{"as_of":"2026-08-20T11:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fa9558a1e3835fe0c603fb42f1b1d447f8c9d1304625300b0cdad347bd269c8d","coverage":[{"denominator":48,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":48,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T12:08:34.811086Z","state":"measured"},{"denominator":49,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":49,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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":"2026-05-10T16:34:45.852421Z","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":"2026-05-11T08:40:58.087141Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"cited_work":{"arxiv_id":"2504.13833","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.13833","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"a1b18939-75eb-4baf-90cc-9c47bcf9d963","year":2025},"citing_paper":{"arxiv_id":"2604.10446","last_updated":"2026-08-11T01:45:43Z","snapshot_observed_at":"2026-08-15T01:47:06.510472Z","submitted_at":"2026-04-12T03:59:07Z","title":"Least singular values of shifted sparse random combinatorial matrices","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-10T16:34:45.852421Z"},"links":{"cited_paper":"/paper/2504.13833","citing_paper":"/paper/2604.10446"},"observation_digest":"sha256:8d736dfc357e08d3375a0af597d5332b27c9ef168c50310091a0918047cd8f76","observation_id":"219b89a2-5c4a-4c6f-a056-9c33df4d4947","resolution":{"observed_at":"2026-05-11T08:40:58.091800Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.13833/citation-record","integrity":"/paper/2504.13833/integrity","json":"/paper/2504.13833/citation-record.json","paper":"/paper/2504.13833"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T12:08:38.062699Z","title":"Random non-Abelian G-circulant matrices","venue":null,"work_id":"ac930fcd-be77-4628-8099-6948231e2ceb","year":2021},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:33.993201Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:a5fecd3fd3b0635eb2de82b57cb7d6d5556cb0f46cbb89089c56dee69644f795","observation_id":"8c0bfe59-0bdc-494e-a62a-7868c80522ee","resolution":{"observed_at":"2026-08-16T12:08:38.145638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:38.049515Z","title":"Random Cayley graphs and ex panders","venue":null,"work_id":"ef748d90-112f-402c-8507-a233ff90a5f3","year":1994},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.007611Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:6554045ed9b37e2bc1cfe4acd09b23e3d2d4359cc449a8b8d97d4722fee29a37","observation_id":"5b83b3fc-3d9e-491c-9c8b-a8f564392688","resolution":{"observed_at":"2026-08-16T12:08:38.054134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.947734Z","title":"The diameter of a ran dom Cayley graph of Zq","venue":null,"work_id":"91e31ffa-b93e-4bdb-84a8-b015a985dc18","year":2010},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.012376Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:d1122bc763c00055719a010829969c2e732c04a787eb69159a3fa5f89ef6937c","observation_id":"c2bafa48-7d07-4db8-b9ba-96a3c458b5cc","resolution":{"observed_at":"2026-08-16T12:08:37.951909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.840967Z","title":"Patterned sparse ran dom matrices: a moment approach","venue":null,"work_id":"75eef1e0-d42e-419b-84d8-554f04ddde7b","year":2017},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.018023Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:02ab328f317fd3861ac5ecbae664cc7014fb11622338321c410c93a9c3ea4be7","observation_id":"7be9d2a6-b6ac-4bc9-8a3f-28a5f8b2160b","resolution":{"observed_at":"2026-08-16T12:08:37.938528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.827010Z","title":"Small sums of ﬁve roots of unity","venue":null,"work_id":"a7d303cf-980e-4256-ba95-68ff59f8d897","year":1906},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.023673Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:f1a9e287f2460de58d7fb7d2e4a28d126653e4c8431279e511f39cd26cf52e43","observation_id":"95027e76-66ea-4af9-90e2-ec510d30075a","resolution":{"observed_at":"2026-08-16T12:08:37.831905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.619876Z","title":"Salem-Zygmund ineq uality for locally sub-Gaussian random variables, random trigonometric polynomials, and r