{"as_of":"2026-08-16T08:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5a8be85827c625d99ee709bdf1748c05897e6eda1f917351c21e6755fe77f717","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":"2026-08-14T14:03:39.437708Z","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":"2026-08-16T06:30:59.297886+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/1908.03880/citation-record","integrity":"/paper/1908.03880/integrity","json":"/paper/1908.03880/citation-record.json","paper":"/paper/1908.03880"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:03:40.144142Z","title":"Moser and W","venue":null,"work_id":"bdeac6ce-89b4-44c9-9365-b9170eddf921","year":1961},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.199772Z"},"links":{"citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:39ef2df73aaefe10bbf56b6a382a0b7f8b64bbb58e0e4f3095ca79a12cb2d704","observation_id":"7105c6d8-8765-4164-a9c7-1937974bd8b5","resolution":{"observed_at":"2026-08-14T14:03:40.152844Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.02385","last_updated":"2018-05-30T20:46:47Z","snapshot_observed_at":"2026-08-14T19:28:15.454936Z","submitted_at":"2018-04-08T00:33:50Z","title":"The chromatic number of the plane is at least 5","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1804.02385","snapshot_observed_at":"2026-08-14T14:03:39.237921Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.237921Z"},"links":{"cited_paper":"/paper/1804.02385","citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:d05a893daef2855c6611f7b81d13ec3b2d2ca35ee835d61e99e4750f09e51df4","observation_id":"e5fe09f0-29ce-4e6d-96d4-e8db0989a131","resolution":{"observed_at":"2026-08-14T14:03:39.237921Z","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":"2026-08-14T14:03:40.103228Z","title":null,"venue":null,"work_id":"4e922254-3d95-46e3-9a46-c1433a683845","year":2019},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.254512Z"},"links":{"citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:c80df71fd0f9c9e0cb2f691f55afd1682032564154be7faaca969b26f05270e1","observation_id":"5ed30a21-6047-43a1-8be7-6cf4feefecf6","resolution":{"observed_at":"2026-08-14T14:03:40.114830Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:03:39.949865Z","title":"Soifer,The Mathematical Coloring Book(Springer-Verlag, 2009)","venue":null,"work_id":"8a339f70-ceee-4fb4-bf61-d0e836d9bcad","year":2009},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.268297Z"},"links":{"citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:450abf6b1d60fc99e569a15bd83854a9b671ae79e14bf7d5018dd5456c09b3f8","observation_id":"d9dd64c1-618d-42ad-9222-4017eb996b0e","resolution":{"observed_at":"2026-08-14T14:03:39.989666Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1501.02441","last_updated":"2015-01-11T10:49:35Z","snapshot_observed_at":"2026-08-14T23:04:31.993827Z","submitted_at":"2015-01-11T10:49:35Z","title":"A probabilistic Hadwiger-Nelson problem","version":1},"cited_work":{"arxiv_id":"1501.02441","doi":null,"metadata_source":"pith","pith_arxiv_id":"1501.02441","snapshot_observed_at":"2026-08-14T14:03:39.587428Z","title":"A probabilistic Hadwiger-Nelson problem","venue":"math.CO","work_id":"d8b580ad-10f7-4a43-ab5f-844297788cf9","year":2015},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.280022Z"},"links":{"cited_paper":"/paper/1501.02441","citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:723b41bf1a4b03c2e059d177632f92be67f9d2d74f75510fa7533d6c6f74a569","observation_id":"5ad2b9e7-8e0d-4555-9b6b-5104a25254a2","resolution":{"observed_at":"2026-08-14T14:03:39.603482Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1705.07621","last_updated":"2017-06-15T19:45:14Z","snapshot_observed_at":"2026-08-14T20:59:09.522407Z","submitted_at":"2017-05-22T09:15:19Z","title":"The grasshopper problem","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1705.07621","snapshot_observed_at":"2026-08-14T14:03:39.293730Z","title":"Goulko and A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.293730Z"},"links":{"cited_paper":"/paper/1705.07621","citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:1a394618519f37b1e98d5d9ad05ab8201089185ee0fe962fb638338565b2da5b","observation_id":"276be0f4-c5fd-4530-9a15-33288ca37900","resolution":{"observed_at":"2026-08-14T14:03:39.293730Z","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":"2026-08-14T14:03:39.919012Z","title":null,"venue":null,"work_id":"c618df3f-50cd-4f9c-922c-b30f62afe787","year":2002},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.301832Z"},"links":{"citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:ba42e3524a40633b504dfac0a9e6d5bbb32ae90029c67a49aa81c1b227a794c3","observation_id":"a588d59a-7f8b-4815-bc5a-69920db3103b","resolution":{"observed_at":"2026-08-14T14:03:39.928206Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:03:39.864275Z","title":"Soifer, Geombinatorics1, 13 (1992)","venue":null,"work_id":"99d21d50-d4f1-4b70-bdcf-806489129780","year":1992},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.310524Z"},"links":{"citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:621b1ec134a6396a9db2f9904c7d333560c327f2174b9cc1ea5d4ee4887fd4ae","observation_id":"7ef9263a-94b2-463b-b0be-9ff63c497ca8","resolution":{"observed_at":"2026-08-14T14:03:39.880428Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:03:39.844894Z","title":"Colorplane,","venue":null,"work_id":"4707cd3e-c6f0-447a-9768-60fbd24fc855","year":2019},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.319721Z"},"links":{"citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:e1a091490b4446ce55cab3eb8156f26523db58f0da38fd0d23c3e170a0683c6f","observation_id":"5aacaa75-2257-46ad-9be7-067fe5fdbd4c","resolution":{"observed_at":"2026-08-14T14:03:39.850714Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:03:39.776126Z","title":null,"venue":null,"work_id":"646be9f0-3af5-41cb-b1fa-28374c86f5df","year":2009},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.378913Z"},"links":{"citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:2a307dd29a1ab370aa838ec6b5ed321425dce9a14fc1b50cbce974086e2c4364","observation_id":"6da48897-56db-4ad3-9828-195254e42c1a","resolution":{"observed_at":"2026-08-14T14:03:39.798225Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:03:39.670585Z","title":"Aalto University, P.O.Box 11000, 00076 AALTO, Finland E-mail: sami.heinasmaki@aalto.fi 20","venue":null,"work_id":"f4cb998e-62a5-4a47-8e9e-11c3de3b5888","year":2019},"citing_paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:03:39.437708Z"},"links":{"citing_paper":"/paper/1908.03880"},"observation_digest":"sha256:71b3d826d29f86ea48939d4bb6ecee2cf5f9108b77bb4049c563c931a2a64755","observation_id":"fc32f9ef-821d-4cc7-9227-fc2347f06820","resolution":{"observed_at":"2026-08-14T14:03:39.695872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.03880","last_updated":"2019-08-27T06:26:40Z","latest_version":2,"primary_category":"cond-mat.stat-mech","snapshot_observed_at":"2026-08-16T02:25:16.968323Z","submitted_at":"2019-08-11T10:17:02Z","title":"Lattice approach to plane colorings"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":1,"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:1908.03880."}