{"as_of":"2026-08-23T15:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:95de13f45e11db71a10854e9cd39137ee8bd5bd9929384a3b02c120614b4f460","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T05:01:31.209887Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+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/2504.21821/citation-record","integrity":"/paper/2504.21821/integrity","json":"/paper/2504.21821/citation-record.json","paper":"/paper/2504.21821"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.130062Z","title":"Appel, W","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.130062Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:914e8de686cfa637b072374154b822a2f32389945b66ca844311c14d60f8b672","observation_id":"907e2c96-0b9a-4d5b-9733-d5a01f98b9b8","resolution":{"observed_at":"2026-08-16T05:01:31.130062Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/jgt.22938","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:08:47.750906Z","title":"Bernshteyn and E","venue":"Journal of Graph Theory","work_id":"739bfd25-44da-4113-a47f-430b01633264","year":2023},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.133548Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:16e9f0e0baf39ef6809b10c7afd0cbe042cab7cb1d2db1bd9f271cd59d876b89","observation_id":"5dc7217b-6957-4e3a-9388-f3e3269bc799","resolution":{"observed_at":"2026-08-16T05:01:31.336503Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.02792","last_updated":"2025-06-04T23:41:21Z","snapshot_observed_at":"2026-08-19T15:26:23.596621Z","submitted_at":"2024-06-04T21:32:35Z","title":"Weak Degeneracy of Planar Graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.02792","snapshot_observed_at":"2026-08-16T05:01:31.137175Z","title":"Bernshteyn, E","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.137175Z"},"links":{"cited_paper":"/paper/2406.02792","citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:9069182678807baf3864879e8452d7a8fc5f9a43dd03774b7545ca39cc64bc36","observation_id":"daec4421-357d-414a-9f22-4694f99e2968","resolution":{"observed_at":"2026-08-16T05:01:31.137175Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jctb.2023.10.010","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.324055Z","title":"Bonamy, M","venue":null,"work_id":"2a06fe5c-9302-4ce7-84fc-e30c513ee92e","year":2024},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.140770Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:f4c5d4c9cd035ea56d9c99c99dc1f951dbb15d3266dc65c0704435ab414af4b6","observation_id":"0ab24f6a-382f-4374-9bc1-85b8f06ddb6a","resolution":{"observed_at":"2026-08-16T05:01:31.327923Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.144127Z","title":"Bonamy, T","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.144127Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:5e8be3016e2fb3d144fec1cfed51c4f1c6f25823ca60236beec2c89506381efd","observation_id":"b7727741-6d6c-43dc-a162-939eff8b187f","resolution":{"observed_at":"2026-08-16T05:01:31.144127Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.148049Z","title":"Borodin, A","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.148049Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:af0885201c1ea53c49ca78c9e6ccdf8702d4cbf569303901fe73d789da341510","observation_id":"9aaea1ff-25c0-4f70-b4bc-3effff4750e9","resolution":{"observed_at":"2026-08-16T05:01:31.148049Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.150863Z","title":"Coloringtriangle-freegraphswith local list sizes.Random Structures & Algorithms, 57(3):730–744, 2020.doi:10.1002/rsa.20945","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.150863Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:21fb2339179dbcecb5b40d706e886d18a73e6ec57788cb773e44901e4edc0b7d","observation_id":"3d0e5e8d-d83e-4b07-b02b-78a71311d040","resolution":{"observed_at":"2026-08-16T05:01:31.150863Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.14361","last_updated":"2020-03-31T16:42:57Z","snapshot_observed_at":"2026-08-19T15:26:21.549974Z","submitted_at":"2020-03-31T16:42:57Z","title":"Graph structure via local occupancy","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.14361","snapshot_observed_at":"2026-08-16T05:01:31.153538Z","title":"Davies, R","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.153538Z"},"links":{"cited_paper":"/paper/2003.14361","citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:c55d3b5effe68ff90858e6824c916a1f643cba80ecb6c93b8fc8ccebf8614915","observation_id":"b1c5e73b-3de9-4581-bc9c-6159e4b2abf8","resolution":{"observed_at":"2026-08-16T05:01:31.153538Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jctb.2020.04.006","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.305222Z","title":"Dvořák, D","venue":null,"work_id":"b06f9671-e114-468b-961b-1c39eba530f1","year":2021},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.157043Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:b0c38e3916c6b47d41ad59413d6bfc736d3aa51c9681388bcf139ae8e90ddb42","observation_id":"0440bd8e-f758-4e25-b6b2-f476ed76ccac","resolution":{"observed_at":"2026-08-16T05:01:31.307972Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jctb.2016.11.004","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.296910Z","title":"Dvořák, B","venue":null,"work_id":"2f4c0a74-0701-4e9a-9d2f-2159271c591e","year":2017},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.159769Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:70f9e7136dc5cf4aeb00aaf047afd36f5d474b6fb01154f33ccee1fd750bb260","observation_id":"3ef7286a-9460-4275-874d-5caadb47d436","resolution":{"observed_at":"2026-08-16T05:01:31.299602Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.673283Z","title":"Dvořák