andom circulant matrices","venue":null,"work_id":"8f732064-cc80-47e9-9ea7-7857950537f0","year":2022},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.029748Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:5f2dc812f36f37a38bcea7f2b5c158e5ba87ff236de093b19e90700e2eb140dd","observation_id":"5131b48c-21e0-4824-bc44-45cd2f66a359","resolution":{"observed_at":"2026-08-16T12:08:37.746783Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.566246Z","title":"Around the circula r law","venue":null,"work_id":"9b74d197-9661-4f22-ac51-13d2c5592eeb","year":2012},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.033941Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:69cc9c861e95f2e34a49fcf77e73a0f6368406537ea2f28c987dd1d01e0367ce","observation_id":"16ae7f51-c021-4096-bed0-df63606f56bf","resolution":{"observed_at":"2026-08-16T12:08:37.571619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.451231Z","title":"Limiting spectral distribution of XX 1 ma- trices","venue":null,"work_id":"56b7ad93-5382-48be-87a1-a803eb8c9765","year":2010},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.037660Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:37a80874dee26a0e668272d5c7557888953210cc256fdb28b046609dab3ef89e","observation_id":"cefe75f7-01dc-4a2d-bf7b-c946c91b08f6","resolution":{"observed_at":"2026-08-16T12:08:37.503564Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.435940Z","title":"Spectra l norm of circulant-type matrices","venue":null,"work_id":"5ac51d54-2a57-4b2d-8e1d-2483b52c1ca7","year":2011},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.151826Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:d8de4d96ced9f7cec7aff60619d0746286971d2903531771545620d6f224d58b","observation_id":"1f47e0fb-f66d-4558-82da-cd6be12b63cd","resolution":{"observed_at":"2026-08-16T12:08:37.442908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.399848Z","title":"Limiting spectral distribu tion of a special circulant","venue":null,"work_id":"2a5010da-549b-42a8-bdf0-1bc33e7036e4","year":2002},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.204148Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:5988b28a88ea2df8b86aaddc87ecff790008dd2613ebaee4b5abcf9ccf17bd8a","observation_id":"6ba3facc-9444-4766-8202-1bd9710aff6e","resolution":{"observed_at":"2026-08-16T12:08:37.424409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.349774Z","title":"Random circulant matrices","venue":null,"work_id":"79784c4c-8726-48ca-9c78-c292d39001e9","year":2019},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.208397Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:b87f4967decf6cd78b049c9f8077fd46cc0927ffcced3fcfa0a02afe4d888f0f","observation_id":"0829f18f-3e50-40db-8e54-14afcb31bedc","resolution":{"observed_at":"2026-08-16T12:08:37.354442Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.296849Z","title":"Another look at the moment metho d for large dimensional random matrices","venue":null,"work_id":"21ac5c8d-ad7e-40ab-8da6-121fd1f01749","year":2008},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.212541Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:1c47247a2ccb707e45ae0e9b56905ce40a853bfbc9ff71549407eb58ecbc2a99","observation_id":"decd1502-43e9-4139-ad31-f28d698c196a","resolution":{"observed_at":"2026-08-16T12:08:37.340374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.280929Z","title":"Patter ned random matrices and method of moments","venue":null,"work_id":"bc0da9fd-f4c2-428a-9779-a50588767e98","year":2010},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.216898Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:388dd24c5cedf7b10abf652503407db158e2c3c9ee850a607b0c3263eb879d67","observation_id":"2bc9d725-027c-4a9d-9638-fd12f81e8b4c","resolution":{"observed_at":"2026-08-16T12:08:37.286535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.181432Z","title":"Uniform expansion boun ds for Cayley graphs of SL2pFpq","venue":null,"work_id":"f136e771-2bd1-4d40-84c1-70270ed8729b","year":2008},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.220422Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:32dc10ec4eaa0a2986dd3a3031460e30f0d5501316feb18cf0fc347f0ae63e17","observation_id":"8cc91232-86b7-4372-8ffe-db85a0e730bf","resolution":{"observed_at":"2026-08-16T12:08:37.242284Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.166657Z","title":"Spect