{"as_of":"2026-08-13T20:59:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1d1c7a0b5f09a5e202bceae54294de7f65e22aefd5f6b62ce6362eaa4e73e29b","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T15:54:46.640441Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2501.13617/citation-record","integrity":"/paper/2501.13617/integrity","json":"/paper/2501.13617/citation-record.json","paper":"/paper/2501.13617"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:47.566702Z","title":null,"venue":null,"work_id":"c4537b56-d5d9-4071-a87b-301df058d91f","year":2022},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.459779Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:a96ab374a714591f32f3a9071dd911f057c0fdc927c4911c45cad03d5c05ed8e","observation_id":"6dfb6800-59cd-4c46-b125-830b2993e16d","resolution":{"observed_at":"2026-08-10T15:54:47.571965Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2007.06455","last_updated":"2022-08-18T15:34:27Z","snapshot_observed_at":"2026-08-13T10:13:38.341007Z","submitted_at":"2020-07-13T15:40:57Z","title":"Asymptotically Optimal Vertex Ranking of Planar Graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.06455","snapshot_observed_at":"2026-08-10T15:54:46.465302Z","title":"Asymptotically optimal vertex ranking of planar graphs, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.465302Z"},"links":{"cited_paper":"/paper/2007.06455","citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:6194cdf3c9487f2f0075ea4926c270bd10f758f6d71c7d234d97ab4060c2d894","observation_id":"2040b7d1-1d18-4aac-b03f-714c1314a322","resolution":{"observed_at":"2026-08-10T15:54:46.465302Z","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":"2026-08-10T15:54:46.470629Z","title":"Graphs with linearly bounded R amsey numbers","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.470629Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:8d062c025a38219d3e5302056a9e71570da0a40d3348fe7c1d50d04b70481650","observation_id":"b944a2b2-89cf-47f5-92e6-f2eba5fdee04","resolution":{"observed_at":"2026-08-10T15:54:46.470629Z","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.dam.2022.06.003","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:47.054284Z","title":"Graph r-hued colorings— A survey","venue":null,"work_id":"7653bc9a-a328-4b25-bf1f-1b2897767624","year":2022},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.475880Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:0aeec3adc7ddceb0345b5a947c2317d9ff9d2b55e9b7e254511246446322985e","observation_id":"728da93d-45bd-45ad-9bd1-cc64780eb530","resolution":{"observed_at":"2026-08-10T15:54:47.062753Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/1.9781611975994.136","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:47.038959Z","title":"Improved bounds for centered colorings","venue":null,"work_id":"3028a46e-b389-4e20-8465-a69dce126b4a","year":2020},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.481950Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:e7c1eea1eb6a48ca9ee5690057a0ee64958707cc714657f356ef64d8018904a1","observation_id":"2b1a391e-df3c-4b81-ae50-98d7473539fb","resolution":{"observed_at":"2026-08-10T15:54:47.043990Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T15:54:46.486987Z","title":"Adjacency labelling for planar graphs (and beyond)","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.486987Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:d9b909b6d01554b0e5b8e87e8ada788c723382f6d66289dad297c8ed4a0a3a86","observation_id":"87a96d49-cd7d-4cd3-be89-9d47f36e338e","resolution":{"observed_at":"2026-08-10T15:54:46.486987Z","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":"2026-08-10T15:54:46.492939Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.492939Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:f4b4ede0a181fc35677da42a7b5a9696f69b814ee68d43daead4f488dd36df67","observation_id":"64f91228-f04b-423e-b2c3-26ad95c66072","resolution":{"observed_at":"2026-08-10T15:54:46.492939Z","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":"2026-08-10T15:54:46.497909Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.497909Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:c41b1c15607084da3efbceb1a1c086d09c5a59e414ea3089d5c6b88c5e88d96e","observation_id":"041c31ff-a921-4abe-9166-82883ee65440","resolution":{"observed_at":"2026-08-10T15:54:46.497909Z","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":"10.4230/lipics.socg.2022.38","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:47.004827Z","title":"On comparable box dimension","venue":null,"work_id":"f32859b7-1737-450f-ae2d-c00f3e1d2254","year":2022},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.502436Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:acadb7b7b40291cb46012dda7e2aa514bac4fa2d5ae7e3a332e7e3c7e693a8ee","observation_id":"6135ac1a-a734-40fc-b048-5b31f1240011","resolution":{"observed_at":"2026-08-10T15:54:47.010385Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.37236/7787","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.989437Z","title":"Boxicity, poset dimension, and excluded