{"as_of":"2026-08-12T03:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4399a813cc3d6323d5f6ac332232bb26821a3a2a92f6a6519d5c53b889bccc6f","coverage":[{"denominator":85,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":85,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T02:13:51.480364Z","state":"measured"},{"denominator":85,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":85,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2607.09549/citation-record","integrity":"/paper/2607.09549/integrity","json":"/paper/2607.09549/citation-record.json","paper":"/paper/2607.09549"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3934/jcd.2019010","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", year =","venue":"Journal of Computational Dynamics","work_id":"383c7e58-8705-48a2-8a7f-e587e47583a2","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:2405098e49f15bbff43581f68a215e90ac8535332daece7377dde8eaf0047f8f","observation_id":"7a4e6d9f-8778-4ba5-ba35-10f21245f9eb","resolution":{"observed_at":"2026-07-13T02:19:16.792879Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:22.956853+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:22.956853+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:7f967ad4b7f68f7a8c545e0448c81abef1b9dafbfabc8bbe528869f061925700","observation_id":"2638963d-7fad-47f6-9171-83f33bd1433f","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"and Viviani, M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:f266c4eef9d1a82c265916698a07198760269917d482932a2c1a3e692a0d3268","observation_id":"2f9e02d8-f36c-4717-93ba-983772253755","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"and Yau, S.-T","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:0bc1245e043296c22b1ea2c7bac8bbd705808c2d10eba00c90bec001259e1482","observation_id":"9e88121f-b2f3-4eae-aef3-2562eb1da924","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:fed5010d750469013eb498efdeb2e9a7305a5d7e3e7ee5d88222e14f48b8fe6c","observation_id":"ea6e7f7c-d2c8-4c5d-8805-37700d491423","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:f5410b816e96f6e2d68a5111c03817f1c0f3cc6823440379a31c9e9595c368dc","observation_id":"b07c2d59-1372-452a-8f67-4f33bb3886ab","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":", journal =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:2cb452d8ae34617745133792edb07ea297781c90eb2db3d1703f259da98624c3","observation_id":"4dc1632c-dec6-452e-9865-466ebc561927","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":", journal =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:55dc5229cdffd6ed2798ac87a47e314025679338ba9b56e0fcbe0cebbf2929f3","observation_id":"e743391c-68e6-4662-9165-cc2198a1fc26","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":", publisher =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:3c4e57475c60bf911c3a1c6938c62f6db7e1d75ad2e1afe814fee73d9fd73560","observation_id":"870dcd9b-0249-4ff3-80c8-2f75949e3d82","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":", journal =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:40f0a24fb2c4fee96fd0024c712cf47f04319a7301a736bdd0a99ad056392ede","observation_id":"daf74bdb-052b-43dc-88c2-a2e10b38d427","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:673d304ed28dff42acdcdc88fe8cf208074e0db2cf2750bece6aa289ec54680a","observation_id":"7f98b0ff-4ba6-4aea-90fa-13fa1636d03a","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:d71abbcc8c1333fd55833ef70eb1fcdf9ef4b4c7f6ca12da75218b6744f5cc6f","observation_id":"ab0f0c8d-1711-45e3-a7f4-f7a5acc04321","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00211-016-0792-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Hamiltonian","venue":"Numerische Mathematik","work_id":"c651d2a7-9e22-49d7-b2d1-f2a7a1b414ec","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:c732cbd65258e6cced38ab542192746a05eb71c75c474152733c37af190a9fdb","observation_id":"5eee47cf-7b5e-43eb-9c3f-ad32e2cf55f0","resolution":{"observed_at":"2026-07-13T02:19:16.784620Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:23.205716+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:23.205716+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s1570-7954(08)00205-2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Handbook of algebra","work_id":"9a5a482c-8280-479c-a1dd-ef1d669c554c","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:c6b7c849ac2272599471ca876aed4a52b558dde724044fcd8a69cdf424e34f49","observation_id":"af694b6e-0bbf-4803-b7ee-76e8bcf46e03","resolution":{"observed_at":"2026-07-13T02:19:16.404149Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:23.541804+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:23.541804+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.10579","last_updated":"2025-03-21T10:31:52Z","snapshot_observed_at":"2026-08-11T16:53:46.912812Z","submitted_at":"2023-02-21T10:17:42Z","title":"An algebraic correspondence between stochastic differential equations and the Martin-Siggia-Rose formalism","version":3},"cited_work":{"arxiv_id":"2302.10579","doi":"10.48550/arxiv.2302.10579","metadata_source":"pith","pith_arxiv_id":"2302.10579","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"An algebraic correspondence between stochastic differential equations and the Martin-Siggia-Rose formalism","venue":"math-ph","work_id":"02b502c7-33b4-42c0-a04c-aa2042375130","year":2023},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2302.10579","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:04652221288e4f80e4dce0a73f60510521f8afe0b88993d2cdbd27c21e7cb703","observation_id":"e7e8d0ae-b533-4a80-ad9b-3aa5db285e5e","resolution":{"observed_at":"2026-07-13T02:19:16.522911Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:23.77201+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:23.77201+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00211-005-0661-y","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Frédéric