{"as_of":"2026-08-13T22:45:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7257168f46400c07fbac7a437b076086fc7db3a309943ec55e28708953d643f2","coverage":[{"denominator":14,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T20:30:38.021504Z","state":"measured"},{"denominator":15,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":15,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T17:38:49.983205Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-02T23:57:28.786625Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"cited_work":{"arxiv_id":"2412.05858","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.05858","snapshot_observed_at":"2026-07-02T23:57:28.786625Z","title":"Agin and B","venue":null,"work_id":"ce203bc8-130d-45ed-850e-49da2795a5b1","year":2024},"citing_paper":{"arxiv_id":"2606.08865","last_updated":"2026-06-07T22:33:28Z","snapshot_observed_at":"2026-08-02T09:43:00.736670Z","submitted_at":"2026-06-07T22:33:28Z","title":"The Dirichlet spectrum with respect to $L_1$ norm is $\\left[\\frac12,1\\right]$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-27T17:38:49.983205Z"},"links":{"cited_paper":"/paper/2412.05858","citing_paper":"/paper/2606.08865"},"observation_digest":"sha256:c61e83a627b631983f2b9bba14f73a78c166df1e6b4f9aacf13b24639ced85a8","observation_id":"3b37a4d5-9d65-4b03-87bc-5c8a038f1969","resolution":{"observed_at":"2026-07-02T23:57:28.787907Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.05858/citation-record","integrity":"/paper/2412.05858/integrity","json":"/paper/2412.05858/citation-record.json","paper":"/paper/2412.05858"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T20:30:38.288506Z","title":null,"venue":null,"work_id":"2ccf71e6-4107-490c-ba57-601b3e255649","year":2024},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.954308Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:60b93d4511c8aec58c86be3e5b37c5837655ebfc6601f2f72c008a7fd1c59acf","observation_id":"00587274-c188-4aeb-a9b4-31d73359801a","resolution":{"observed_at":"2026-08-11T20:30:38.293980Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.273630Z","title":"Akhunzhanov and D.O","venue":null,"work_id":"3703fe35-f124-454a-84cd-3ac456b791f0","year":2013},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.960252Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:6a5ecf942c3927e36f0273b5eadfa46fdfee4509f80a833d8c10a4dd11d57785","observation_id":"2aecd60a-ed36-4726-8083-5a90e204317c","resolution":{"observed_at":"2026-08-11T20:30:38.278702Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.257646Z","title":"An introduction to diophantine approximation","venue":null,"work_id":"68874faf-9def-45de-8229-6d04a6c866bf","year":1957},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.965388Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:a7e979b931d28aa2ecf026ec2b72c736032dd7dbd0fce67f1e6746117ad1e2f9","observation_id":"70522062-a2cb-4d18-b41d-d1ff13123d91","resolution":{"observed_at":"2026-08-11T20:30:38.262768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.239506Z","title":null,"venue":null,"work_id":"9bfb7e24-02fd-46f4-96a0-66eb9117fe5b","year":1985},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.970593Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:d73cf24de283931b6a349c188e728a34b6544203eb84bcdb9fdee7cc1468457d","observation_id":"4dc74758-5fb8-4cd1-b529-c4496d413cfd","resolution":{"observed_at":"2026-08-11T20:30:38.245574Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.220956Z","title":"Davenport and W.M","venue":null,"work_id":"611e6bde-3114-4d9b-a4ff-fb91a8a91a26","year":1969},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.976179Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:07d8db8a0a3509c121f10204528c33cb33e8542ec0fb72456328379a52c5178c","observation_id":"37a216df-5c27-4d9f-a135-b4c23da7c4ce","resolution":{"observed_at":"2026-08-11T20:30:38.225927Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.13451","last_updated":"2025-02-13T22:30:24Z","snapshot_observed_at":"2026-08-13T04:14:06.891702Z","submitted_at":"2024-02-21T01:11:05Z","title":"On the Folklore set and Dirichlet spectrum for matrices","version":3},"cited_work":{"arxiv_id":"2402.13451","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.13451","snapshot_observed_at":"2026-08-11T20:30:38.062301Z","title":"On the Folklore set and Dirichlet spectrum for