{"as_of":"2026-08-09T01:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:59f1db44d1437c4d63211fb923ef4d2b01d63359111498db4a527888d9a628e4","coverage":[{"denominator":59,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":59,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T17:34:45.066591Z","state":"measured"},{"denominator":59,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":59,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2512.09397/citation-record","integrity":"/paper/2512.09397/integrity","json":"/paper/2512.09397/citation-record.json","paper":"/paper/2512.09397"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T17:34:37.321120Z","title":"Arsovski","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:37.321120Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:576625c54382beaf2b37481ff29cd3ca2d97b14a765f5d42f4f2c070199d803d","observation_id":"e3a83059-2da9-4d75-aff8-d5c8f878f06c","resolution":{"observed_at":"2026-08-03T17:34:37.321120Z","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":"2026-08-03T17:34:37.436508Z","title":"Balog and E","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:37.436508Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:b2af0f06618cfff6e3aa12fc216a92ce0fa68ce7170439cf45f02acae8bbc497","observation_id":"932aef65-8304-4316-971c-dc8916b5d27b","resolution":{"observed_at":"2026-08-03T17:34:37.436508Z","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":"2026-08-03T17:34:37.573514Z","title":"Bennett, A","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:37.573514Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:5d90a3f4a6e463fac7697608c67ba081f5a5324021a09d3c9c42716476e6c169","observation_id":"50551857-4948-404d-bf3a-a729d353a10e","resolution":{"observed_at":"2026-08-03T17:34:37.573514Z","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":"2026-08-03T17:34:37.784254Z","title":"Besicovitch","venue":null,"work_id":null,"year":1919},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:37.784254Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:4b6bceeae747ac7f410bb453a00e22ca6bd36ad27759bac9b4e5a0f68b46aacc","observation_id":"0151905b-323d-4464-b0db-1a8d51cba4ef","resolution":{"observed_at":"2026-08-03T17:34:37.784254Z","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":"2026-08-03T17:34:37.922589Z","title":"Bourgain","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:37.922589Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:db2f259908cb06380fdfa0d23ff5843ad4e022876e164ae73b76ad97460a306e","observation_id":"ecc941b0-807b-4113-9130-19160030bde9","resolution":{"observed_at":"2026-08-03T17:34:37.922589Z","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":"2026-08-03T17:34:38.056264Z","title":"Bourgain","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:38.056264Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:5224bdf53ae07e7ca67705874fea15afa4a1b024d8a7b3b50c2f3f9e1db40a8d","observation_id":"7c768d7d-0180-4852-b7f9-d9accaf4ed40","resolution":{"observed_at":"2026-08-03T17:34:38.056264Z","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":"2026-08-03T17:34:38.182957Z","title":"Bourgain","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:38.182957Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:f5a8ca784481391a4dd4193d47da18187195a5aeef3da2bfbd72fa1886ecf332","observation_id":"a3b10ecf-6529-47be-9ad4-c7fcea2756a3","resolution":{"observed_at":"2026-08-03T17:34:38.182957Z","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":"2026-08-03T17:34:38.325280Z","title":"Bourgain","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:38.325280Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:89e46dd3fd87265b2781a632e9cd6557ea32b388c6762c5318685852a9b72145","observation_id":"0ff5bff7-1624-4bbd-bf2c-3b044e9f234b","resolution":{"observed_at":"2026-08-03T17:34:38.325280Z","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":"2026-08-03T17:34:38.467861Z","title":"Bourgain and