and Laurent-Varin, Julien , date =","venue":"Numerische Mathematik","work_id":"d725a9e6-e920-4567-a06d-cb88c3ee35b4","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:61fe0556b4dd3ffb438a376d3f3a1a259f11039e5e096c1c007e092cebaf8950","observation_id":"55a81e76-2682-4e61-92e2-b173ce8bb4f1","resolution":{"observed_at":"2026-07-13T02:19:16.818612Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:24.016332+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:24.016332+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.02943","last_updated":"2025-01-08T10:07:07Z","snapshot_observed_at":"2026-08-11T03:32:55.992578Z","submitted_at":"2025-01-06T11:36:54Z","title":"Efficient Langevin sampling with position-dependent diffusion","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.02943","snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"Efficient","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2501.02943","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:324eaa0b18a66f85d3e649f700d3440f64e48cf27656a8f3a8450988a6e6da9c","observation_id":"e5d4fd94-36fe-4af3-89f9-90b4ae4a418c","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2209.11046","last_updated":"2023-10-16T15:13:36Z","snapshot_observed_at":"2026-08-08T05:31:14.398981Z","submitted_at":"2022-09-22T14:42:05Z","title":"Exotic B-series and S-series: algebraic structures and order conditions for invariant measure sampling","version":2},"cited_work":{"arxiv_id":"2209.11046","doi":"10.48550/arxiv.2209.11046","metadata_source":"pith","pith_arxiv_id":"2209.11046","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Exotic B-series and S-series: algebraic structures and order conditions for invariant measure sampling","venue":"math.NA","work_id":"e6314264-4f3a-419d-8b80-963b4fa51b5a","year":2022},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2209.11046","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:24ae83175742a9a925ff23e772cebf2fdda7bdbf67c9f3bf234ce4df0d229604","observation_id":"9961385e-39ed-4d81-87d0-4757c99182e0","resolution":{"observed_at":"2026-07-13T02:19:16.878381Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:24.528685+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:24.528685+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.21855","last_updated":"2025-06-18T08:51:50Z","snapshot_observed_at":"2026-08-07T16:32:13.605770Z","submitted_at":"2025-03-27T17:20:10Z","title":"High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.21855","snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"High Order Integration of Stochastic Dynamics on","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2503.21855","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:ccb21a373e89d509b464a9b58945a4cca3fda2b099dffe2559f28fcc0a030e17","observation_id":"f5671bd1-ee6e-4838-a2fc-59d65cac7c88","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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/s1446788700027932","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of the Australian Mathematical Society","work_id":"ee7442bc-51ec-400d-9e3e-c346da97d4c4","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:4e53b25ae22cec574cfe894519ae81717c8fa03bd030eba58b25fb44df120856","observation_id":"f8b1ded2-9d59-4a89-a6a1-d68611eb273c","resolution":{"observed_at":"2026-07-13T02:19:16.868851Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:25.040001+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:25.040001+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0806.2238","last_updated":"2011-12-17T21:07:10Z","snapshot_observed_at":"2026-07-06T01:43:38.797197Z","submitted_at":"2008-06-13T12:53:55Z","title":"Two interacting Hopf algebras of trees","version":4},"cited_work":{"arxiv_id":"0806.2238","doi":null,"metadata_source":"pith","pith_arxiv_id":"0806.2238","snapshot_observed_at":"2026-07-13T02:19:16.903865Z","title":"Two interacting Hopf algebras of trees","venue":"math.CO","work_id":"3d49dc56-22b7-4889-ba6b-bc3eed765c2f","year":2008},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/0806.2238","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:b9d3160774d160a91557c2e73e66f38453232663ed872930109f3073f5f3c315","observation_id":"4471db84-388b-4507-a565-e3f18f9a3c34","resolution":{"observed_at":"2026-07-13T02:19:16.906160Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/2369158","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"doi:10.2307/2369158 , url =","venue":"American Journal of Mathematics","work_id":"be989c1e-37ee-4904-83db-34917221c7a2","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:a1f9b885b90e45afd52780acaea00c4271e1b83323fb1188feae806832da0de0","observation_id":"faa0df42-33fe-4249-807a-7ad6e4daeb6a","resolution":{"observed_at":"2026-07-13T02:19:16.318194Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:25.605178+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:25.605178+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:9faf99c538ef412746f5bc5db483869551766d24a2a0cf8e09b7366f3a7dd65b","observation_id":"2a10425b-f9ea-4e04-87b7-f984771b8aed","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"10.1093/imanum/drl039","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"doi:10.1093/imanum/drl039 , url =","venue":"IMA Journal of Numerical Analysis","work_id":"e6192892-9778-4bc1-8874-10f87a1adee9","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:2f35ca7ff3bcd663b3edd2e29e45a0e0aa00420ca9cea732ae9e9d429a24f68d","observation_id":"ff5adb41-515f-4a33-84f3-2595420dbfa4","resolution":{"observed_at":"2026-07-13T02:19:16.721352Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:26.072471+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:26.072471+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s002200050499","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Communications in Mathematical Physics","work_id":"d582b79f-a973-4b5a-b8b3-993e4147a68b","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:c38987719056e87a9c288c13b03ec5c243d5846388e47fcc0ed44522b8a1bd59","observation_id":"5e8b26bb-e113-41c6-bdbe-c7fc922fefd3","resolution":{"observed_at":"2026-07-13T02:19:16.688388Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:26.298669+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:26.298669+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1712.09415","last_updated":"2017-12-18T18:28:12Z","snapshot_observed_at":"2026-08-09T10:43:13.891318Z","submitted_at":"2017-12-18T18:28:12Z","title":"What is a post-Lie algebra and why is it useful in geometric integration","version":1},"cited_work":{"arxiv_id":"1712.09415","doi":"10.1007/978-3-319-96415-7","metadata_source":"pith","pith_arxiv_id":"1712.09415","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"What is a post-Lie algebra and why is it useful in geometric integration","venue":"math.NA","work_id":"33ab052e-5560-4404-b014-81b82c7c45d9","year":2017},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/1712.09415","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:4d09ea75e6402ba27208e6a98a58fbd8212f82e6605541c2ae798cebc2aca258","observation_id":"4fd57363-4a90-41f0-a769-18a707743687","resolution":{"observed_at":"2026-07-13T02:19:16.639004Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:26.53118+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:26.53118+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.08425","last_updated":"2024-05-05T07:57:10Z","snapshot_observed_at":"2026-08-09T11:13:17.407021Z","submitted_at":"2023-06-14T10:37:42Z","title":"Fine structures inside the PreLie operad revisited","version":3},"cited_work":{"arxiv_id":"2306.08425","doi":"10.48550/arxiv.2306.08425","metadata_source":"pith","pith_arxiv_id":"2306.08425","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Fine structures inside the PreLie operad revisited","venue":"math.KT","work_id":"5f723ea7-8f2b-4a2e-8f1d-4af87fa6b3b3","year":2023},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2306.08425","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:e6c4e734e3811e2b3b1ed8cd5c0690cdbc08d9845f89c06718223102091518f7","observation_id":"c3804d12-c264-4625-a0e7-f3522eb051ef","resolution":{"observed_at":"2026-07-13T02:19:16.348973Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:26.80017+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:26.80017+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.14143","last_updated":"2024-11-21T14:05:40Z","snapshot_observed_at":"2026-08-08T14:10:02.505878Z","submitted_at":"2024-11-21T14:05:40Z","title":"Volume preservation of Butcher series methods from the operad viewpoint","version":1},"cited_work":{"arxiv_id":"2411.14143","doi":"10.48550/arxiv.2411.14143","metadata_source":"pith","pith_arxiv_id":"2411.14143","snapshot_observed_at":"2026-07-13T06:15:01.053796Z","title":"Volume preservation of Butcher series methods from the operad viewpoint","venue":"math.CT","work_id":"97be0fe0-0e83-44db-80c7-5f37e8ce2f00","year":2024},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2411.14143","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:2bc4954bc8f7e7730f91af87631fe489d46247db5cd5d1087271de8307bed65b","observation_id":"d96771c5-7c0d-414d-9957-f1624a98f13a","resolution":{"observed_at":"2026-07-13T02:19:16.493466Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:27.024429+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:27.024429+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"and Marsden, Jerrold , date =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:06e463a66f5f4b61a185af75b7ef216a11923b81721e40a6971b969d06b43fd0","observation_id":"f5d5e78a-e0f9-4d7c-b3d6-9a9aa3d85ec0","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:bb22866056bdf2a164fae31d9dbd04f0ec0c1b5bcfbae89437a79d5ca270190d","observation_id":"b9b89cce-1e33-46f0-8d96-64fac46bcfbd","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.04381","last_updated":"2024-07-15T12:12:50Z","snapshot_observed_at":"2026-08-04T03:01:54.438901Z","submitted_at":"2023-06-07T12:25:38Z","title":"A Survey on the Munthe-Kaas-Wright Hopf Algebra","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.04381","snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2306.04381","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:1d61531caed7752ed3584999e35509ae2dcdce1721dfdf158292d23166932032","observation_id":"b230cdae-1a84-4cf2-bb85-ec03b17141af","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0036142999364212","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Numerical","venue":"SIAM Journal on Numerical Analysis","work_id":"dfedae72-5ab8-47c0-88db-9c8ad9008126","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:bd6bce92177afd951144a3a354a21e91e72c8462f1949ff4d0a4eae446088db1","observation_id":"922570ce-b554-461f-845c-2997848f7425","resolution":{"observed_at":"2026-07-13T02:19:16.703289Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:27.77988+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:27.77988+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1022336301001","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", date =","venue":"BIT Numerical