ral measure of large random Hankel, Markov and Toeplitz matrices","venue":null,"work_id":"e217138a-efab-4f46-b222-f50bacc55eb7","year":2006},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.224042Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:9da08412d4fe5cb42796967147cfacd202136e2c58908371572fb45b63c6dce3","observation_id":"9f40c011-6592-4ebb-8dc5-982de0551d67","resolution":{"observed_at":"2026-08-16T12:08:37.171631Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.076033Z","title":"On the independence number of sparser random Cayley graphs","venue":null,"work_id":"d5ee0d71-497b-45ec-a696-27155069b2d4","year":2024},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.272557Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:2cb04dee2076597fb79b170677165d6f01fd65b630e4e85ac18e457aa4d92b9d","observation_id":"f8d0beb0-de07-4f5f-92f7-8e5abe0b57f6","resolution":{"observed_at":"2026-08-16T12:08:37.127405Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:37.061457Z","title":"Around the circular law: an update","venue":null,"work_id":"82964b52-eeac-49ce-abae-480cd5f3fc3b","year":2018},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.277280Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:a4f8a70161c3bafaf90e98995faf9fbb62cf528f2846456a5ae5226ad4649c6b","observation_id":"178256b4-b282-4489-a365-ce43936c0d72","resolution":{"observed_at":"2026-08-16T12:08:37.067240Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.962843Z","title":"The threshol ds for diameter 2 in random Cayley graphs","venue":null,"work_id":"318810b1-77cf-4da6-9510-550696dab0b0","year":2014},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.281731Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:fda7e40e93274a9e38e39d3d3e49aab8ac837076963ec1ab8a0dc8f658ad143e","observation_id":"df0b2876-d956-4e72-8abe-b802c41027d0","resolution":{"observed_at":"2026-08-16T12:08:36.979355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.21194","last_updated":"2024-12-30T18:57:48Z","snapshot_observed_at":"2026-08-19T20:06:13.636338Z","submitted_at":"2024-12-30T18:57:48Z","title":"On the clique number of random Cayley graphs and related topics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.21194","snapshot_observed_at":"2026-08-16T12:08:34.287433Z","title":"On the clique number of random Cayley graphs and related topics","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.287433Z"},"links":{"cited_paper":"/paper/2412.21194","citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:f366c6265f870aec6d187939de3a87f830239011108f0ebb751ddbf753edd010","observation_id":"631d5750-279e-4825-90ef-eae64e4ca250","resolution":{"observed_at":"2026-08-16T12:08:34.287433Z","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":"2026-08-16T12:08:36.855389Z","title":"Group representations in probability and statistics , volume 11 of Institute of Mathematical Statistics Lecture Notes—Monograph Series","venue":null,"work_id":"47ebf88b-4fe7-4b48-8e73-6b69ead1fc84","year":1988},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.292821Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:82d83f272f69ef5788e383d6eb89ead513fcb25c1cac076102da974978e322ef","observation_id":"d0bb084f-ac53-4e73-bbd8-b5f91821ba52","resolution":{"observed_at":"2026-08-16T12:08:36.909109Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.842516Z","title":"Babai’s conjecture f or high-rank classical groups with random generators","venue":null,"work_id":"f5accc4f-3339-42f1-8a30-c651a1ac4717","year":2022},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.298809Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:3caf4e3deefbb313f08495d569b1b2bd6c6ee1137593518a735a56442b1d1ecd","observation_id":"fe50ed8e-49bd-4951-9ca6-d4154c4a1d5c","resolution":{"observed_at":"2026-08-16T12:08:36.847183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.730920Z","title":"Random circulant d eterminants","venue":null,"work_id":"4b69516b-1ef8-4b2b-93fe-0fded28414c8","year":null},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.381880Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:5bee539b8c72bfd3fd4d376d835f67aebdab76e9cbf73c039ff601af70083464","observation_id":"9788b94a-0de3-4f8e-af36-b4b3bb7d813a","resolution":{"observed_at":"2026-08-16T12:08:36.784390Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.718370Z","title":"Proof