{"as_of":"2026-08-21T10:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6c3b0d5d41a32bbc6324be5ef723c8e3a2606dcb785333ae114fde15b890a2c9","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T14:35:04.737857Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.11904/citation-record","integrity":"/paper/2412.11904/integrity","json":"/paper/2412.11904/citation-record.json","paper":"/paper/2412.11904"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T14:35:04.611279Z","title":"Abels, H","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.611279Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:83debf62245f42ca96bb2ad1c5b450da30d83f91a69c746ff8b4e0d339e6071b","observation_id":"7eb0e74d-468a-431b-8513-192dfb21ce9f","resolution":{"observed_at":"2026-08-11T14:35:04.611279Z","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":"2026-08-11T14:35:05.210442Z","title":null,"venue":null,"work_id":"946c0f32-b131-40db-a23a-3284b2e2c243","year":1998},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.616843Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:2860533164e655dfffa70931a77c7899cd053557fb44926192cb964080472ea5","observation_id":"693a5086-4c4f-46d1-abe0-56f5d6ca7848","resolution":{"observed_at":"2026-08-11T14:35:05.216162Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.194326Z","title":"Boyer and C","venue":null,"work_id":"098420cb-09f5-45f4-adce-1033d7308421","year":2006},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.621877Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:ba2bcea01acd886a9a9c43e9ae1ce6a9a43072b46b253703add04a9ae114e8a2","observation_id":"af04ba9c-4c09-4d35-92b1-7e9fcc814b66","resolution":{"observed_at":"2026-08-11T14:35:05.200059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.177793Z","title":null,"venue":null,"work_id":"6c56936d-37ca-4b4f-a9e3-370025b9e747","year":1967},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.626678Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:ce1d2a5e67c6bc5a532c29dda5cd2fddfed69ea0dfd40d637821bf9effe715e3","observation_id":"f831d782-5148-496a-96f9-e98f568a85ff","resolution":{"observed_at":"2026-08-11T14:35:05.183571Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.160441Z","title":null,"venue":null,"work_id":"01074542-78e6-4129-86c8-a4c7b6c80c06","year":1967},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.631604Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:cc61a7a081a6660f13be4b5766a76a3eab5a8cc1aa29bd80eb152fa961250a64","observation_id":"d67798b9-f23d-4bc3-895e-3d0009d31efe","resolution":{"observed_at":"2026-08-11T14:35:05.166378Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.143320Z","title":null,"venue":null,"work_id":"6c9b5764-5bca-43cc-8098-98266c2f809f","year":1968},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.636424Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:8b9486dfd377da7abf91d6006d9e72f890c36be2cb31e416fae7f6216b77622e","observation_id":"6dbc5ae9-9969-465d-9eae-bc2d418e35ea","resolution":{"observed_at":"2026-08-11T14:35:05.149307Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.126932Z","title":"Dhaouadi and M","venue":null,"work_id":"42fb47e7-97e3-497c-b205-197797c76f00","year":2022},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.641725Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:b36e9e4586591b2412eb76c1f38af697cc0649f7dcdfa3fc53558ead1b9e7ede","observation_id":"74eb1172-baab-4d5f-9fa1-9bdc8bf98f44","resolution":{"observed_at":"2026-08-11T14:35:05.132540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.03862","last_updated":"2024-08-07T16:11:30Z","snapshot_observed_at":"2026-08-17T07:18:09.826773Z","submitted_at":"2024-08-07T16:11:30Z","title":"A first-order hyperbolic reformulation of the Cahn-Hilliard equation","version":1},"cited_work":{"arxiv_id":"2408.03862","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.03862","snapshot_observed_at":"2026-08-11T14:35:04.799600Z","title":"A first-order hyperbolic reformulation of the Cahn-Hilliard equation","venue":"math.NA","work_id":"f5af7b43-1e71-4a49-aeee-91c6f9e1797d","year":2024},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.646211Z"},"links":{"cited_paper":"/paper/2408.03862","citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:5aa3f192078871bffa946eb65cbb95a4c16f49d367e275d787e95d3ca5174127","observation_id":"1d06c0c0-c7a6-42f8-a41f-a8bdbc4108ec","resolution":{"observed_at":"2026-08-11T14:35:04.805472Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.110801Z","title":"Engel, A","venue":null,"work_id":"db25322c-4f4c-42f3-82f4-9a1c89f6ef56","year":2013},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.651406Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:cc5860216a054e1074559614dd7df49ebafb0607575b61079be849ba17f345b0","observation_id":"b690280f-0157-44c9-a57d-19c2a380b31f","resolution":{"observed_at":"2026-08-11T14:35:05.116389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.094884Z","title":null,"venue":null,"work_id":"8d8a83c3-50da-4bcb-9812-658d91074303","year":1971},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.656130Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:7ae9093aeca6db71fc02ddaf35fd9dd336aaeb11f9f20718cfdecd15dee67574","observation_id":"a94cefca-6a4b-43f0-9e17-294c5537ea2c","resolution":{"observed_at":"2026-08-11T14:35:05.100147Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.078941Z","title":"Gatti, M","venue":null,"work_id":"3beb655d-0b39-4de3-9c45-70840fee830a","year":2005},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.660893Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:256bee647ba842a09fec9e869f0e902ebf4ff509b8ba5e2fb8bc5e827653f835","observation_id":"02b8c93d-f1d9-42da-8c22-e876975b4eae","resolution":{"observed_at":"2026-08-11T14:35:05.084493Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.063191Z","title":"Giesselmann","venue":null,"work_id":"43b259d5-3ac5-48b8-9279-028213cbdb8a","year":2014},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.665449Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:b41b0d7414d833a8b3f0610d1bc436218d31c492e8e9be339b4ef8482b954374","observation_id":"136c4896-a1d1-4f2b-b963-85b6e212f05a","resolution":{"observed_at":"2026-08-11T14:35:05.068658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.046515Z","title":"Giorgini and R","venue":null,"work_id":"6ff9deaa-3df5-40a0-b02a-bea0ad25d089","year":2020},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.670194Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:2ea5ab72b2909dd9efe6e70d38b74674302ba3263c98494688f2ae9752a46beb","observation_id":"589cc5c0-d764-405d-98aa-cb847c43972f","resolution":{"observed_at":"2026-08-11T14:35:05.052514Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.030652Z","title":null,"venue":null,"work_id":"48bc890e-9a35-4c92-ac95-245e84c2a658","year":1961},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.674558Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:54ab1de37077af8cd2b7264ac7b87c21732f4961f08e316a69109263bbdd7142","observation_id":"204b0668-788d-462a-9586-51e9837e18c8","resolution":{"observed_at":"2026-08-11T14:35:05.036085Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:05.013468Z","title":null,"venue":null,"work_id":"656ee727-f1e5-4a4a-9089-088dd8694d1c","year":1991},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.679424Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:992ae192d3f8d9107a1507061a3251e5c99fc71d609a37cebd59d1f0ea864755","observation_id":"e9cea5ea-6618-414e-9f2d-66147986558d","resolution":{"observed_at":"2026-08-11T14:35:05.019519Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.997472Z","title":null,"venue":null,"work_id":"5860050a-b9c0-464e-b82b-4b3084f8aa11","year":2020},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.683820Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:5b7cbe798391d5a2426e9be029104ff71d8d8bad8436e87cf1bd80f7b6306a21","observation_id":"60effc98-f655-422e-bc1a-b71df27eac3f","resolution":{"observed_at":"2026-08-11T14:35:05.002972Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.980744Z","title":null,"venue":null,"work_id":"62cffa12-8397-4b3f-ba4a-7b1b81b65db3","year":1977},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.688031Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:105cee311ba10a30ac9075a947f882bc50dc776e73ec71ed501cc9aaedb5a596","observation_id":"1bd2a6fe-d33f-4412-854f-763e12d37e5e","resolution":{"observed_at":"2026-08-11T14:35:04.986564Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.15575","last_updated":"2024-11-23T14:36:52Z","snapshot_observed_at":"2026-08-12T14:07:04.537426Z","submitted_at":"2024-11-23T14:36:52Z","title":"A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility","version":1},"cited_work":{"arxiv_id":"2411.15575","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.15575","snapshot_observed_at":"2026-08-11T14:35:04.773507Z","title":"A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility","venue":"math.AP","work_id":"44e6ffaf-1030-4cf3-8ee0-9f0fe55e422d","year":2024},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.692233Z"},"links":{"cited_paper":"/paper/2411.15575","citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:fa65968e02426bd752981cdaa5122d2d9e481a1be790cff9075cab2f02ddc739","observation_id":"b42a34b5-28d7-431d-970f-40f164656fac","resolution":{"observed_at":"2026-08-11T14:35:04.780668Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.962580Z","title":"Keim, H.