Mathematics","work_id":"6af8e9d0-fbf8-4227-b90d-24597ecb6f23","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:df2f05385da4c526afba65ba4ad61de0b3e9e98cb136d11f6f1fc1bed8ee9470","observation_id":"9d660d04-2e0c-447e-8adf-e05a4416b87c","resolution":{"observed_at":"2026-07-13T02:19:16.445270Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:28.118797+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:28.118797+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.03271","last_updated":"2025-05-06T08:02:07Z","snapshot_observed_at":"2026-08-07T15:49:40.428517Z","submitted_at":"2025-05-06T08:02:07Z","title":"Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation","version":1},"cited_work":{"arxiv_id":"2505.03271","doi":"10.48550/arxiv.2505.03271","metadata_source":"pith","pith_arxiv_id":"2505.03271","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Fully discrete backward error analysis for the midpoint rule applied to the nonlinear Schroedinger equation","venue":"math.AP","work_id":"b9a1492b-2cd7-45a3-91ec-3156e382ad0c","year":2025},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2505.03271","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:3c7c6b0bf20c5f35cd1fb045ac9180e67c248cdbed6a9b49950cecce567ac4c1","observation_id":"c4cf6488-95a8-475f-a077-93b422f36166","resolution":{"observed_at":"2026-07-13T02:19:16.512846Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:28.386265+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:28.386265+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"Geometric","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:b01b3d250eecb7422ee107b74990d655914f03c6d257a18af9b3c35d9f4d3172","observation_id":"0e25ddad-f0c5-48df-a51c-44c277dde777","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0912.2882","last_updated":"2009-12-15T13:30:54Z","snapshot_observed_at":"2026-07-06T02:01:55.161148Z","submitted_at":"2009-12-15T13:30:54Z","title":"Hamiltonian interpolation of splitting approximations for nonlinear PDEs","version":1},"cited_work":{"arxiv_id":"0912.2882","doi":"10.48550/arxiv.0912.2882","metadata_source":"pith","pith_arxiv_id":"0912.2882","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Hamiltonian interpolation of splitting approximations for nonlinear PDEs","venue":"math.NA","work_id":"33258feb-e13e-4e13-a89b-79e906f3abe4","year":2009},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/0912.2882","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:0b15cbae7512b45c7cb8a179ecc1a939851cdd0d33e693a7c1d2e0030f512e87","observation_id":"45d4a801-e6fb-46ab-82fb-21f2f3b0d909","resolution":{"observed_at":"2026-07-13T02:19:16.673555Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:28.649788+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:28.649788+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-78346-4_9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", editor =","venue":"Springer proceedings in mathematics & statistics","work_id":"89fef11c-c7cd-4175-8880-e590b3260f05","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:1d7d32458fc7c4e1e9358ec9aa5c7b3854d764d0ec1491f88b73b71360f0f843","observation_id":"e94a4819-e2af-42c8-984a-5668d25b8a1e","resolution":{"observed_at":"2026-07-13T02:19:16.553764Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:28.911688+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:28.911688+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"An Introduction to","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:249a6620c4bf267f1f8ac6e857ccb0f7bb3c14d3de7a3d05823db270710dc461","observation_id":"c4fc6b8c-273e-4542-96a8-25ff010cbd66","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"doi:10.1016/j.jde.2009.11.015 , url =","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:494f1e864029f5708c87c54cd77c021d753f59642c5b2cea30a8e6fa0c5db8d1","observation_id":"3f734988-4cdd-47d8-8ae7-e68368319860","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"and Wanner, G","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:5887638e4a130b997f86b6c82dece76552658ec832d7c35b18145069a4a28a1e","observation_id":"1943bd14-d70d-4881-bc96-80f509689ff0","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"doi:10.1007/s00222-014-0505-4 , url =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:abf0ae2db0359b3d4749e9b39e58bdf383c6d7a959902597011429d44c3b9d77","observation_id":"3aa53990-01a7-4561-a7e4-f4bc1cb814f5","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"Geometric","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:0ec63dad9cf6503bdfe140e754fc99bdb285300942ed08c0252ab0b7a3c87885","observation_id":"cac13832-b0d4-4370-8301-0ca680b59704","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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/jgm.2011.3.81","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Fri Apr 01 00:00:00 UTC 2011 , journaltitle =","venue":"The Journal of Geometric Mechanics","work_id":"0a23b3b9-eb97-478e-8fe0-afddd8e6d72f","year":2011},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:408fae0345b05d9922cedb446c7c73cdb7ffbfae14d15ca07a374b838008eec2","observation_id":"a2093505-bbfc-4875-be47-9cedae808603","resolution":{"observed_at":"2026-07-13T02:19:16.766793Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:29.881101+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:29.881101+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00332-023-09986-y","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Hamiltonian","venue":"Journal of Nonlinear Science","work_id":"525874fb-ab25-4c21-958c-8e5f86498419","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:a405c84b552da19ce3799da89bc9d0ae1680e1e59916639c6c500e6f9592ba7b","observation_id":"3137e0ad-1fdf-4906-9803-6e8f8bdff487","resolution":{"observed_at":"2026-07-13T02:19:16.776358Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:30.133626+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:30.133626+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10543-006-0114-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Quispel, G.R.W","venue":"BIT Numerical Mathematics","work_id":"b9759a06-55b7-41e0-a480-c4ab43a21708","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:1717217649d7a05f47044082cbb6da138442c0a122f56a42295b186b20844d13","observation_id":"010d8cbd-6033-4c23-aa21-7f1b08602699","resolution":{"observed_at":"2026-07-13T02:19:16.390235Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:30.381344+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:30.381344+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10208-021-09495-y","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"doi:10.1007/s10208-021-09495-y , url =","venue":"Foundations of Computational Mathematics","work_id":"5e89f684-39ba-4186-b24a-d9f43340e3d7","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:996508de19fc7e6f809e0b054ec7c0bf63309b834b24607df581e194f9d3488b","observation_id":"53a6039a-c698-4507-bfb7-ad06fd584995","resolution":{"observed_at":"2026-07-13T02:19:16.417790Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:30.700343+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:30.700343+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.12174","last_updated":"2022-03-23T03:32:08Z","snapshot_observed_at":"2026-08-10T15:59:45.133638Z","submitted_at":"2022-03-23T03:32:08Z","title":"Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation","version":1},"cited_work":{"arxiv_id":"2203.12174","doi":"10.48550/arxiv.2203.12174","metadata_source":"pith","pith_arxiv_id":"2203.12174","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation","venue":"math-ph","work_id":"36ebe640-9701-4b90-a766-da20bebb289e","year":2022},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2203.12174","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:ea56080adf1eff54895625aad0550065fd03d7e97241ba8f9907c4e59fdfef94","observation_id":"3e69118d-1afb-4423-9a71-37db3a9c0972","resolution":{"observed_at":"2026-07-13T02:19:16.330401Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:30.941216+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:30.941216+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"q-alg/9505024","last_updated":"1995-05-19T17:34:20Z","snapshot_observed_at":"2026-07-07T07:00:01.119534Z","submitted_at":"1995-05-19T17:34:20Z","title":"Hopf algebroids and quantum groupoids","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"q-alg/9505024","snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"doi:10.48550/arXiv.q-alg/9505024 , url =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/q-alg/9505024","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:fe840e016ac8df997033d2166c441f2628247ec70274ec45b01e3bd960be79f7","observation_id":"8d5edc41-a227-4e7b-b0e4-53eef8596033","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"doi:10.1142/S0129167X96000050 , url =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:da5b5d8b0ef5e5f57b23c8c4c49dae1181506156fa562226dddb1b17aced0edc","observation_id":"ee75b46c-1e6b-4439-83a8-356f658c6ba6","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1106.1071","last_updated":"2012-06-26T10:27:48Z","snapshot_observed_at":"2026-07-06T02:28:53.275929Z","submitted_at":"2011-06-06T14:03:40Z","title":"Backward error analysis and the substitution law for Lie group integrators","version":2},"cited_work":{"arxiv_id":"1106.1071","doi":"10.1007/s10208-012-9130-z","metadata_source":"pith","pith_arxiv_id":"1106.1071","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Backward error analysis and the substitution law for Lie group integrators","venue":"math.NA","work_id":"c82ce5a5-d53b-4cbd-ad14-5b6667e94a70","year":2011},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/1106.1071","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:c3e0d8c53c0d1f61f6defecfa4773dbb608accb4aa24f31d67682acf8df97f7e","observation_id":"08516cf4-a723-429d-8bd0-d00b9c7dbac6","resolution":{"observed_at":"2026-07-13T02:19:16.458610Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:31.651092+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:31.651092+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"and Ratiu, Tudor S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:ee8f163a67ba4cdf227bdc400373f6f04971135f4870913080566cecf57554bb","observation_id":"6f03054f-b53f-4467-819a-6ff45c116b40","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"Manifolds,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:b3b53bd5879e8ad67496240e8bc2bd141e6a410cdb8d7a80255da29e31ed18cf","observation_id":"f1551438-a7d2-44e0-bf74-5eac00853019","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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/jgm.2022014","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Offen, Christian , year =","venue":"The Journal of Geometric Mechanics","work_id":"9dfc1759-8875-4732-840e-f73b7459b3ee","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:194086c2da555bb2157c8f54e52fa27ff8555d2ec108abc8d163640a9ac91ad7","observation_id":"2e96f145-e4f1-44c2-a4f0-ecdb8c17bdd2","resolution":{"observed_at":"2026-07-13T02:19:16.838020Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:32.154703+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:32.154703+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:01de3bc631e5c031cf895d1a541759a585e4fbd9aaa22bafd224f46ee847d834","observation_id":"93ae891f-4676-4da5-ac2e-22df1d991762","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10208-019-09428-w","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Foundations of Computational