matrices","venue":"math.NT","work_id":"8cfb9e9c-4bb4-4edb-9f84-4989afe59260","year":2024},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.981937Z"},"links":{"cited_paper":"/paper/2402.13451","citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:1f32a837a06f180e11e0961f7f5b319a4484dd73f302a915a698ceb240edb17a","observation_id":"87fa34c6-ccc4-4715-b2ea-5fe85056ae8a","resolution":{"observed_at":"2026-08-11T20:30:38.070065Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.203672Z","title":"Khintchine","venue":null,"work_id":"8c34c599-c3d4-4a35-bbba-72a35cafc829","year":1926},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.987114Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:901fb09245d26237d1a0dcfffbd21404dabbf696acda581446a963d86883b2a7","observation_id":"02aebdd9-5ab9-4400-b60b-cc7e3bcd76a6","resolution":{"observed_at":"2026-08-11T20:30:38.208876Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.187721Z","title":"Kleinbock, N","venue":null,"work_id":"f7337c37-4160-4c61-86cf-bbb9b783afc7","year":2021},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.991615Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:f693ed6d4dae39823a5d1f83b61d7dc7ee57a0168b7a981ea3497cc2b30a0fab","observation_id":"fed2b333-4002-4a9a-bc55-9296b0d085a5","resolution":{"observed_at":"2026-08-11T20:30:38.192943Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.172285Z","title":"Kleinbock and A","venue":null,"work_id":"cb1b5f01-42ad-4803-a509-099c2030b656","year":2021},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:37.996089Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:e6ce9fc7357ec23872c3ae79c8ae8773a5e573183ac5b93b43fd6acc32b5ab0b","observation_id":"aa3fcef8-5718-453e-992f-189210c70d71","resolution":{"observed_at":"2026-08-11T20:30:38.177371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.152693Z","title":"Kleinbock and A","venue":null,"work_id":"e124741b-c051-4830-8c62-b920d3cbf0c8","year":2022},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:38.000925Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:bb4f47dcd00fca27987171e55d2cd91b0205f92b054d19f36f0662dffdf75a50","observation_id":"af1c5675-ae0a-4c8e-a7dd-0ef13099911f","resolution":{"observed_at":"2026-08-11T20:30:38.160169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.132513Z","title":"Kleinbock and B","venue":null,"work_id":"14964c55-48a1-4bad-b2c7-b529db1646ec","year":2008},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:38.005814Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:7c9e36e08d87bde5b6af59e2fe1e37d24bf02d05d9a9bb28e536b208bd1e8dde","observation_id":"823dbe9b-93fa-4696-9358-d1d1822805df","resolution":{"observed_at":"2026-08-11T20:30:38.139310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.114701Z","title":"Schleischitz","venue":null,"work_id":"cd3ebfba-b918-410e-864c-de1654d6582c","year":2023},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:38.010524Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:2d418c90ff843b5d4a8ebbba4a162001fa1b338580765ef85848e18a7550bfc0","observation_id":"ca7ed664-47a7-41c9-81ff-250be6b36999","resolution":{"observed_at":"2026-08-11T20:30:38.120088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.096861Z","title":"Schleischitz","venue":null,"work_id":"765647e3-b6c6-4395-a2ba-7f96ac90fa41","year":2023},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:38.015576Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:4c4191a1864951b526434cc92f107603df9c5c8e232e7c5306f96d1555f33588","observation_id":"9197a392-5c15-45d6-aea0-d2a60cfe7b39","resolution":{"observed_at":"2026-08-11T20:30:38.101343Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-11T20:30:38.082200Z","title":null,"venue":null,"work_id":"61958afe-9857-4e70-8596-1ccb6f6a74bb","year":2004},"citing_paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-11T20:30:38.021504Z"},"links":{"citing_paper":"/paper/2412.05858"},"observation_digest":"sha256:7c5508a742aec4ff3c1c8c83357a56a610ff2751642e1ea4a5824a29074be2e8","observation_id":"ebdd24de-0d87-441d-a813-06c89f86597b","resolution":{"observed_at":"2026-08-11T20:30:38.086722Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.05858","last_updated":"2024-12-08T08:44:22Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-11T20:14:09.393266Z","submitted_at":"2024-12-08T08:44:22Z","title":"The Dirichlet spectrum"},"reference_resolution":{"displayed":14,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":1,"verified_fuzzy":10},"total_outbound_references":14},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2412.05858."}