minors","venue":null,"work_id":"f1719fb0-1caa-4c77-93a3-464041049892","year":2018},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.506897Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:57e89ef0a4255e817ea813c1d46da6ff245ec253d00cf08f6404f94aaf8b44c3","observation_id":"62805d37-a977-463a-a0f2-19e68477f97e","resolution":{"observed_at":"2026-08-10T15:54:46.994371Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/18m1168753","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.974030Z","title":"Coloring and covering nowhere dense graphs","venue":null,"work_id":"2c7fdf3f-5315-479b-9190-771d6176e1a8","year":2018},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.511860Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:d57158bbf1d581107517ae61a2d9558765831a2c68dfa1c70fcaef95215850b7","observation_id":"b95cc620-f82d-4d67-b394-1af92411046b","resolution":{"observed_at":"2026-08-10T15:54:46.978880Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T15:54:46.516825Z","title":"Deciding first-order properties of nowhere dense graphs","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.516825Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:0f58d6b6d52bddb9b801b3970cf4378846a325aa082d50428284b1a9cb94cd3b","observation_id":"d4caf3d8-da2b-4847-b238-854b7f5ec302","resolution":{"observed_at":"2026-08-10T15:54:46.516825Z","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.endm.2007.07.079","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.948622Z","title":"List colouring squares of planar graphs","venue":null,"work_id":"2e18f02b-3eda-4c41-8c86-d718a5a8f399","year":2007},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.521392Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:95c396c181e37e4652e51064b3cd72104b39f10727332c87744b025117077480","observation_id":"02f34cb0-07b2-4f41-ba3c-cf5331be67f6","resolution":{"observed_at":"2026-08-10T15:54:46.953622Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T15:54:47.548045Z","title":"Odd colourings, conflict-free colourings and strong colouring numbers","venue":null,"work_id":"21fdc621-f25a-4b51-9f42-aac8ddabf72e","year":2023},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.525979Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:4b75dad110235c73c831540c1947983f6b9287c8cfb5f50e1686dcbe40fc33ed","observation_id":"acfd76b8-436d-4977-b97f-198c6b32df3e","resolution":{"observed_at":"2026-08-10T15:54:47.553503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"1999.1927","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:47.318136Z","title":"A simple competitive graph coloring algorithm","venue":null,"work_id":"138a3642-a2f8-45ff-ab27-0f8b7f01aaf3","year":2000},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.530504Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:f20f810485677a47a49677fad9a11ffce56d3b935c25278f9b4b8cd4916e7947","observation_id":"6ae7cc1a-1e4b-4400-89d5-f1bdd62693aa","resolution":{"observed_at":"2026-08-10T15:54:47.328343Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/jgt.3190180605","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T11:03:20.376878Z","title":"Planar graph coloring with an uncooperative partner","venue":"Journal of Graph Theory","work_id":"2f8ca6a1-70d3-4faa-ab4d-e1922440ea4e","year":1994},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.535225Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:ef1d38d284ca581b0718d139c5ce482b4470ba5cce4d5e658681f8d1a5892a7e","observation_id":"c1a5b72f-f32c-41cc-bdb7-b7df63032e11","resolution":{"observed_at":"2026-08-10T15:54:46.937901Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"6489.93166","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:47.226390Z","title":"Orderings on graphs and game coloring number","venue":null,"work_id":"fef64a64-97f0-4128-b347-89c104e574a3","year":2003},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.539957Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:fbd57a9d78081b484bd0a9873e581520988083d4307dab900ad77c2c65011507","observation_id":"1c8c3718-1036-46a0-b901-a7a64520d79e","resolution":{"observed_at":"2026-08-10T15:54:47.234294Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.37236/1611","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.915709Z","title":"Kierstead and William T","venue":null,"work_id":"d32bfa8d-181a-4813-91dc-9cb96b92d9f1","year":2001},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.544249Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:799f64431f02df017ded37c45542ed1938914317d72fa1cb982a08155bab533d","observation_id":"e8d11018-d36a-491b-945c-921663e42d0d","resolution":{"observed_at":"2026-08-10T15:54:46.921260Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.dam.2016.01.022","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.901086Z","title":"Dynamic coloring of graphs having no K5 minor","venue":null,"work_id":"d5e3bb73-916e-459a-afed-588940309548","year":2016},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.548750Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:46b29a5847271e14bc137fe718f4d544fff846742a5761183309e8b58eb70097","observation_id":"586c3875-c307-4cbd-9ccc-4b3a353275f5","resolution":{"observed_at":"2026-08-10T15:54:46.905613Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.disc.2006.11.059","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.886000Z","title":"A