8af2-da9395ed4d41","resolution":{"observed_at":"2026-08-14T13:39:55.155466Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:55.138825Z","title":"Trautwein, Finite-Elemente Approximation der Cahn–Hilliard-Gleichung mit Neumann- und dynamischen Randbedingungen","venue":null,"work_id":"58c9576c-5dc1-4718-93e7-633ff3a39fb7","year":2018},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.550635Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:7244ee864e84f691251fe6869597b97af42ebb6ffec39d4976a0fdc5f4da5a4e","observation_id":"99451e02-7dc1-4363-be25-7c81dfe87a0f","resolution":{"observed_at":"2026-08-14T13:39:55.143079Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.554573Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.554573Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:fcd5451192ad5a690041ea31bb099c7a7e8bbeb1965800256cd3ef8044407492","observation_id":"74e90505-948b-4811-bf3d-f699cd08c2ac","resolution":{"observed_at":"2026-08-14T13:39:54.554573Z","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.jde.2004.05.004","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.616655Z","title":"Wu and S","venue":null,"work_id":"48c36965-7d7b-49e6-b2db-a6c0f7ac055c","year":2004},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.558860Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:11571e3cd533a22efaf0af46e5992b977c9a242fc7ba41ae9cb15b2375049bea","observation_id":"6e1b6eb0-f642-47cf-a177-cb7f035bcfab","resolution":{"observed_at":"2026-08-14T13:39:54.620041Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:39:54.563210Z","title":"Xu and T","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.563210Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:dcdd825a2643ea127750586977f4a8340e52b410cd26796629d6694ca6be3a3f","observation_id":"a16b761e-618e-4959-b7d2-a61fc064da69","resolution":{"observed_at":"2026-08-14T13:39:54.563210Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1712.02760","last_updated":"2017-12-07T18:14:18Z","snapshot_observed_at":"2026-08-14T20:05:49.268274Z","submitted_at":"2017-12-07T18:14:18Z","title":"Numerical approximations of the Cahn-Hilliard and Allen-Cahn Equations with general nonlinear potential using the Invariant Energy Quadratization approach","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1712.02760","snapshot_observed_at":"2026-08-14T13:39:54.566755Z","title":"Yang and G","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.566755Z"},"links":{"cited_paper":"/paper/1712.02760","citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:dd19e76cebcbb87166c5df47e6ce4e96527574b0b3ddfa3d06cc26345eaadf77","observation_id":"238861d9-e352-402a-a67b-cda854cfb42f","resolution":{"observed_at":"2026-08-14T13:39:54.566755Z","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":"10.1080/00036818608839639","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:39:54.597186Z","title":"Zheng , Asymptotic behavior of solution to the Cahn–Hillard equation, Applicable Analysis, 23 (1986), pp","venue":null,"work_id":"ab5d8a91-a2d0-4960-96e7-5106b9434383","year":1986},"citing_paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-14T13:39:54.570241Z"},"links":{"citing_paper":"/paper/1908.04910"},"observation_digest":"sha256:ec43fc6801474da79d468f1bc5d1977ca1ffdf8dcdfb97ff627a1f78b1f4855a","observation_id":"00fb10b9-5f3f-4dcd-a9ea-df67227d961b","resolution":{"observed_at":"2026-08-14T13:39:54.602565Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.04910","last_updated":"2020-10-20T11:31:00Z","latest_version":2,"primary_category":"math.NA","snapshot_observed_at":"2026-08-16T07:09:53.144085Z","submitted_at":"2019-08-14T01:32:51Z","title":"An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions"},"reference_resolution":{"displayed":58,"state_counts":{"malformed_identifier":8,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":25,"verified_fuzzy":5},"total_outbound_references":58},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 1 inbound Pith citation observation for arXiv:1908.04910."}