{"as_of":"2026-08-12T11:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:82db4788d2ea85782a86305e7ffde9ead055cbf37b25426c97318308aae01541","coverage":[{"denominator":48,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":48,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T11:02:30.064997Z","state":"measured"},{"denominator":48,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":48,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2608.02239/citation-record","integrity":"/paper/2608.02239/integrity","json":"/paper/2608.02239/citation-record.json","paper":"/paper/2608.02239"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T11:02:24.268213Z","title":"Journal of Combinatorial Theory, Series B , volume=","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.268213Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:d6818aa758d57e381419120c3a40bb4b73715ea2184abb3b9c8bc3bf4adbfd65","observation_id":"abd215c1-efb2-409e-9e9c-1967b6358518","resolution":{"observed_at":"2026-08-04T11:02:24.268213Z","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":"2026-08-04T11:02:24.349693Z","title":"Doklady Akademii Nauk , volume=","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.349693Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:fb60b80f72360c944a7c5ed9a1744351e620f4f06c8ac4bb7975fd17da40038f","observation_id":"67ecb1e2-86db-4bee-ad50-c2665fb23346","resolution":{"observed_at":"2026-08-04T11:02:24.349693Z","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":"2026-08-04T11:02:24.452833Z","title":"Studia Sci","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.452833Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:d5fac2eb303432f292f2a47768074eb1fee6258c6ecb5a7b6e1e62a24af7e516","observation_id":"346a4047-e305-401b-8a4c-d29ef6833a94","resolution":{"observed_at":"2026-08-04T11:02:24.452833Z","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":"2026-08-04T11:02:24.515611Z","title":"2015 , publisher=","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.515611Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:297b19fe2c958a28d3feb0d158e602f57933f67f3e5b213b837dcdc2c2895bb8","observation_id":"cf5dabd7-62f9-4280-a20d-c3e88afa300f","resolution":{"observed_at":"2026-08-04T11:02:24.515611Z","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":"2026-08-04T11:02:24.572772Z","title":", author=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.572772Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:5fa5f9076b2967d16b9884bc5cc9d3da8796a767a9327eec4091cf7a458cade6","observation_id":"1f76bf85-3911-4211-ae0a-eeaeada4b101","resolution":{"observed_at":"2026-08-04T11:02:24.572772Z","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":"2026-08-04T11:02:24.716253Z","title":"Journal of Graph Theory , volume=","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.716253Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:6d3234c8b5d092ab62ca9fbc42e77b07eb2e8fba01f3b7ce55ce62d7f9c42cd2","observation_id":"db2f21a3-938d-46a2-aee8-3d57ab58ebfa","resolution":{"observed_at":"2026-08-04T11:02:24.716253Z","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":"2026-08-04T11:02:24.810554Z","title":"European Journal of Combinatorics , volume=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.810554Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:a78b927602866dccbe7c4d2d3c7dac26cdbb7cf2507767c6de794bfef6497bd2","observation_id":"6d505913-4c5f-4dd4-94fa-f678efb2e73a","resolution":{"observed_at":"2026-08-04T11:02:24.810554Z","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":"2026-08-04T11:02:24.919094Z","title":"North-Holland Mathematics Studies , volume=","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.919094Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:345ddaf97829b757d931fa59a6b74ec1de26aa13d04b8e4cce44979f2814cef2","observation_id":"517fcd7f-2062-4aed-9f65-b1c9fc89fc06","resolution":{"observed_at":"2026-08-04T11:02:24.919094Z","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":"2026-08-04T11:02:24.990486Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:24.990486Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:ca7747110f52fd01db28d4507c9a668913c59fc928acb96f0486697c999ec806","observation_id":"854adad6-571d-47d1-8be8-5203fb2be71b","resolution":{"observed_at":"2026-08-04T11:02:24.990486Z","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":"2026-08-04T11:02:25.048336Z","title":", title =","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:25.048336Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:49b9d0ac433e60275485dfa4cb873e07787870bac02c9396095845061c95c471","observation_id":"854c692a-a91c-4d22-bf50-c6b5d34dd768","resolution":{"observed_at":"2026-08-04T11:02:25.048336Z","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":"2026-08-04T11:02:25.099579Z","title":"Graphs and Combinatorics , volume=","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:25.099579Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:54f1d74f7d9d93b3f4aab52fa5b2fcbdc1665cb4104b5276a55429667c4ab491","observation_id":"2fe78746-509b-43b5-a866-8ba5b5c104cc","resolution":{"observed_at":"2026-08-04T11:02:25.099579Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.13119","last_updated":"2025-06-10T13:23:38Z","snapshot_observed_at":"2026-07-06T12:22:17.012426Z","submitted_at":"2021-12-24T18:30:21Z","title":"Tur\\'an Number of Subdivisions of Multipartite Graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.13119","snapshot_observed_at":"2026-08-04T11:02:25.217019Z","title":"arXiv preprint arXiv:2112.13119 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:25.217019Z"},"links":{"cited_paper":"/paper/2112.13119","citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:13881fbbd58e3620a061b669ef55c95020646bc42a9644e76dd7d41efa86e78c","observation_id":"cdc4e9bd-83e0-4f61-bb36-144b6f6d451c","resolution":{"observed_at":"2026-08-04T11:02:25.217019Z","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":"2026-08-04T11:02:25.363655Z","title":"Journal of Combinatorial Theory, Series B , volume=","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:25.363655Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:53866bda27c436a5860514c5d2240eb2591125aeb665c819129e94171c7afcbd","observation_id":"b523db17-16b3-49ea-b870-9267fa26d933","resolution":{"observed_at":"2026-08-04T11:02:25.363655Z","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":"2026-08-04T11:02:25.496056Z","title":"Journal of the European Mathematical Society , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:25.496056Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:11da2085faa9b76cbb64658533e27de402680c871e7a50e151204bed3e76bf59","observation_id":"8fb6d51a-5eb7-4760-9014-a7cd8532a5e5","resolution":{"observed_at":"2026-08-04T11:02:25.496056Z","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":"2026-08-04T11:02:25.621364Z","title":"SIAM Journal on Discrete Mathematics , volume=","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:25.621364Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:3c02d18451f1101920127e133a479ee231e77c4a5336d8f8397ce2e191781aab","observation_id":"d3c37657-08f7-4a08-ab1c-27bf489bec3f","resolution":{"observed_at":"2026-08-04T11:02:25.621364Z","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":"2026-08-04T11:02:25.797410Z","title":"The mod k chromatic index of graphs is","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:25.797410Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:2415b7edcd128596272377477befb390825a7c4e997e00a5d90de6fc2bd1fde3","observation_id":"33068091-5492-4ae6-a070-2385cef009a4","resolution":{"observed_at":"2026-08-04T11:02:25.797410Z","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":"2026-08-04T11:02:25.953841Z","title":"Discrete Mathematics & Theoretical Computer Science , volume=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:25.953841Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:1fd508beb21779b4c644b2fa7a17f71b2f52c036a5ceec13034f7b81f0806135","observation_id":"fe9d3d27-5b8a-4afd-b6b5-9567885e6636","resolution":{"observed_at":"2026-08-04T11:02:25.953841Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2103.10200","last_updated":"2023-02-18T22:05:49Z","snapshot_observed_at":"2026-07-06T10:51:09.551898Z","submitted_at":"2021-03-18T12:07:26Z","title":"On the Tur\\'an Number of Generalized Theta Graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2103.10200","snapshot_observed_at":"2026-08-04T11:02:26.026660Z","title":"arXiv preprint arXiv:2103.10200, to appear, SIAM Journal on Discrete Mathematics , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.026660Z"},"links":{"cited_paper":"/paper/2103.10200","citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:2a382a2453536e4ce320a0ac05dde9d5068e0784ed506998aab7948827895b93","observation_id":"268dd018-1873-46ef-9cac-1f850a45ff9a","resolution":{"observed_at":"2026-08-04T11:02:26.026660Z","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":"2026-08-04T11:02:26.089209Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.089209Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:a9f1907cc580d9611c4a11e292f2f790e64153e5d7f486f05f207a9929a54f10","observation_id":"534184ab-122e-41bc-b03a-faf1563f62a4","resolution":{"observed_at":"2026-08-04T11:02:26.089209Z","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":"2026-08-04T11:02:26.202075Z","title":"Colloquia Mathematica Societatisj","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.202075Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:79bec59b7e6cf7c44bca8c8b684eb7fe31d65086d93c3ab56d51ce2b8fe8357c","observation_id":"746c46fc-0dd9-4e6c-b2b5-c2adc12b47b9","resolution":{"observed_at":"2026-08-04T11:02:26.202075Z","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":"2026-08-04T11:02:26.307082Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.307082Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:8794086d672af4cf5da28def22f4a107a33d7b78a9de3ce4ad9b5707f7c05fb8","observation_id":"2c13fab6-6e12-4eee-a11a-d6b5ee134c9d","resolution":{"observed_at":"2026-08-04T11:02:26.307082Z","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":"2026-08-04T11:02:26.400449Z","title":"Journal of Combinatorial Theory, Series B , volume=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.400449Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:a1eb3ebad66d335f2f76ed5152a048fa8442d706cc2263143d23538dd2dd24f1","observation_id":"27035287-908b-4f41-93d2-b8fc61a87b7d","resolution":{"observed_at":"2026-08-04T11:02:26.400449Z","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":"2026-08-04T11:02:26.589094Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.589094Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:71d59439493e935a0b6515f8a8ebadeb73308304d667a39350c6164db1adf75a","observation_id":"f384ff03-a55b-47a3-941f-ab5325622ffc","resolution":{"observed_at":"2026-08-04T11:02:26.589094Z","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":"2026-08-04T11:02:26.680024Z","title":"Bulletin of the London Mathematical Society , volume=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.680024Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:0cd1121d2cc731580b84e72cfb425d8d1d86a97db25c5d425381dc25d3625b79","observation_id":"cfc82f7a-5419-4d42-a029-7762e8e05544","resolution":{"observed_at":"2026-08-04T11:02:26.680024Z","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":"2026-08-04T11:02:26.869797Z","title":"Combinatorics, Probability & Computing , volume=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.869797Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:2ad28e1b9e57a897c2d5c47fdaddffd9adb9d2a951eeff917c67078a0abef947","observation_id":"3952670e-33fc-422e-8ad4-fbe420c8d5bd","resolution":{"observed_at":"2026-08-04T11:02:26.869797Z","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":"2026-08-04T11:02:26.918421Z","title":"2020 , journal=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.918421Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:914e31450d983bc23e13e398fec672e73df602b7b5f16ee007546a27d1fce409","observation_id":"33344e36-3c01-4b1b-a990-3461fb52a1b8","resolution":{"observed_at":"2026-08-04T11:02:26.918421Z","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":"2026-08-04T11:02:26.980787Z","title":"2020 , journal=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:26.980787Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:e3e9a51e6cdae08c2a786c60db13a02a79f3d2cf943ae51e91fd200a2e79465f","observation_id":"1cd398eb-9e89-4e1c-95e1-d15f2449759d","resolution":{"observed_at":"2026-08-04T11:02:26.980787Z","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":"2026-08-04T11:02:27.115707Z","title":"SIAM Journal on Discrete Mathematics , volume=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:27.115707Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:09642c5bad7420b2610200491f0e1430110581d8aac642150605d51921593d5a","observation_id":"99d387d3-fd1d-4211-b666-e59edb812a80","resolution":{"observed_at":"2026-08-04T11:02:27.115707Z","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":"2026-08-04T11:02:27.267885Z","title":"Combinatorica , volume=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:27.267885Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:d9af0f8980d5e4eff98d82214ed0fea43d22b09a37fb9ae199e9623031b8ebf4","observation_id":"542caf1e-c045-469f-96bb-a7044330ee04","resolution":{"observed_at":"2026-08-04T11:02:27.267885Z","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":"2026-08-04T11:02:27.386741Z","title":"On the rational Tur","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:27.386741Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:b3d282831c3e7b9fb989dba6223021cf01968bc021db4170a45f220b53bb7197","observation_id":"01bf91ec-5d04-413d-8b64-d35e24cae8d4","resolution":{"observed_at":"2026-08-04T11:02:27.386741Z","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":"2026-08-04T11:02:27.594670Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:27.594670Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:448521c58e413e9b5b0c726e31e2694450b1c0ff9c566fa463d572059e85a6d1","observation_id":"7e5f1513-42ea-4b1a-b495-8a4db475d5cc","resolution":{"observed_at":"2026-08-04T11:02:27.594670Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.03375","last_updated":"2022-12-13T16:24:40Z","snapshot_observed_at":"2026-08-06T18:07:17.774221Z","submitted_at":"2022-03-07T13:32:50Z","title":"Rational exponents near two","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.03375","snapshot_observed_at":"2026-08-04T11:02:27.782779Z","title":"arXiv preprint arXiv:2203.03375 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:27.782779Z"},"links":{"cited_paper":"/paper/2203.03375","citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:b964f2e5ba893348e27167a1713516f167ae35025e812906f8f9ef2833492203","observation_id":"0d13efe8-cb5a-4116-9a05-5196fa107f47","resolution":{"observed_at":"2026-08-04T11:02:27.782779Z","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":"2026-08-04T11:02:27.897700Z","title":"Many Tur","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:27.897700Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:5dad8f359be9f982eefc453af532ac0ffff7b7c85f76409e9db02a38358a2a71","observation_id":"9c209998-0996-4281-b081-2ea9ab25769c","resolution":{"observed_at":"2026-08-04T11:02:27.897700Z","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":"2026-08-04T11:02:28.049476Z","title":"Combinatorica , volume=","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:28.049476Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:9c6e5aee48cde961aff125651102bf10569380628e67715d4d49ff675a59ee6b","observation_id":"0bf15d60-d584-4d37-8a11-63b774376f4d","resolution":{"observed_at":"2026-08-04T11:02:28.049476Z","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":"2026-08-04T11:02:28.152653Z","title":"Combinatorica , volume=","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:28.152653Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:9b97c1552d8a2f442167b0b4cc9ca79fa3d5b455f195f20e1f704796e5c9aff1","observation_id":"7a913d91-4e9e-4ec1-aab5-1fbc26db5549","resolution":{"observed_at":"2026-08-04T11:02:28.152653Z","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":"2026-08-04T11:02:28.338122Z","title":"Mat.Fiz.Lapok (Hungarian) , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:28.338122Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:35e99a9d13dc596d3c8ec8a6049e8602496f9ebf8f48597c1c15098bcff286f8","observation_id":"3981c010-e458-4a17-8f0d-84d54524a800","resolution":{"observed_at":"2026-08-04T11:02:28.338122Z","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":"2026-08-04T11:02:28.542055Z","title":"2008 , publisher=","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:28.542055Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:d4c8539d0e6bb2694d0387c0f7bb373e61a92935c78942554212fe33ee0b439e","observation_id":"5f33b3a2-d2c5-498b-8a13-98d18000b838","resolution":{"observed_at":"2026-08-04T11:02:28.542055Z","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":"2026-08-04T11:02:28.746817Z","title":"Journal of Combinatorial Theory, Series B , volume=","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:28.746817Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:029f5b75388b48b9065ccaa062bbb7d3d566c32bc094c0c1b069115dcb9430e7","observation_id":"b26bf7d1-f34d-489b-b466-da9bc857bfd9","resolution":{"observed_at":"2026-08-04T11:02:28.746817Z","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":"2026-08-04T11:02:28.921094Z","title":"On the