L","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:38.467861Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:020a91a49ab85179e47d3158b762e49bc86aa51196ff933f5239e1c636b1828e","observation_id":"b7961d18-bfcb-443d-8813-5815395cf604","resolution":{"observed_at":"2026-08-03T17:34:38.467861Z","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":"2026-08-03T17:34:38.612491Z","title":"Bourgain, N.H","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:38.612491Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:17d305a78aec7e7761d654158edda759d44090dacf7f1b8fe32c842f66f96727","observation_id":"1b0639e7-d750-4e7b-9d09-5ac0f4696c5b","resolution":{"observed_at":"2026-08-03T17:34:38.612491Z","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":"2026-08-03T17:34:38.736184Z","title":"Bukh and T.W","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:38.736184Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:553bade810aa97ff32418d32ada3947fe5a930bd244ed73c577b942887006759","observation_id":"59a37115-f8a2-4ce5-bceb-6697985b4663","resolution":{"observed_at":"2026-08-03T17:34:38.736184Z","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":"2026-08-03T17:34:38.850362Z","title":"Carbery and S","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:38.850362Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:0e516033e6db1e2fcc9146dad91a779f0b628d7efc33e70dc0dbe9e12dccac17","observation_id":"4c848879-610f-40f6-a4f3-0a11b995b6b2","resolution":{"observed_at":"2026-08-03T17:34:38.850362Z","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":"2026-08-03T17:34:38.965901Z","title":"Christ, J","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:38.965901Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:05899c8022c28aa938f82e85572c1f2cfea973fc148ecb261679bf3639fdbe41","observation_id":"6c21da2b-2a78-4a5e-8ca7-9c18c9dc713f","resolution":{"observed_at":"2026-08-03T17:34:38.965901Z","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":"2026-08-03T17:34:39.046803Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.046803Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:22b0145fc7d94a547b4688fe4472db884432930ff5d646055fa05616c19a55eb","observation_id":"7cfc9c21-7d3d-46ed-b2e1-2b034b435314","resolution":{"observed_at":"2026-08-03T17:34:39.046803Z","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":"2026-08-03T17:34:39.112598Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.112598Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:2585f3f9cc864e6c65525740e8bb21463b15e0362e292e3fda9fa7b36470bfd1","observation_id":"f93f64ff-e4ab-4032-9ef3-7687780775b8","resolution":{"observed_at":"2026-08-03T17:34:39.112598Z","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":"2026-08-03T17:34:39.203385Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.203385Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:b52cf1f557143618f13f2041a94242a93fc9abdf74e90b04a7c6813b437c5ca5","observation_id":"621541da-9088-408f-82ee-b010a7d3e452","resolution":{"observed_at":"2026-08-03T17:34:39.203385Z","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":"2026-08-03T17:34:39.312089Z","title":"Drury.L p estimates for the x-ray transform.Ill","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.312089Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:3dceb60618daf6a15eb8f73461b2042cac9e180f91f4755a47b84da7eacf5f8f","observation_id":"90966475-ebd5-479e-91d4-e9d20fdedc9d","resolution":{"observed_at":"2026-08-03T17:34:39.312089Z","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":"2026-08-03T17:34:39.420936Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.420936Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:3b56ab9036fbf2c80deef43096ef2b5628a986858eeeb1356c876f639ef12d3a","observation_id":"6d8b4325-5328-443a-a2c8-05f9c4c73d6c","resolution":{"observed_at":"2026-08-03T17:34:39.420936Z","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":"2026-08-03T17:34:39.530675Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.530675Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:4daccf804a8be85daadc99a3fb4de22afcf7ee7313e05a22e5182eb666f55d8b","observation_id":"5984c049-0fd1-4dc5-8e77-6987a909f941","resolution":{"observed_at":"2026-08-03T17:34:39.530675Z","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":"2026-08-03T17:34:39.601822Z","title":"Erdős and