survey on the distance-colouring of graphs","venue":null,"work_id":"9d4642b0-6556-47f7-b8a9-b12a1929d00d","year":2008},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.554376Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:09949e5a782e2335bd52c9f8fe04cb51403e765bcdab0048bb47c47ad0ccee86","observation_id":"9f0ea318-9160-4e34-a005-7531173def8e","resolution":{"observed_at":"2026-08-10T15:54:46.890972Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.disc.2006.03.052","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.871765Z","title":"Conditional colorings of graphs","venue":null,"work_id":"5115f2c9-833b-4a1d-959e-7a5b61c2c2ce","year":1997},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.559442Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:4e4da0579a1da3b78c33d4e01917178e030c7b652413a9bc9838e4437413c274","observation_id":"b1a8df4e-ba04-4b00-8298-a7057c2173ba","resolution":{"observed_at":"2026-08-10T15:54:46.876451Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T15:54:47.530681Z","title":"Upper bounds of dynamic chromatic number","venue":null,"work_id":"c9bd2742-1603-44c4-acba-976865cfc3b2","year":2003},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.564571Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:760ffa2e2f6be1594a230c36ba8ee9cfb2723b8f72f116bfe282c1e52ba6cd70","observation_id":"4b8ae1b8-32c3-4ea9-883c-884d707c09b4","resolution":{"observed_at":"2026-08-10T15:54:47.536185Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.dam.2017.09.013","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.855323Z","title":"Dynamic coloring parameters for graphs with given genus","venue":null,"work_id":"caeb4f01-ff37-490c-aca5-e5a1c794835f","year":2018},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.569103Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:bcaa86662ff28d7c5fca3f8a195b566ebe940c96a0aa4e55399b729913c1d7c6","observation_id":"356fbc1b-a3b8-49e4-aac3-a328587556e5","resolution":{"observed_at":"2026-08-10T15:54:46.861106Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T15:54:46.573608Z","title":"Ramanujan graphs","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.573608Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:e7539e7bf11fc15340936d6b01604e9afbe612ce29559ea2d848386d208fd5a7","observation_id":"a00ebe1e-87e2-49ff-9308-8de2f5b8ccc4","resolution":{"observed_at":"2026-08-10T15:54:46.573608Z","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.disc.2016.01.009","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.830753Z","title":"Element deletion changes in dynamic coloring of graphs","venue":null,"work_id":"73ef975b-749d-415e-b7a9-8e0cd083364a","year":2016},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.578555Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:2a9861f79defd2ca960451bbfce77148dff79605f0612a731d7865002a5ec64a","observation_id":"76df80f8-b579-43c9-910e-313205534db6","resolution":{"observed_at":"2026-08-10T15:54:46.835928Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.33915/etd.1397","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.815630Z","title":"Dynamic coloring of graphs","venue":null,"work_id":"9b121d94-554f-4dd2-95fc-b022f1824d0a","year":2001},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.583155Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:92878b27d375b5dda956568e6d898b447d030a4cfedd817c659d09c9c79697c8","observation_id":"b8e9207f-8849-4c0f-a246-b22e31cc7e3b","resolution":{"observed_at":"2026-08-10T15:54:46.820678Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T15:54:46.587606Z","title":"Grad and classes with bounded expansion I","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.587606Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:930df7e3675ecf03b621a37d270e9d92dd5b1ad04e5df703f3d59a3853609fbd","observation_id":"a1aa9837-83b0-48db-b1d0-31c3f9b68620","resolution":{"observed_at":"2026-08-10T15:54:46.587606Z","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":"2026-08-10T15:54:46.592477Z","title":"On nowhere dense graphs","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.592477Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:71bacaa85be4bb4dc4f6fada5479aa851d9c1e094a321fcecc9e21ddaf0579d9","observation_id":"1837b8ac-b6ba-4058-a09e-ebff67adeb4a","resolution":{"observed_at":"2026-08-10T15:54:46.592477Z","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":"2026-08-10T15:54:46.597566Z","title":"Sparsity: G raphs, structures, and algorithms , volume 28","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.597566Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:03d53a85a63099f8ffcdfcbe20d54078b1c36f08cdd36b767cc02c10d30cd11c","observation_id":"c88b352c-34e3-497a-aa16-6e0ae36cf42d","resolution":{"observed_at":"2026-08-10T15:54:46.597566Z","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.ejc.2011.09.008","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.770627Z","title":"Characterisations and examples of graph classes with bounded