and L","venue":null,"work_id":"f4ad5a41-a1a1-4f4c-afa6-edcc77c84d8b","year":null},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.162501Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:780e4c54eaf7d765208cf1aee167734fe998f0018052be5e48fe7de33289ae8e","observation_id":"ceca0619-6c68-47ff-a91e-340821b28869","resolution":{"observed_at":"2026-08-16T05:01:31.675892Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.665809Z","title":"Erdős, A","venue":null,"work_id":"863457c6-350c-4341-a0af-30f8bd42eb61","year":1979},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.169692Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:3b4e72cd5fb48bd06598e641a93414b2c3f79d9652df0d167eabf21b671ae303","observation_id":"9f595ac7-96a9-4827-a713-d1cea0371eeb","resolution":{"observed_at":"2026-08-16T05:01:31.668623Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.657365Z","title":"Grötzsch","venue":null,"work_id":"54217d62-8c0e-4538-9802-fc3eb167bd63","year":1959},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.172465Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:2e6c55be7931b769b473eb226a159867347884de852e6d084cf28f0b906a8d8c","observation_id":"ddc22d2d-faf7-4a29-bf5c-403504139c10","resolution":{"observed_at":"2026-08-16T05:01:31.660420Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.07901","last_updated":"2023-03-14T13:41:35Z","snapshot_observed_at":"2026-08-19T15:26:26.444738Z","submitted_at":"2023-03-14T13:41:35Z","title":"Weak degeneracy of planar graphs and locally planar graphs","version":1},"cited_work":{"arxiv_id":"2303.07901","doi":null,"metadata_source":"pith","pith_arxiv_id":"2303.07901","snapshot_observed_at":"2026-08-16T05:01:31.533974Z","title":"Weak degeneracy of planar graphs and locally planar graphs","venue":"math.CO","work_id":"9be653dd-5a47-454d-844a-e61bcabcc3be","year":2023},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.175397Z"},"links":{"cited_paper":"/paper/2303.07901","citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:f89033d21b9d19849db683d5209da8f237c99ccac9d5c507db3020b7241f6a97","observation_id":"15a80dab-13a6-4cf6-a1ef-653e8f3ce185","resolution":{"observed_at":"2026-08-16T05:01:31.537525Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jctb.2019.08.001","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.282900Z","title":"Kelly and L","venue":null,"work_id":"42a72c39-0eff-45d2-ae68-4e773a3fd6c1","year":2020},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.178470Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:b59c847ff29570ed701f07a778fe6bc5e44b3f86eafbd183e1305c96e1f96144","observation_id":"19564366-fcec-4aa6-89ab-d02ec68b78ef","resolution":{"observed_at":"2026-08-16T05:01:31.286274Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[{"edge_observation":{"observed_at":"2026-08-16T06:31:06.135077+00:00","source":"paper_reference_links","state":"open"},"event_date":"2021-06-23","event_type":"correction","notice_doi":"10.1016/j.jctb.2021.06.004","provenance":{"observed_at":"2026-07-11T03:14:47.305468+00:00","source":"crossref","source_record_id":"10.1016/j.jctb.2021.06.004->10.1016/j.jctb.2019.08.001:correction"}}],"reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.dam.2020.06.009","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.273945Z","title":null,"venue":null,"work_id":"3f34c3c6-d639-4e64-813f-5a4de905ea59","year":2020},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.181029Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:38c5d3793ebb594069e5ff768f0dfd6084c3278bd78802807ca5a61664861fa6","observation_id":"e1be4ffa-11ef-4eb4-b000-37d38e0d645f","resolution":{"observed_at":"2026-08-16T05:01:31.277795Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.15215","last_updated":"2021-11-25T15:55:41Z","snapshot_observed_at":"2026-08-16T17:52:44.033719Z","submitted_at":"2021-09-30T15:38:51Z","title":"Colouring locally sparse graphs with the first moment method","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.15215","snapshot_observed_at":"2026-08-16T05:01:31.183565Z","title":"Pirot and E","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.183565Z"},"links":{"cited_paper":"/paper/2109.15215","citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:89fa438d94d68ced04372aea1f8f79e931dbdd32313bc73dbfe9ac4e4aabb504","observation_id":"26bda535-02b7-499f-8566-ad92120ec4b8","resolution":{"observed_at":"2026-08-16T05:01:31.183565Z","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":"10.19086/aic.2022.8","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.265217Z","title":"Postle and