E","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.601822Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:3c2e2f753defedc9c01e84b1f94eef010bbc759f159ec9003aacee0990a73c02","observation_id":"432d765f-a3ad-4e55-a8f5-071bb2543876","resolution":{"observed_at":"2026-08-03T17:34:39.601822Z","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":"2026-08-03T17:34:39.674768Z","title":"Fefferman","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.674768Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:bd0b66e81af78adc9baa46d86874390a85d944b4b77d179924262207c910c009","observation_id":"8ef56baa-1c93-4f6d-9c8c-9207e23bf82a","resolution":{"observed_at":"2026-08-03T17:34:39.674768Z","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":"2026-08-03T17:34:39.748167Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.748167Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:ed4e2bfec0d2afe9c37232c0f418bec5dd78c4ac7f4549a2afb2b455fec7507b","observation_id":"52c0add2-c4cc-41e2-9e6c-01c4fdf16a25","resolution":{"observed_at":"2026-08-03T17:34:39.748167Z","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":"2026-08-03T17:34:39.825212Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.825212Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:8e1103451ddefa95cf7d8b9e6f5811bd1de4f268eb2419848d8dfd1f6b59e85d","observation_id":"61bfafc1-3308-4a31-b2cb-436e0cbafabc","resolution":{"observed_at":"2026-08-03T17:34:39.825212Z","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":"2026-08-03T17:34:39.968888Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:39.968888Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:b74a5662bf1bdeb8d4ce6edb5e0401e38cda48296121b6b42a84351485dc319b","observation_id":"5a96b7c8-7b9b-4aef-9fe0-0c7eb64b7dac","resolution":{"observed_at":"2026-08-03T17:34:39.968888Z","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":"2026-08-03T17:34:40.094851Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.094851Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:07075712464e877e8695ac505c9ce188249bc69ad9ccbec8f7447b1692f67008","observation_id":"296daca0-ca4a-4066-a29f-4a64b13b0b67","resolution":{"observed_at":"2026-08-03T17:34:40.094851Z","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":"2026-08-03T17:34:40.213669Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.213669Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:57104f99b57cc6378161d19e9441ab5229364aa7e3d4ff09c7528f45a640f110","observation_id":"5bcacdb3-12d5-4418-866a-002c22b1c5af","resolution":{"observed_at":"2026-08-03T17:34:40.213669Z","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":"2026-08-03T17:34:40.294754Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.294754Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:b7a6994a506c50392460065253e5ed81867945724b5f8cc5a0ae6a92a9ff2f6d","observation_id":"7bf8a9fd-0f9b-4d04-907c-d701bc2a64df","resolution":{"observed_at":"2026-08-03T17:34:40.294754Z","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":"2026-08-03T17:34:40.374525Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.374525Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:36d6ce14be26fa289c6678a9d259055ed906902e6c7ea0e0561c5679e4e0c27f","observation_id":"16f8026c-5ea1-4011-8a45-4cc156f7e4ca","resolution":{"observed_at":"2026-08-03T17:34:40.374525Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.07695","last_updated":"2025-05-12T16:03:41Z","snapshot_observed_at":"2026-08-07T15:47:49.445559Z","submitted_at":"2025-05-12T16:03:41Z","title":"Introduction to the proof of the Kakeya conjecture","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.07695","snapshot_observed_at":"2026-08-03T17:34:40.476294Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.476294Z"},"links":{"cited_paper":"/paper/2505.07695","citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:80e9ac5aa8c68569a22220f7db0137e4207c9acd1ba553d8a5797c7f9c2236d3","observation_id":"4bec52ba-78c4-4f84-b7ca-e7e8cf6e9964","resolution":{"observed_at":"2026-08-03T17:34:40.476294Z","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":"2026-08-03T17:34:40.587177Z","title":"Guth and N.H","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.587177Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:09b386e48e400ce736d05c765234a5a8d9ff205140fedf024e633a8540dd3c98","observation_id":"c7263e6b-f8a5-4466-99b0-9b7758d4d3c8","resolution":{"observed_at":"2026-08-03T17:34:40.587177Z","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":"2026-08-03T17:34:40.695430Z","title":"Guth and