expansion","venue":null,"work_id":"59f487e9-036b-4131-92de-8876b95f2e23","year":2012},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.602911Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:045c34203c7473c131c8fbe511df6a781ee2b14b2ff0ced64ddcbc8d2ed0da36","observation_id":"84d28341-eca0-439b-b7cf-072489482a20","resolution":{"observed_at":"2026-08-10T15:54:46.775729Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4171/077-1/7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.754614Z","title":"From sparse graphs to nowhere dense structures: D ecompositions, independence, dualities and limits","venue":null,"work_id":"2cc0651b-df1b-4a69-8df3-b7314c61cdb9","year":2010},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.607529Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:d2758967465ccd21025740b6f1b2d1ae3a1300b6b49e3a882d30fe484227e991","observation_id":"ce2ffac7-3f1e-4694-805d-d7bb66caaff7","resolution":{"observed_at":"2026-08-10T15:54:46.759508Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-642-60406-5_20","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-13T11:03:48.094449Z","title":"Arrangeability and clique subdivisions","venue":"Algorithms and combinatorics","work_id":"bcc4e674-6421-4a91-8d1c-28a1a3dd10ea","year":2013},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.611923Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:239b0eef67b449ce8eff15cf7beb2c97f9476444590a0596ed09a8941e95e25a","observation_id":"4e99c2a5-2614-4882-92d6-02cb142e08b4","resolution":{"observed_at":"2026-08-10T15:54:46.742601Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.dam.2017.12.041","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.721366Z","title":"Upper bounds of r-hued colorings of planar graphs","venue":null,"work_id":"3d847191-93da-40ec-85ea-d8cd1bceddcf","year":2018},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.616414Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:7af434b9b94115e1d4dbcffcbb3123a811e8aa4c95d9751fe8e9dff73f66146d","observation_id":"edf1690a-eef2-4fa0-9c95-4cf63e0a2d6a","resolution":{"observed_at":"2026-08-10T15:54:46.726229Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1704.06536","last_updated":"2018-02-22T23:02:45Z","snapshot_observed_at":"2026-08-12T06:37:59.813258Z","submitted_at":"2017-04-21T13:37:54Z","title":"Improper Colourings inspired by Hadwiger's Conjecture","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1704.06536","snapshot_observed_at":"2026-08-10T15:54:46.621123Z","title":"Improper colourings inspired by H adwiger's conjecture","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.621123Z"},"links":{"cited_paper":"/paper/1704.06536","citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:71a262339d147a13634317c5b44940e53a3f60f7b2232d3ef1f4a5ce3c56b3f8","observation_id":"b1de1368-6eb6-4747-b879-831ea58ef21a","resolution":{"observed_at":"2026-08-10T15:54:46.621123Z","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":"10.1112/jlms.12127","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T15:54:46.686538Z","title":"Improper colourings inspired by H adwiger's conjecture","venue":null,"work_id":"476ee0e2-8780-4ece-8c80-8708f032d929","year":2018},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.626354Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:7ca5c54520df699277664d2a5dabc2fa5dae49cafa1d2c9e8d0b51340a4b9026","observation_id":"c2880966-b1c5-4116-a913-c7632b1d10b6","resolution":{"observed_at":"2026-08-10T15:54:46.693511Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T15:54:47.511328Z","title":"Graphs with given diameter and a coloring problem","venue":null,"work_id":"75edfc95-fe6d-4d2c-9357-56777f6e33a6","year":1977},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.631138Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:29e4717e609e03fa8941253b3324e6ae8c7c108cfaaf6522c0aefe8cb15f6de5","observation_id":"85170768-eeaa-436c-9a2c-4265502fd17d","resolution":{"observed_at":"2026-08-10T15:54:47.516643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-10T15:54:46.635838Z","title":"Colouring graphs with bounded generalized colouring number","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.635838Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:a2309d804e85f30958c2d37ffa96bffedb0dab5d7ba74d483bf891a80a69d667","observation_id":"5c2fa1b4-34b9-4b8c-a1e6-d97625055309","resolution":{"observed_at":"2026-08-10T15:54:46.635838Z","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":"2026-08-10T15:54:46.640441Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-10T15:54:46.640441Z"},"links":{"citing_paper":"/paper/2501.13617"},"observation_digest":"sha256:f88b14225876b9d494e32e4cf2c0c4ec5740ba7567afdbd71a73e15b7e997aae","observation_id":"ecc51df2-abd7-4c94-80ed-8349720515c4","resolution":{"observed_at":"2026-08-10T15:54:46.640441Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2501.13617","last_updated":"2025-01-23T12:38:15Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-13T13:34:08.989605Z","submitted_at":"2025-01-23T12:38:15Z","title":"The r-Dynamic Chromatic Number is Bounded in the Strong 2-Coloring Number"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":19,"verified_fuzzy":3},"total_outbound_references":38},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2501.13617."}