{"as_of":"2026-08-12T23:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:55ad00297e2a17ec3fdefff8aa9c482a7dc36789e1238e67b946917b52bc6353","coverage":[{"denominator":11,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":11,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T22:34:04.197893Z","state":"measured"},{"denominator":11,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":11,"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/2412.03482/citation-record","integrity":"/paper/2412.03482/integrity","json":"/paper/2412.03482/citation-record.json","paper":"/paper/2412.03482"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1603.02504","last_updated":"2016-03-14T09:04:42Z","snapshot_observed_at":"2026-08-09T23:11:40.081953Z","submitted_at":"2016-03-08T12:48:38Z","title":"The Erdos-Posa Property for Directed Graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1603.02504","snapshot_observed_at":"2026-08-11T22:34:04.164060Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.164060Z"},"links":{"cited_paper":"/paper/1603.02504","citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:d7cd32c7d664471aeb4ef1b9a85caf3e1bd008d7ba0ed486f478a98aa9102fdd","observation_id":"2aacb3db-e7d3-4619-96fb-c53df4e6095e","resolution":{"observed_at":"2026-08-11T22:34:04.164060Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.14704","last_updated":"2025-06-16T10:23:14Z","snapshot_observed_at":"2026-07-06T18:18:43.328203Z","submitted_at":"2024-05-23T15:37:50Z","title":"Connectoids I: a universal end space theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.14704","snapshot_observed_at":"2026-08-11T22:34:04.168553Z","title":"Bowler and F","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.168553Z"},"links":{"cited_paper":"/paper/2405.14704","citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:fdc18f20729f32ed530b7624c0bdd4b9accbefc624ac948fcb4fe4ac9f65099c","observation_id":"56b11438-41f5-45f3-8b92-ad776c8441d8","resolution":{"observed_at":"2026-08-11T22:34:04.168553Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2009.03295","last_updated":"2020-09-07T17:55:27Z","snapshot_observed_at":"2026-08-10T13:17:19.681717Z","submitted_at":"2020-09-07T17:55:27Z","title":"Ends of digraphs I: basic theory","version":1},"cited_work":{"arxiv_id":"2009.03295","doi":null,"metadata_source":"pith","pith_arxiv_id":"2009.03295","snapshot_observed_at":"2026-08-11T22:34:04.308523Z","title":"Ends of digraphs I: basic theory","venue":"math.CO","work_id":"24b2b6bb-e831-47ca-97d3-9f18223b2b6d","year":2020},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.172219Z"},"links":{"cited_paper":"/paper/2009.03295","citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:023940016f8df5ae781a3cbd38e9fdd747052b5ac316d6458950567ff09c3e18","observation_id":"ed7f7e5e-938c-455c-8fa3-9fe188c1d3ad","resolution":{"observed_at":"2026-08-11T22:34:04.313314Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:34:04.385446Z","title":"Diestel,Graph Theory, 6th ed., Springer (print edition); Reinhard Diestel (eBooks), 2024","venue":null,"work_id":"10af3665-8d12-4cbb-845c-af6806b8ab11","year":2024},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.176061Z"},"links":{"citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:9e59baf736464b55c0066b4893bd72ce6b34ee22c1ab894cf7d600635e7229f8","observation_id":"6bee95dc-1061-49ce-8348-5f21dcf82d69","resolution":{"observed_at":"2026-08-11T22:34:04.389179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:34:04.375448Z","title":"Georgakopoulos and M","venue":null,"work_id":"7a2d0f11-4c7b-492d-8e3b-b580bda05d78","year":2024},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.179535Z"},"links":{"citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:689e67e9b4e801cf66b1705544a8d6dff777ad987c2ba2770f7a681943345b72","observation_id":"eb552b99-b87c-4677-8126-f8c8e960c5e9","resolution":{"observed_at":"2026-08-11T22:34:04.378910Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:34:04.365017Z","title":"Halin, ¨Uber die Maximalzahl fremder unendlicher Wege in Graphen, Mathematische Nachrichten30 (1965), no","venue":null,"work_id":"d2a4b175-961c-4bd5-9f23-7f3eb40adc09","year":1965},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.182769Z"},"links":{"citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:96b9feeba0da2c8ae5d84a68d95303f5615936be6ab2008e5857adc2cd01fc47","observation_id":"ebb48b32-4d67-4c4e-9a2e-d8670cc58902","resolution":{"observed_at":"2026-08-11T22:34:04.368572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:34:04.185934Z","title":"Hamann and K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.185934Z"},"links":{"citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:22a2af8f079cb03c04a54218177bd763ef14fe83e3338a26d58a770813be8483","observation_id":"15820505-d010-4f7a-b962-3bc6562174bb","resolution":{"observed_at":"2026-08-11T22:34:04.185934Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:34:04.353608Z","title":"Heuer,Excluding a full grid minor, Abhandlungen aus dem Mathematischen Seminar der Universit¨ at Hamburg, 2017, pp","venue":null,"work_id":"d0ecb1a3-d365-4f30-90f5-6dea8dcbfd7d","year":2017},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.188587Z"},"links":{"citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:5dcc2c51bf8fc28d95a158a44b01f76250cccf008674af7e06a4470e678779c9","observation_id":"cf920ec5-5e7a-4fd4-9f93-7ea26e77b42e","resolution":{"observed_at":"2026-08-11T22:34:04.358430Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:34:04.343940Z","title":"Kurkofka, R","venue":null,"work_id":"a456d4a0-bf35-443e-a2af-4bbb5875f68a","year":2022},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.191565Z"},"links":{"citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:35c7e04373eca24f07bcc040d536cc0f0f87eb685015e9a8e505eac287660995","observation_id":"2a1d0410-9fa1-4317-8989-4ed31bfafa63","resolution":{"observed_at":"2026-08-11T22:34:04.347367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.04877","last_updated":"2025-06-13T13:10:21Z","snapshot_observed_at":"2026-08-12T18:00:01.576987Z","submitted_at":"2024-06-07T12:18:53Z","title":"A star-comb lemma for infinite digraphs","version":3},"cited_work":{"arxiv_id":"2406.04877","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.04877","snapshot_observed_at":"2026-08-11T22:34:04.224966Z","title":"A star-comb lemma for infinite digraphs","venue":"math.CO","work_id":"ca37bd48-cb58-49f3-a66e-a6bee341398a","year":2024},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.194723Z"},"links":{"cited_paper":"/paper/2406.04877","citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:6ce879090882f083288f703574ea7b4fde3b4a2cded7b12b2330ecb1b1f596f9","observation_id":"71b30afe-1a32-4d9f-8abb-8e0a4187ea12","resolution":{"observed_at":"2026-08-11T22:34:04.230101Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:34:04.197893Z","title":"Zuther,Ends in digraphs, Discrete mathematics184(1998), no","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T22:34:04.197893Z"},"links":{"citing_paper":"/paper/2412.03482"},"observation_digest":"sha256:025c530bcfb529b8e94649c24b8561f35006331dcce139d54ed546100e60fcdc","observation_id":"5d93d85f-d41b-41e3-9b5e-0d1d047de796","resolution":{"observed_at":"2026-08-11T22:34:04.197893Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.03482","last_updated":"2025-06-16T11:11:33Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-12T15:16:44.406998Z","submitted_at":"2024-12-04T17:17:26Z","title":"Halin's grid theorem for digraphs"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":2,"verified_fuzzy":5},"total_outbound_references":11},"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 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2412.03482."}