{"as_of":"2026-08-08T04:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:087107dfa5dfbaeb48c25a87014619b5844ce9abb1fb70b55eddfcd289ea77a7","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:43:03.566916Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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/2506.04991/citation-record","integrity":"/paper/2506.04991/integrity","json":"/paper/2506.04991/citation-record.json","paper":"/paper/2506.04991"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"stable/1967631","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:43:03.833051Z","title":null,"venue":null,"work_id":"89d5e8dc-0a6f-47e8-958f-01e27af09064","year":1901},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.481744Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:f6363089a2dbcef6770d7282f1f3e8bb75bd0c2d93a406ad06e4b9b5012bc51f","observation_id":"f0f2eb6d-4f21-4d65-8ac0-4d1036e5fb5b","resolution":{"observed_at":"2026-08-07T10:43:03.838542Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:04.000399Z","title":null,"venue":null,"work_id":"a533d43b-640e-4751-9bc1-398d1d3672cf","year":1935},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.486138Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:61d15e75b175624457eb496b6af069921aadedbda5709010aa43d8d80e79e337","observation_id":"a7550a70-bc08-4094-9a9f-bbe18e9e9316","resolution":{"observed_at":"2026-08-07T10:43:04.003936Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.990359Z","title":null,"venue":null,"work_id":"73f8aa93-697a-4620-b4bd-d344545369c0","year":1939},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.489703Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:a1f5496c4f9adbe2ae00af1927fc15565c1a581438c90678e27378102456f5c4","observation_id":"07bdbfdb-66fd-47dc-ba25-79cfcc5263ed","resolution":{"observed_at":"2026-08-07T10:43:03.993660Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.980701Z","title":"Sato, On maya game (notes by h","venue":null,"work_id":"7090b823-d524-4487-b79a-7ce631d7fbd0","year":1970},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.493292Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:acc34f6ce4bed4dbbd0b4a3d551f9baf334553c30d051cfe6525c385a77de065","observation_id":"3705169e-5345-4b40-b47a-9923bd6b41b6","resolution":{"observed_at":"2026-08-07T10:43:03.983928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.971076Z","title":"Irie, p-saturations of welter’s game and the irreducible representations of symmetric groups, Journal of Algebraic Combinatorics 48 (2018) 247–287","venue":null,"work_id":"9ac760e1-d918-402a-8815-4ac3eb47a1b3","year":2018},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.496839Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:2bde19660fd1aebee8c4ede1d7fb496beff071318451815923ee820a590b4067","observation_id":"720686c9-6df9-4bfe-9e67-a5a92e376cec","resolution":{"observed_at":"2026-08-07T10:43:03.974550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.961420Z","title":"Abuku, M","venue":null,"work_id":"24743a70-6c37-455b-80fe-b06ff8e59479","year":2023},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.501035Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:0196a2238b09fc65294bb88f73d56a659b27d42c7bf8684bf994ac290b34ac4a","observation_id":"49b59b11-4b07-44ce-9975-1b695b31295b","resolution":{"observed_at":"2026-08-07T10:43:03.964535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.14200","last_updated":"2021-12-28T16:00:44Z","snapshot_observed_at":"2026-07-06T12:23:01.375661Z","submitted_at":"2021-12-28T16:00:44Z","title":"Game positions of Multiple Hook Removing Game","version":1},"cited_work":{"arxiv_id":"2112.14200","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.14200","snapshot_observed_at":"2026-08-07T10:43:03.766004Z","title":"Game positions of Multiple Hook Removing Game","venue":"math.CO","work_id":"0f4efe5b-311f-4612-8316-c578f7dd3392","year":2021},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.504776Z"},"links":{"cited_paper":"/paper/2112.14200","citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:f73a659b5f91f6262fdac8a0464353829ccb2bec843d22edc823b0f2228f8725","observation_id":"c59b793c-c96b-4190-87cd-134c3cb3860b","resolution":{"observed_at":"2026-08-07T10:43:03.769939Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.951643Z","title":"Gottlieb, M","venue":null,"work_id":"53e00c81-390e-4e9b-983b-ae444fdab4c3","year":2024},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.508857Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:bfca9881c29f282b155c9093f432b3db509280a4680f5340e63c6947cdd25f55","observation_id":"6665