-C","venue":null,"work_id":"9daec4a8-163a-4dec-9109-0f9e416cf2b4","year":null},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.697010Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:3121ba741244d19367cc8db71e388eca9e82b041f3027cf6ee18d0ed2db0240d","observation_id":"415bafda-0b7a-4333-998e-667579259dc9","resolution":{"observed_at":"2026-08-11T14:35:04.967978Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.946268Z","title":"Keim, C.-D","venue":null,"work_id":"c92f8be4-cc31-4838-9a3e-aa5d7f70a068","year":2023},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.701546Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:6a1117594c24c5ae6dfb757d675e41b73097f8e885c7e6cfef3a47a92b8d25a5","observation_id":"837eccb7-a833-48ee-a7fb-fc718a3dc454","resolution":{"observed_at":"2026-08-11T14:35:04.951619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.929316Z","title":"Lattanzio and A","venue":null,"work_id":"f9f049f5-e331-40dc-8613-0a4fee63c08d","year":2017},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.706274Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:88d70b636f64213d09ed1473922dacccd5f66171e6798162301b0492b5c30fb3","observation_id":"a311902f-8517-4c70-aa0d-f297a4bbca0a","resolution":{"observed_at":"2026-08-11T14:35:04.935095Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.911966Z","title":"Massa, L","venue":null,"work_id":"35248ff7-6aa0-4be6-b82b-f826a1fd402c","year":2022},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.710999Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:91bbf9ecef587d39e25eabc5834352be944807228eeb67cb8d9ac24c5f58657f","observation_id":"6c57df8e-fc4b-4ea6-854c-90d89c343c26","resolution":{"observed_at":"2026-08-11T14:35:04.917731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.895016Z","title":"Nithiarasu","venue":null,"work_id":"afde7179-5d6b-4324-a855-4a2f5fceb504","year":2003},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.715734Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:b3723a81a4a839acee925a9c24fc046d62a6dcbcb1c0f7b029c31c1bae5d2cef","observation_id":"9972158e-a1ed-49f6-81bc-f3abd5f8fbd0","resolution":{"observed_at":"2026-08-11T14:35:04.900706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.879865Z","title":null,"venue":null,"work_id":"bd3530ef-f3a5-4458-aed0-4f44d6227c1b","year":2010},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.719764Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:66b71bd0ee3b329a557fc6b70b71677a2f3a6ce79dfe573dc80a0fa8a556a86c","observation_id":"4c4acef9-a3e6-4e4f-a262-5a3f572bd3ee","resolution":{"observed_at":"2026-08-11T14:35:04.884651Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.863962Z","title":"Rohde and L","venue":null,"work_id":"e48315d0-c9d4-4848-a2de-df0806764a22","year":2020},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.724010Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:21e9a07dc72dcab3a63ad38246c1519c9dcdd16766736cb27f7f2cb1429f9d28","observation_id":"bd38dc85-45c7-4a9b-88cc-91d78489ac16","resolution":{"observed_at":"2026-08-11T14:35:04.869125Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.848390Z","title":"Rohde and L","venue":null,"work_id":"3d1eea39-d336-4326-91ee-3c762382f3c7","year":2021},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.728260Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:8717a0df59c26605cb06ca5bcd0ffb72e105922a9570ca996e6fe5eb74a8d620","observation_id":"d15204a9-6486-44af-87a2-165bc5fbfb01","resolution":{"observed_at":"2026-08-11T14:35:04.853130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.832084Z","title":null,"venue":null,"work_id":"fbbec2b9-9579-40ed-b2f4-9c76bbb7726c","year":1969},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.733010Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:525bb463322af859089b0a8e1e85d3a70da8adadcbc5face5c614b59774219c0","observation_id":"fa8cea3e-27ea-4952-8bf6-7d9f1255ce29","resolution":{"observed_at":"2026-08-11T14:35:04.837723Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-11T14:35:04.816635Z","title":null,"venue":null,"work_id":"a3523303-2a69-4eb1-b0bb-1d4d711b636f","year":1969},"citing_paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T14:35:04.737857Z"},"links":{"citing_paper":"/paper/2412.11904"},"observation_digest":"sha256:f7a4224fc59f5937a384fcd011c3255826f74103127d6ebb1808d4a98f79e295","observation_id":"a680ab8f-a2d2-499f-8c33-df723f612abf","resolution":{"observed_at":"2026-08-11T14:35:04.821540Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.11904","last_updated":"2024-12-17T17:56:31Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-17T01:52:39.199337Z","submitted_at":"2024-12-16T15:50:06Z","title":"A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":13,"verified_exact":2,"verified_fuzzy":13},"total_outbound_references":28},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2412.11904."}