Mathematics","work_id":"8139ca5f-41e6-407d-8e47-f96b78c585f2","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:12f0be4794bf985858fbf28d1795ab96e39ebcf3c0d6f0a1694279668f583047","observation_id":"f32b6d5b-2c09-48fd-8162-0d005764583c","resolution":{"observed_at":"2026-07-13T02:19:16.898257Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[{"edge_observation":{"observed_at":"2026-07-13T06:30:08.464003+00:00","source":"paper_reference_links","state":"open"},"event_date":"2024-07-09","event_type":"correction","notice_doi":"10.1007/s10208-024-09661-y","provenance":{"observed_at":"2026-07-11T03:03:10.430807+00:00","source":"crossref","source_record_id":"10.1007/s10208-024-09661-y->10.1007/s10208-019-09428-w:correction"}}],"reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/s0002-9939-10-10347-5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Mrčun, J","venue":"Proceedings of the American Mathematical Society","work_id":"8e82132e-e6d0-4d30-bbba-852c1d04738c","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:a84088fada7ece91b92093b6023b281bf7c16e46ef075ddafb3c58513842a3fa","observation_id":"6acd6d0e-05aa-4abd-9c0c-d79018e0df65","resolution":{"observed_at":"2026-07-13T02:19:16.891306Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:32.726676+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:32.726676+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"Aromatic","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:2659a23d594bcee64f1aaea14ff97b908675acbe790762c4c3154323252c61ad","observation_id":"04bfaf48-3e42-4edf-b99a-7a16a1ba5d26","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0603023","last_updated":"2006-03-01T15:20:59Z","snapshot_observed_at":"2026-08-09T05:49:15.211157Z","submitted_at":"2006-03-01T15:20:59Z","title":"On the Hopf Algebraic Structure of Lie Group Integrators","version":1},"cited_work":{"arxiv_id":"math/0603023","doi":"10.48550/arxiv.math/0603023","metadata_source":"pith","pith_arxiv_id":"math/0603023","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"On the Hopf Algebraic Structure of Lie Group Integrators","venue":"math.AC","work_id":"b62877e7-83b2-4a56-a97f-49766c1f9cac","year":2006},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/math/0603023","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:4b74dffbc352478b64a23161e47d5fbe612954f31b49284b74263f1da5800eb5","observation_id":"bfc264fb-a14b-4dc1-801a-dc3c583c939c","resolution":{"observed_at":"2026-07-13T02:19:16.831665Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:33.218181+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:33.218181+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"High Order","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:0c7f5fa4893d5e1ac9ba4914617b5e05b1a6b03e82f5dce0bc3b1054abc04650","observation_id":"68524aa6-03e0-4120-a0df-90db6cca42a6","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-01397-4_3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Føllesdal, Kristoffer K","venue":"Springer proceedings in mathematics & statistics","work_id":"bab84cac-ec0b-4140-8189-8f7b4b60358d","year":2018},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:2e0f3b45137e921bac0c281f2c4750e2f11b1b881b94e5e2b0013e56c175f38f","observation_id":"8da76e2c-4035-40de-8d9a-640d9f4fb4ee","resolution":{"observed_at":"2026-07-13T02:19:16.468027Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:33.672088+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:33.672088+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:38689a2a909f5fbec5f26d0676940c0c5e489cc680abaaef6931af188b9f5d27","observation_id":"e8ea07a3-684e-4eb6-8ce8-1a174fb6e874","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:c3d6f46f811859da2f9f49829f7a9b705963edb3a9e089b14817cdc42d295423","observation_id":"742fde9c-78f4-4315-aeb5-d9eb6d2d3174","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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/s0168-9274(98)00064-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", date =","venue":"Applied Numerical Mathematics","work_id":"d4abfb9a-5cf7-4a72-87ae-950010add366","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:6e2df971d8768b37dac2c46406ff2bb0bd694a3f0698c7977cf365957a4d21e0","observation_id":"81cf40c1-722d-4a42-ad83-4b6eb69bdf2b","resolution":{"observed_at":"2026-07-13T02:19:16.529851Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:34.45636+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:34.45636+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0036142995285162","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"SIAM Journal on Numerical Analysis","work_id":"af302f28-d0f6-4978-8447-390677f1afcd","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:d51e0165a218d7dc44d0097f0e500e0fda8bea879f9086d83d68d5b5f16a20c1","observation_id":"039e6319-3338-4d56-8a2e-5eda77f386e0","resolution":{"observed_at":"2026-07-13T02:19:16.801662Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:34.705608+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:34.705608+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/is008001011jkt037","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Guin, D","venue":"Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology","work_id":"f66e45c1-9b01-48b6-9b77-de34151e1a15","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:d885dae21f99f857b5fa460e1dc116d7e8d029d06f41391bd5cd533a559d35a1","observation_id":"26a77bd1-b220-40a2-98fd-67d49defa0fa","resolution":{"observed_at":"2026-07-13T02:19:16.884986Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:34.947561+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:34.947561+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1022325426017","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Marthinsen, A","venue":"BIT Numerical