180d-6d28-4d26-9599-0d962f905275","resolution":{"observed_at":"2026-08-07T10:43:03.954864Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2140/involve.2023.16.529","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:43:03.619659Z","title":"Gottlieb, J","venue":null,"work_id":"3ad9885f-330c-4927-b306-69cd91b6866d","year":2023},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.512304Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:a030e7161fd4d71aab1a7f9d27351d53544c687e272133046c3c8ea541b34040","observation_id":"d35b4398-0706-4150-a075-741559e8641b","resolution":{"observed_at":"2026-08-07T10:43:03.623791Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.26493/scores23","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:43:03.607153Z","title":"Bašić, E","venue":null,"work_id":"7d7a0f44-a900-4638-8199-54cb1e5161c8","year":2022},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.515769Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:fbc8e555d18c3d4f22d4889ef6dda02cbc90eaf77973141bb0234f3c1c7e1f31","observation_id":"87e0824c-8f07-498e-9a4b-4b61938a43fd","resolution":{"observed_at":"2026-08-07T10:43:03.611706Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.941176Z","title":"Bašić, Column-Row game, Master’s thesis (2023)","venue":null,"work_id":"af27854c-4c88-42d0-9c5c-955056f40791","year":2023},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.518939Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:4c227ef69c03290a873d4c0d9642aa6aaf94af29ea617f7d4e8eee99e2de5391","observation_id":"09a28492-7469-47e7-ba5b-54091a5042dc","resolution":{"observed_at":"2026-08-07T10:43:03.944693Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.931015Z","title":null,"venue":null,"work_id":"22d68653-7a7d-4b80-8676-ef25426b3f77","year":2017},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.522322Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:26580f3990c5f039c87d5365da841acf6c91098f82e89f4dd3af4753185e61e0","observation_id":"a221d9d2-9158-4bb4-8293-d7492bb17016","resolution":{"observed_at":"2026-08-07T10:43:03.934405Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.14640","last_updated":"2025-01-24T16:59:56Z","snapshot_observed_at":"2026-07-06T20:25:40.715105Z","submitted_at":"2025-01-24T16:59:56Z","title":"Impartial Chess on Integer Partitions","version":1},"cited_work":{"arxiv_id":"2501.14640","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.14640","snapshot_observed_at":"2026-08-07T10:43:03.751890Z","title":"Impartial Chess on Integer Partitions","venue":"math.CO","work_id":"1bc1245b-7beb-4f8e-a2de-ce227e352777","year":2025},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.525559Z"},"links":{"cited_paper":"/paper/2501.14640","citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:2075bab17d76c6de20b346a8a0569ea77059266fe77b39c0c160647b2de1d472","observation_id":"b4838981-7b0a-49d6-b749-8bec9d202d79","resolution":{"observed_at":"2026-08-07T10:43:03.755494Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.921628Z","title":"Meit, Two partizan games on integer partition, Master’s thesis, Rhodes College (2025)","venue":null,"work_id":"10811217-1500-473a-a341-c06302b9114b","year":2025},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.529306Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:fd1dadcf3d170bc56a15ace9b47285c98618d5c322bf235f889897ddab2f41e3","observation_id":"d4e94a8b-7c89-4848-ad24-5d99620d3519","resolution":{"observed_at":"2026-08-07T10:43:03.925078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.912150Z","title":null,"venue":null,"work_id":"eeec2a1e-2c92-421a-a9b0-e27f39f24176","year":1944},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.532495Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:dcf168b9e17b0d614b50b2f14f8fda8873219a6b0fb4545d935af0ef882739cf","observation_id":"12fb90b4-004d-4729-bd7a-d833705b03fc","resolution":{"observed_at":"2026-08-07T10:43:03.915542Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.901924Z","title":null,"venue":null,"work_id":"0977b1f9-7c42-4c13-8086-c7e4e2b1f867","year":1998},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.535912Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:562bde476774b072f82b0f2d2d00242f087a8b0d5bf1837050d7bf55c6d65400","observation_id":"e0146e56-e41e-4fdb-b4cd-d9b480030063","resolution":{"observed_at":"2026-08-07T10:43:03.905516Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.539017Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.539017Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:85dad72fe2a46b8337cc30ffa381a9df094c9fc49c32369df9244cab697d5099","observation_id":"8ea79335