N.H","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.695430Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:b6d72e95078dbc7c4a8a99f5261927ddf4b5bce527f10081128fb240accd83cb","observation_id":"de66dd8c-bf69-47a9-bb40-97296b642767","resolution":{"observed_at":"2026-08-03T17:34:40.695430Z","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":"2026-08-03T17:34:40.794124Z","title":"Guth and J","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.794124Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:796ec58c6c3acb2056e952e251def8ed60ee786314b5846fbca449c78503f21b","observation_id":"f5ff1bb8-ed4d-4f5a-867a-eb63a96fbcbd","resolution":{"observed_at":"2026-08-03T17:34:40.794124Z","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":"2026-08-03T17:34:40.892900Z","title":"Hickman and K.M","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.892900Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:e48945cd06470ec989da8c4593a9c52d66ad1f7e70aa90006594af4cb19112e2","observation_id":"700c266a-10b6-46dd-8941-fb0fc6411944","resolution":{"observed_at":"2026-08-03T17:34:40.892900Z","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":"2026-08-03T17:34:40.989631Z","title":"Hickman, K.M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:40.989631Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:c22b66afb919660ae2238c462ee87954651f6ec94c696c01aaacf085097526c0","observation_id":"73ca4adb-fa92-425c-9630-f2b1a6a8c4e9","resolution":{"observed_at":"2026-08-03T17:34:40.989631Z","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":"2026-08-03T17:34:41.104414Z","title":"Hickman and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:41.104414Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:3ed4f8178997213f07de4d6b2ae0c71fe77c89b8596cb3b410976c61530b17e1","observation_id":"08af8dbf-8639-4f68-9559-0074dfd1fdd9","resolution":{"observed_at":"2026-08-03T17:34:41.104414Z","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":"2026-08-03T17:34:41.197794Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:41.197794Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:008ebeff365bd97c8dd0c419a923bfbf0fa340033f602fdc2dc7269d59f2945e","observation_id":"80cfdc14-4828-4d55-9dfb-27edc657eed7","resolution":{"observed_at":"2026-08-03T17:34:41.197794Z","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":"2026-08-03T17:34:41.263079Z","title":"Katz and K","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:41.263079Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:9093448c7b3db725f10b3082a0bb6e3ed3a86a04edf307f4e422e6a789de3017","observation_id":"a1813e14-4cb6-4fa4-bde8-a41315cad91a","resolution":{"observed_at":"2026-08-03T17:34:41.263079Z","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":"2026-08-03T17:34:41.356762Z","title":"Katz and T","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:41.356762Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:76c064061d800e2bed40af4af20d71b6d36981abac1e520bc5309c35d6e12bad","observation_id":"6f995b89-d9a5-4b9d-adbe-a12dfbb07a1e","resolution":{"observed_at":"2026-08-03T17:34:41.356762Z","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":"2026-08-03T17:34:41.455352Z","title":"Katz and T","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:41.455352Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:ae10805e5f0077b93a3e7fddad576233cfc83e3c039cf7cdb250e1e557e0c799","observation_id":"9a534cf3-a6bd-46dd-a922-9c32083af1ae","resolution":{"observed_at":"2026-08-03T17:34:41.455352Z","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":"2026-08-03T17:34:41.538090Z","title":"Katz and T","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:41.538090Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:3ea8cf29de3b1dfd967626271e9b9f0364b0d0f36ea0d820017d208a1f8edbb7","observation_id":"e16fbaf9-997c-49f4-a020-29fa3b23717c","resolution":{"observed_at":"2026-08-03T17:34:41.538090Z","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":"2026-08-03T17:34:41.743571Z","title":"Katz and J","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:41.743571Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:0cf75d8dc6d3beb0d7fb604d4bf4317f23928eead6466d08234b9f4757157b7e","observation_id":"c5c86ebd-6602-461e-b621-90fba5873cdf","resolution":{"observed_at":"2026-08-03T17:34:41.743571Z","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":"2026-08-03T17:34:41.954124Z","title":"Katz and