Mathematics","work_id":"52792c91-413c-4748-acc6-d3b9a94b5374","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:ac87010a869d787ba5562863e96ee2b3585745fcd6d52f3c3a48d784bc061c7c","observation_id":"17f16f09-9b5f-4526-8a32-c2ffef89cb9b","resolution":{"observed_at":"2026-07-13T02:19:16.433785Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:35.204261+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:35.204261+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0036142997329797","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Backward","venue":"SIAM Journal on Numerical Analysis","work_id":"3e190c01-d5e9-4b3d-be4e-553ac3e20869","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:aef8c55f4ea743917a59a454c5616ff77b23a21b20fd1fa7ea50ae3fa7fc6dd5","observation_id":"1d82c70b-0e28-4ae6-9c5c-e988b1d36e5b","resolution":{"observed_at":"2026-07-13T02:19:16.545119Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:35.434761+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:35.434761+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"Numerical","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:ec8f5455ea4ce46e9ebc0adbed3992020d7ff77cd5dc449c2620914001dd2bc7","observation_id":"d37e0dd4-5087-4404-9cd3-8300cb40b3cb","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":"Perturbative","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:2141519dc61180a3c58685f3f5d07fc2e669141de8ba2c8925025d9bee42dfec","observation_id":"5cbad66b-6c9b-491b-a193-4ff36abf4f72","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1503.04021","last_updated":"2015-06-19T16:50:12Z","snapshot_observed_at":"2026-08-05T02:11:33.367576Z","submitted_at":"2015-03-13T10:59:17Z","title":"Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more","version":2},"cited_work":{"arxiv_id":"1503.04021","doi":"10.48550/arxiv.1503.04021","metadata_source":"pith","pith_arxiv_id":"1503.04021","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more","venue":"math.NA","work_id":"0fb8754c-1bd1-4d9d-ba25-188894a43768","year":2015},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/1503.04021","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:b0780fcaf9d2b4b8eee12b2003d64f3b68a7fc9c6cf8acb4064b5b38e452c3c8","observation_id":"a53329a6-1fc5-4449-9a33-c1856f9a6c42","resolution":{"observed_at":"2026-07-13T02:19:16.739934Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:35.895049+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:35.895049+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"doi:10.1080/07362999008809220 , url =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:bd1adddc4dcf0e3922c514a0d7ea5470f90c501d83c150e042c3bdf1b9198a54","observation_id":"8a30555a-b073-4593-8efa-fa1186c15f89","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.07451","last_updated":"2024-07-10T08:08:56Z","snapshot_observed_at":"2026-08-12T03:11:16.304229Z","submitted_at":"2024-07-10T08:08:56Z","title":"Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations","version":1},"cited_work":{"arxiv_id":"2407.07451","doi":"10.48550/arxiv.2407.07451","metadata_source":"pith","pith_arxiv_id":"2407.07451","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations","venue":"math.NA","work_id":"e9613e6a-cc6b-4e08-81e9-a63f8300979b","year":2024},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/2407.07451","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:fc61cc4de2a7e2d94f23af2a0792114ce3de7658919ed649eb36fb90fb4d231c","observation_id":"7fc0e53f-6262-4272-8672-43210da26542","resolution":{"observed_at":"2026-07-13T02:19:16.381164Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:36.345504+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:36.345504+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00205-025-02154-4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Archive for Rational Mechanics and Analysis , year =","venue":"Archive for Rational Mechanics and Analysis","work_id":"aa5cbe97-4ae9-4a28-a003-55a3376f6d77","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:ebf5dd444f45b848a59d55e38e213c802b51c6cb0b841bcc5f2c43af2c96ad21","observation_id":"3b63bc31-1fa8-41fc-863e-3617d2399ac1","resolution":{"observed_at":"2026-07-13T02:19:16.537601Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:36.653348+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:36.653348+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1505.02436","last_updated":"2015-11-20T07:05:41Z","snapshot_observed_at":"2026-08-06T15:18:15.893139Z","submitted_at":"2015-05-10T21:10:00Z","title":"Post-Lie Algebras and Isospectral Flows","version":3},"cited_work":{"arxiv_id":"1505.02436","doi":"10.3842/sigma.2015.093","metadata_source":"pith","pith_arxiv_id":"1505.02436","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Post-Lie Algebras and Isospectral Flows","venue":"math.RA","work_id":"7992d16f-b91a-4589-82ad-b28d41176d7b","year":2015},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"cited_paper":"/paper/1505.02436","citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:c5af683156339aebd5ffd93e1c160a6b8d4a751326112215350808974e1b82e9","observation_id":"4e022fa7-f505-4481-a99e-d46068a7e13f","resolution":{"observed_at":"2026-07-13T02:19:16.294283Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:36.913579+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:36.913579+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/fms.2022.12","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"An Operadic Approach to Substitution in","venue":"Forum of Mathematics