E","venue":null,"work_id":"708c6889-befb-4fd5-9bf9-1a8e83b3a885","year":2022},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.187169Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:daef04fcbf537d5dad47d2f43bb937e6e1c61e4a161de94c5794d5691c8fe7f5","observation_id":"72deeb08-79b1-44d6-b805-0829dd8785a1","resolution":{"observed_at":"2026-08-16T05:01:31.268287Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.17291","last_updated":"2023-09-29T14:48:57Z","snapshot_observed_at":"2026-08-21T19:32:21.790628Z","submitted_at":"2023-09-29T14:48:57Z","title":"Exponentially Many Correspondence Colourings of Planar and Locally Planar Graphs","version":1},"cited_work":{"arxiv_id":"2309.17291","doi":null,"metadata_source":"pith","pith_arxiv_id":"2309.17291","snapshot_observed_at":"2026-08-16T05:01:31.514483Z","title":"Exponentially Many Correspondence Colourings of Planar and Locally Planar Graphs","venue":"math.CO","work_id":"1822af4c-f2fe-41d1-b373-f93c61487ca4","year":2023},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.189819Z"},"links":{"cited_paper":"/paper/2309.17291","citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:5372f422c51afea3a7dd177cb2aff8873c088745525ccab017ef6302d8e9f21f","observation_id":"674ec467-7b8f-4fa5-8897-15bb0d47857f","resolution":{"observed_at":"2026-08-16T05:01:31.518394Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.192529Z","title":"Thomassen","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.192529Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:2b8b4f53162d201b6dc622dbf1fe0bd09931f42de3c0ddaf1ed9834a6bb06767","observation_id":"bcc003a5-bc78-4038-93ea-5de9f606f10f","resolution":{"observed_at":"2026-08-16T05:01:31.192529Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.195187Z","title":"Thomassen","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.195187Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:a98fe2bbba17af5cc805085e5004a97aea7266c8d42fa050ea591557284940fb","observation_id":"e8882bae-9773-4cdd-8e42-5011be4c5157","resolution":{"observed_at":"2026-08-16T05:01:31.195187Z","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/s0095-8956(03)00029-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.256466Z","title":"Thomassen","venue":null,"work_id":"bfa41d6e-cc68-4c0f-9a47-8829da680674","year":2003},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.197761Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:2d74e9201004118eee8f8f418c7aabbcc5507265870a631aba0086119f68f2f5","observation_id":"d659f42b-e6f9-4409-8174-114f579c0e24","resolution":{"observed_at":"2026-08-16T05:01:31.259728Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jctb.2006.09.002","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.247904Z","title":"Thomassen","venue":null,"work_id":"262cfdd2-f020-4cda-b844-0b4bf3917499","year":2007},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.200413Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:adc009e1853279f49713ff624da14ba86a7b6f9982593247038dffdc2f87e4d6","observation_id":"dbb059e5-974d-42f2-bed7-680c760342f9","resolution":{"observed_at":"2026-08-16T05:01:31.250729Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.646417Z","title":null,"venue":null,"work_id":"809cebc7-0b87-47bc-9828-0c40f0318037","year":1976},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.203410Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:ae9063d85cf0dc6902648a5b8541eb8e2d04ed9983291d4dbc39aa5c7e657003","observation_id":"c3901d0f-cda7-4d9c-bbe6-82502b23a626","resolution":{"observed_at":"2026-08-16T05:01:31.649086Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0012-365x(93)90579-i","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-20T11:03:42.707129Z","title":null,"venue":"Discrete Mathematics","work_id":"1eb04469-a8ac-4629-b18b-2069d1bc0db3","year":1993},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.206665Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:ab9748dfa1e9bc11d952d56b207a8c2ae17e7b8d12a8f61d35a600c780a3fd0a","observation_id":"620a342a-8e3a-4a7b-8ce2-02dd51dcd5a0","resolution":{"observed_at":"2026-08-16T05:01:31.242218Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0012-365x(94)00180-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-20T11:03:42.707129Z","title":null,"venue":"Discrete Mathematics","work_id":"eba3f915-5965-44b6-baae-d6bfa5ce6bdd","year":1995},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.209887Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:78d2a3b9e34313d48ac4b06ddbe2faa7264aa4ea7076cf36ab7292e847088090","observation_id":"bbb80696-939c-4c28-8e08-0468e6aa9a85","resolution":{"observed_at":"2026-08-16T05:01:31.232325Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:01:31.166028Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs","version":1},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-16T05:01:31.166028Z"},"links":{"citing_paper":"/paper/2504.21821"},"observation_digest":"sha256:678d539211c00700d4fd0953bb88bbd7a6599210d4df6cc956d2413a47a6701b","observation_id":"511ed5c6-b745-4118-9790-50a4351e7d41","resolution":{"observed_at":"2026-08-16T05:01:31.166028Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2504.21821","last_updated":"2025-04-30T17:26:36Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-16T06:37:40.855278Z","submitted_at":"2025-04-30T17:26:36Z","title":"Local Weak Degeneracy of Planar Graphs"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":13,"verified_fuzzy":3},"total_outbound_references":27},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2504.21821."}