J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:41.954124Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:5acd118228dcea8886ff92451e920d911a014e0b80739eac492c92404938c93a","observation_id":"366d9d07-2ee8-436d-90b6-a43d62bdab54","resolution":{"observed_at":"2026-08-03T17:34:41.954124Z","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":"2026-08-03T17:34:42.121615Z","title":"Kulkarni.A Kakeya Estimate for Sticky Sets Using a Planebrush","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:42.121615Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:93d38985ee1130529752a97f842198957d79a43acc96fd63d10801ddfaa86a05","observation_id":"b1cc7ca7-5967-49ec-9063-b2a5ff1a8c05","resolution":{"observed_at":"2026-08-03T17:34:42.121615Z","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":"2026-08-03T17:34:42.333094Z","title":"Łaba and T","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:42.333094Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:d00576b06840e0cfdd8f5a6615f9be78680386ffcf828c2f65ac4ddeee2727a0","observation_id":"c67197b6-f4c7-4683-bed6-14fbd26722d5","resolution":{"observed_at":"2026-08-03T17:34:42.333094Z","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":"2026-08-03T17:34:42.500731Z","title":"Orponen, P","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:42.500731Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:e82880b5a211be98663c66f12e7334805f143cadc9216a5ee74a43096e1a4be6","observation_id":"a98a0716-d247-4916-91af-6d2c537151f2","resolution":{"observed_at":"2026-08-03T17:34:42.500731Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.02259","last_updated":"2024-10-25T21:25:53Z","snapshot_observed_at":"2026-07-06T13:28:10.204136Z","submitted_at":"2022-07-05T18:42:41Z","title":"A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\\mathbb{R}^3$","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.02259","snapshot_observed_at":"2026-08-03T17:34:42.671596Z","title":"Pramanik, T","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:42.671596Z"},"links":{"cited_paper":"/paper/2207.02259","citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:543b89be50e7983c424e53863d93a914dfb455cb0e3be32c9d292aa5087db0dd","observation_id":"1f78b3b3-1554-4f82-aff1-2e9b3e690cb1","resolution":{"observed_at":"2026-08-03T17:34:42.671596Z","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":"2026-08-03T17:34:42.838881Z","title":"Saraf and M","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:42.838881Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:c3e08b0bd25a97ea3148c1bb220229e3e0bd1407b886fcac2bfaec53f8ae3389","observation_id":"aa5ca872-3106-4b6d-a4e9-dda1dda537b7","resolution":{"observed_at":"2026-08-03T17:34:42.838881Z","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":"2026-08-03T17:34:42.958190Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:42.958190Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:6b9ec551bc77498d1c33952fdc61cb29ead37a968c3dcfc42d1c24588c5206a1","observation_id":"23b1345b-1106-49f3-865e-4b7dbfc3784f","resolution":{"observed_at":"2026-08-03T17:34:42.958190Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.08871","last_updated":"2024-12-19T16:38:43Z","snapshot_observed_at":"2026-08-07T19:15:32.753976Z","submitted_at":"2024-11-13T18:50:52Z","title":"Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.08871","snapshot_observed_at":"2026-08-03T17:34:43.185039Z","title":"Wang and S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:43.185039Z"},"links":{"cited_paper":"/paper/2411.08871","citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:f2e4d1a7f632600de8e8e9271b3da1583e7f8798529d73c98e63e2dba027efb7","observation_id":"2ce4a1b7-9595-403c-8561-54aa4e121626","resolution":{"observed_at":"2026-08-03T17:34:43.185039Z","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":"2026-08-03T17:34:43.337285Z","title":"Wang and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:43.337285Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:dd7cc2a3524a3cb36c176093eb8e9d2c4b6089df2d037e3ede9c85646e5800df","observation_id":"a5d4d013-39cf-4da8-a551-7f9afb084fc7","resolution":{"observed_at":"2026-08-03T17:34:43.337285Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.17655","last_updated":"2025-02-24T21:08:02Z","snapshot_observed_at":"2026-08-07T17:51:53.356178Z","submitted_at":"2025-02-24T21:08:02Z","title":"Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.17655","snapshot_observed_at":"2026-08-03T17:34:43.594830Z","title":"Wang