Sigma","work_id":"372df2e3-7339-4899-a9cd-c31019a4e815","year":2022},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:36df1aac9c1e94f7075bdb09f04536a6ab648a8450c97dc949def9e00bcec382","observation_id":"d060ef6a-2f32-4beb-84b7-5d3fd573855a","resolution":{"observed_at":"2026-07-13T02:19:16.572768Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:37.174747+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:37.174747+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10208-013-9167-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"and Lundervold, Alexander , year =","venue":"Foundations of Computational Mathematics","work_id":"aecdf894-8f74-4730-8a5f-21568211b7d9","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:ee68c855771a18fc31006225ff14e98f6387945bd4f9b3a07b7a49bf511b427c","observation_id":"e4f64cf2-798f-4f6e-a7f7-564f2e33dc6f","resolution":{"observed_at":"2026-07-13T02:19:16.306325Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[{"edge_observation":{"observed_at":"2026-07-13T06:30:08.461222+00:00","source":"paper_reference_links","state":"open"},"event_date":"2018-09-24","event_type":"correction","notice_doi":"10.1007/s10208-018-9398-8","provenance":{"observed_at":"2026-07-11T03:02:32.393203+00:00","source":"crossref","source_record_id":"10.1007/s10208-018-9398-8->10.1007/s10208-013-9167-7:correction"}}],"reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"doi:10.1080/00207160.2021.1966772 , url =","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:c2016bf7bc55ffeca363b41a5fcd5ddf4e7fffdaa6e62174a39f354019ecb366","observation_id":"1784f9e8-dbdf-41fc-b57d-c1a02a5907fc","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"2026-07-13T02:13:51.480364Z","title":", title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:947a34bc436ec24aa3b2f51028cd06c29a014ccb81ceed53a906564f63a6716a","observation_id":"d60c10ce-d8b1-4e4c-b770-a05cbb967024","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00220-024-05047-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Eulerian and","venue":"Communications in Mathematical Physics","work_id":"d1005613-5788-403a-b22d-c8f00ad4815b","year":null},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:12afd0ec36f39d2101c9e378046ce3e693d77cba23875f50dd20298662fb7519","observation_id":"a953cea6-bdf3-4db0-87b9-ab19e9bfe687","resolution":{"observed_at":"2026-07-13T02:19:16.844741Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:38.06311+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:38.06311+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"1998 , school =","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:5bea5afef983566c04afca53d7946d5256fe7bf649f0763c49b7954838086d95","observation_id":"dfc20ec8-357b-434a-bfc8-61c8a385b825","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10208-003-0111-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":", year = 2006, month = nov, journal =","venue":"Foundations of Computational Mathematics","work_id":"b84cb0d8-12ef-4c7d-a41c-e78a3235351d","year":2006},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:01242d20d11f9ddd4ae22ff5b15fb3a1f8ad49854331b89b45601a448e7da024","observation_id":"5446dedd-3a8a-4068-a9c4-fe905e025720","resolution":{"observed_at":"2026-07-13T02:19:16.300426Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:38.299006+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:38.299006+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":"Numerical","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:fe88002d46e2fe2e2714eaa0e60aabc2a254d4f5f71dfffd70b536e92153dca5","observation_id":"cb3a4464-8350-4383-8e62-dd598eec6167","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10208-010-9065-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Algebraic","venue":"Foundations of Computational Mathematics","work_id":"a0b3a133-57d0-4545-bfb4-854e238de36a","year":2010},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:32b89b88a500c945f7d940c16484b7d42521ec5cc3bac7d673bbd46f45a3d1a8","observation_id":"2bcb16fd-db7b-4c94-b82b-36ea8fc11604","resolution":{"observed_at":"2026-07-13T02:19:16.850806Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:38.625805+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:38.625805+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-13T02:13:51.480364Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:a66faceb8fa263898bfb937ca5d557de4b790dc3edf8dd03cd0c2544230990e0","observation_id":"5c25347f-a001-41d0-af21-92b24a06992c","resolution":{"observed_at":"2026-07-13T02:13:51.480364Z","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":"10.2307/1969046","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Annals of Mathematics","work_id":"b2a05bd9-2932-4d95-8dc0-d6f3841b7806","year":1948},"citing_paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations","version":1},"reference_index":88,"source":"arxiv_source","source_observed_at":"2026-07-13T02:13:51.480364Z"},"links":{"citing_paper":"/paper/2607.09549"},"observation_digest":"sha256:87080f374f0e2f397b596dbc73e369f08e1576510c2fe875a5f0f60e46df639d","observation_id":"ed505129-a3d9-449c-877c-dce6f6156980","resolution":{"observed_at":"2026-07-13T02:19:16.861395Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-07-20T16:53:39.114359+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-20T16:53:39.114359+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2607.09549","last_updated":"2026-07-10T15:58:51Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-10T04:20:28.705168Z","submitted_at":"2026-07-10T15:58:51Z","title":"Backward error analysis for matrix discretizations of 2-D Euler equations"},"reference_resolution":{"displayed":85,"state_counts":{"malformed_identifier":0,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":40,"verified_exact":43,"verified_fuzzy":0},"total_outbound_references":85},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 85 of 85 outbound references and 0 inbound Pith citation observations for arXiv:2607.09549."}