-982e-460a-be67-fe6992414427","resolution":{"observed_at":"2026-08-07T10:43:03.539017Z","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":"2026-08-07T10:43:03.891995Z","title":null,"venue":null,"work_id":"a73ccca7-f43e-40db-bad4-07cabccdc7a1","year":2001},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.542393Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:d4cd6701dcf47c5eecab3f5f31fb87a719df4a5433ed9ae7c4844587887f24e5","observation_id":"25025e31-0667-4285-a6b7-72a40207936f","resolution":{"observed_at":"2026-08-07T10:43:03.895513Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.881149Z","title":"Berlekamp, J","venue":null,"work_id":"2c968794-50fc-4422-a584-27900692dd50","year":2018},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.545981Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:73f65c0b849bc5e4119322a62418ad892a433240393e005544f88e256f9cb3f8","observation_id":"ebafe2fb-6bd8-414b-a35c-cf06d9ca0c49","resolution":{"observed_at":"2026-08-07T10:43:03.884919Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"stable/2304500","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:43:03.736521Z","title":null,"venue":null,"work_id":"9e7fd542-0507-4588-9d2b-be4d54f9ca72","year":1947},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.549133Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:22f690d25536086a6ad85dfeb23100e38c1d1019880b50ae2eef09a77c097343","observation_id":"ddaad5a2-4340-4aa6-a337-df4732def2d6","resolution":{"observed_at":"2026-08-07T10:43:03.741737Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1001.1783","last_updated":"2011-03-20T19:01:48Z","snapshot_observed_at":"2026-08-03T17:03:25.320303Z","submitted_at":"2010-01-12T02:49:44Z","title":"The number of nonzero binomial coefficients modulo p^alpha","version":3},"cited_work":{"arxiv_id":"1001.1783","doi":null,"metadata_source":"pith","pith_arxiv_id":"1001.1783","snapshot_observed_at":"2026-08-07T10:43:03.634341Z","title":"The number of nonzero binomial coefficients modulo p^alpha","venue":"math.NT","work_id":"fd9fc1fe-69a5-40c8-acaf-0eda4e511b30","year":2010},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.552386Z"},"links":{"cited_paper":"/paper/1001.1783","citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:b0c62e45372c610452b91db155f57309120576d23e915f878939640330264e9a","observation_id":"ddb286e3-b040-410e-8a09-c5a5061430cb","resolution":{"observed_at":"2026-08-07T10:43:03.638695Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.556597Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.556597Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:477a0746fa200b8681c762674b60e1d30cdcf874ec00d85daee95144f2958f64","observation_id":"7461ece2-f99b-4eb9-8472-24a09d5d07d9","resolution":{"observed_at":"2026-08-07T10:43:03.556597Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-07T10:43:03.868881Z","title":null,"venue":null,"work_id":"1e009382-6f8f-4402-8591-bce72a9176cc","year":1907},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.560018Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:b0c19f06e1e418af1a5dff462102fea5684379f666fe9e7955a6b362b8998242","observation_id":"c7a67877-4f52-48c9-8d0b-3187aba38d1d","resolution":{"observed_at":"2026-08-07T10:43:03.872787Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.858128Z","title":null,"venue":null,"work_id":"b630e266-5858-4731-8792-a576c96f6dcc","year":2005},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.563489Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:e0790344a77addc46351e9c5b2d0d7492d9bfd50ae49cc31cdf3ab2819ebe55c","observation_id":"675cb3dd-9c3e-4388-9d3f-21ba83a9fec1","resolution":{"observed_at":"2026-08-07T10:43:03.861707Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T10:43:03.846504Z","title":null,"venue":null,"work_id":"429b4166-10c8-48c7-ab02-8585d76c91d2","year":2016},"citing_paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T10:43:03.566916Z"},"links":{"citing_paper":"/paper/2506.04991"},"observation_digest":"sha256:51015affff65081d455528830b7de448f2e5950a2b6169a4df5cfb23af2d46ea","observation_id":"c2a639de-9022-4215-8ffe-0c9b7b6de0b9","resolution":{"observed_at":"2026-08-07T10:43:03.850873Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.04991","last_updated":"2025-06-05T13:02:23Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-07T10:26:33.476539Z","submitted_at":"2025-06-05T13:02:23Z","title":"Nim on Integer Partitions and Hyperrectangles"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":7,"verified_fuzzy":7},"total_outbound_references":25},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2506.04991."}