and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:43.594830Z"},"links":{"cited_paper":"/paper/2502.17655","citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:54abc7a68faf0fd0be9a5ea66ee39fc1f685e4c897c5c2e60dbb58710a24a3db","observation_id":"be0c340d-872d-4ce4-9545-90fce7629bd7","resolution":{"observed_at":"2026-08-03T17:34:43.594830Z","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":"2026-08-03T17:34:43.809830Z","title":"Wang and J","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:43.809830Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:8f56710ebd99a3bc92aec0ab899657ec5eebc7f50a20168aa9930e07a179da5a","observation_id":"981a16f8-6f00-4aa7-b941-028deb31ffca","resolution":{"observed_at":"2026-08-03T17:34:43.809830Z","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":"2026-08-03T17:34:43.985391Z","title":"An improved bound for Kakeya type maximal functions.Rev","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:43.985391Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:efe772a8e493be365c47bc98c4a6bff21e393663fe5ba09257d7e10990120e9f","observation_id":"3d80b10d-cb02-4572-822c-dd6f13475fec","resolution":{"observed_at":"2026-08-03T17:34:43.985391Z","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":"2026-08-03T17:34:44.193516Z","title":"A Kakeya-type problem for circles.Am","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:44.193516Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:c279e939c241d7ec4292cd89f1dd6cc16b4026868cf683ec8c840334a269b432","observation_id":"77e7190a-17fa-4eeb-8ece-fbc5e9f745a0","resolution":{"observed_at":"2026-08-03T17:34:44.193516Z","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":"2026-08-03T17:34:44.365993Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:44.365993Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:2e080b10a554c240e6c55a441788bd70cfdae19b4d8208bf434e9862f14b0627","observation_id":"b1444cb6-4bd6-446b-a57b-d43ec339d51b","resolution":{"observed_at":"2026-08-03T17:34:44.365993Z","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":"2026-08-03T17:34:44.540379Z","title":"Wolff.Lectures on Harmonic Analysis","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:44.540379Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:7475fb29b8d4bab9f0db9d1e204a8ca363d3bac9f07151b35b2edce7dcd10ad5","observation_id":"47acfb1b-aa1d-49f2-91e8-ce494939eda6","resolution":{"observed_at":"2026-08-03T17:34:44.540379Z","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":"2026-08-03T17:34:44.713539Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:44.713539Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:22d1cc0b535aaed98383e70a2b1790b076c8693ea9c24281b5319b80c4f1ac83","observation_id":"496a0686-6ffb-4cfb-bfbb-814f0ad8c9e8","resolution":{"observed_at":"2026-08-03T17:34:44.713539Z","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":"2026-08-03T17:34:44.890920Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:44.890920Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:8c9a8e3bd1ec403a7164cc347e1c94f0e74cbe2f880e006ea567568c83ff7772","observation_id":"cf799138-3f56-4481-81a3-cff3ffab85f8","resolution":{"observed_at":"2026-08-03T17:34:44.890920Z","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":"2026-08-03T17:34:45.066591Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-03T17:34:45.066591Z"},"links":{"citing_paper":"/paper/2512.09397"},"observation_digest":"sha256:11567311292bcc9da6f3d34afd668bffa1ca2c38bc6ce8c2af36fc88a8862d67","observation_id":"49f2562b-03d3-4dff-a015-0d028a79081d","resolution":{"observed_at":"2026-08-03T17:34:45.066591Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.09397","last_updated":"2025-12-10T07:47:30Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-07T19:17:19.879696Z","submitted_at":"2025-12-10T07:47:30Z","title":"A Survey of the Kakeya conjecture, 2000-2025"},"reference_resolution":{"displayed":59,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":59,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":59},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 0 inbound Pith citation observations for arXiv:2512.09397."}