Tur","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:28.921094Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:a7c611a37b37abe24bc94bbedca27d375687d1f3bfc77b7f94121040b71b4ba4","observation_id":"fb6a146f-f3f6-4fca-99f9-4b9e7aa9d2b9","resolution":{"observed_at":"2026-08-04T11:02:28.921094Z","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":"2026-08-04T11:02:29.034566Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:29.034566Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:02df96f4a872277c13126c3d473bbe9ae12457bca723b928ce6f936d666e68b2","observation_id":"983d46b6-33b2-4df4-ba7a-0790f0a3020f","resolution":{"observed_at":"2026-08-04T11:02:29.034566Z","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":"2026-08-04T11:02:29.206882Z","title":"2011 , publisher=","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:29.206882Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:944d26165979c8badfce9f032574a55d50762ca6be491c43e78958103f8f044b","observation_id":"712f407d-2cd7-4f06-acb6-03e686151126","resolution":{"observed_at":"2026-08-04T11:02:29.206882Z","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":"2026-08-04T11:02:29.303410Z","title":"Journal of Graph Theory , volume=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:29.303410Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:c71719effc31d2ca5483c7fdd28ce1a6f5706a453043891dfc194bf3ee5765f5","observation_id":"161157cc-f23c-4885-9e36-f810cc57a151","resolution":{"observed_at":"2026-08-04T11:02:29.303410Z","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":"2026-08-04T11:02:29.458632Z","title":"Journal of Graph Theory , volume=","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:29.458632Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:146b54c414e5ce1e26defd9f4dd709bd69f5d5ed3edc21b87ad080c800ed6c1e","observation_id":"53df69fe-2265-4330-85e5-be542505df92","resolution":{"observed_at":"2026-08-04T11:02:29.458632Z","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":"2026-08-04T11:02:29.540662Z","title":"Journal of Graph Theory , volume=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:29.540662Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:4cc156b8552460fe15013beefc094526ed486737b197aca6eca605a8c7ce5af3","observation_id":"e5adfb89-8cdb-420d-baf4-8dc261c0265c","resolution":{"observed_at":"2026-08-04T11:02:29.540662Z","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":"2026-08-04T11:02:29.659123Z","title":"Ars Mathematica Contemporanea , volume=","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:29.659123Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:c6da4034cfa1d3b2f7205d091614fc0c9d6b52ff96cac75cf0be16de4320dfea","observation_id":"26630ca8-37ef-4ae4-9202-feeaac5a1dcf","resolution":{"observed_at":"2026-08-04T11:02:29.659123Z","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":"2026-08-04T11:02:29.763484Z","title":"preprint , pages=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:29.763484Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:4f091b1f668d54385bdb3a73ef021bc1e6235c229a295b32b6fd13a2abbcd7f8","observation_id":"3ea71921-2205-4860-8294-a6c0bb6ef890","resolution":{"observed_at":"2026-08-04T11:02:29.763484Z","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":"2026-08-04T11:02:29.919864Z","title":"Journal of Graph Theory , volume=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:29.919864Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:c40e83ba6303ca6a4ab8f348193154b4d68f2ad9f2799b65920107211f482584","observation_id":"01e65a98-7738-4d28-88ec-9540ae1139f3","resolution":{"observed_at":"2026-08-04T11:02:29.919864Z","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":"2026-08-04T11:02:30.064997Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-04T11:02:30.064997Z"},"links":{"citing_paper":"/paper/2608.02239"},"observation_digest":"sha256:bc7caa977dbeaf9642ef8684be9843fba7f829c7a554ae0d573bea3ab0e4cf74","observation_id":"aa475507-161c-4195-8571-7ef1dfdd1db7","resolution":{"observed_at":"2026-08-04T11:02:30.064997Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2608.02239","last_updated":"2026-08-03T13:51:55Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-06T23:37:04.986712Z","submitted_at":"2026-08-03T13:51:55Z","title":"Linear Lower Bounds for the Modular Chromatic Index"},"reference_resolution":{"displayed":48,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":48,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":48},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2608.02239."}