methods in r andom matrix theory","venue":null,"work_id":"ffd46c73-f1b7-42ec-8220-355beb39d5f8","year":2023},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.411843Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:4e40ba12d8f4bb844ee3708f4a7991173c63c40deaf42f27167d4726dc5c5072","observation_id":"b4bc68f0-6ea8-49ee-b3b4-0895038c4d9e","resolution":{"observed_at":"2026-08-16T12:08:36.722495Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.619647Z","title":null,"venue":null,"work_id":"d30892ff-a887-439a-8374-9d40d3a000ea","year":1984},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.416680Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:0166fe2c71d7aca49c7e25661c1de723ea657bfd8389fc1efd97e287d0b980e5","observation_id":"7b669018-3afa-41d9-ba87-571c4df1e279","resolution":{"observed_at":"2026-08-16T12:08:36.680969Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:34.421544Z","title":"Classical Fourier analysis , volume 249 of Graduate Texts in Mathematics","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.421544Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:129ce07be63586968e9b0d26a4acf83815107ceab0c9dc9c4e97642b642207c1","observation_id":"7b9885fc-4bcd-440f-a85d-e449b8290e1e","resolution":{"observed_at":"2026-08-16T12:08:34.421544Z","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":"2026-08-16T12:08:36.598636Z","title":"Some applications of harmonic analysis to ar ithmetic combinatorics","venue":null,"work_id":"a9f5235e-5ccb-4865-89a8-075c2d0af967","year":2001},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.425681Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:12828d09e328232582019fa3389b7023c7119e5c376f51274302572ee51ad432","observation_id":"9e6f132a-0a1b-4494-b9d2-41fec427c94b","resolution":{"observed_at":"2026-08-16T12:08:36.602957Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.505379Z","title":"Counting sets with small sumset, and the cliq ue number of random Cayley graphs","venue":null,"work_id":"8a672858-80e5-45e8-8802-addfb7d81255","year":2005},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.429811Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:3633ebb7c9d95f21c58a7f7ac02566ca1bd68f96702889ef36fc2ead9879b3d8","observation_id":"6a00ff25-bc36-45b3-9448-5ebaf177e057","resolution":{"observed_at":"2026-08-16T12:08:36.589587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.493739Z","title":"On the chromatic number of random Cayley grap hs","venue":null,"work_id":"801254f8-0f49-4376-81aa-5b9370cc0b8f","year":2017},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.435835Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:e71a30839d6b64da1148378196d4d68f66eaab8cc02e3e4e3aeb0976c66122f7","observation_id":"b808c3d6-8aaa-4fbc-9f33-f134368fd505","resolution":{"observed_at":"2026-08-16T12:08:36.498069Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.283696Z","title":"100 open problems","venue":null,"work_id":"7f794f3b-de87-49e7-b5ce-65a3dfc5f45b","year":2024},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.440510Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:81e7ea6889f90e6308cb1ee538e54ae935e7bfd01200f4602029c33634b1fe02","observation_id":"d8e4407b-0b04-4bbe-80c8-2f428f019346","resolution":{"observed_at":"2026-08-16T12:08:36.418138Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.271365Z","title":"Helfgott, Ákos Seress, and Andrzej Zuk","venue":null,"work_id":"07787b58-bdcb-416c-a977-31f482e34596","year":2015},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.444040Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:ba1dd68482f154676d890d002805fe6ae22225faeec6252f20d4345162c31495","observation_id":"f13c74a9-6b84-4f40-b284-d5a998240488","resolution":{"observed_at":"2026-08-16T12:08:36.276224Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.160464Z","title":"Basic algebra","venue":null,"work_id":"33d5147b-f66b-403b-a80c-b024845a686a","year":1985},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.447993Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:83cbec696e41a2e27b76e733ee08b9d30c4ebbc98c42571c0e4eea5795b93875","observation_id":"33f7ad30-bd50-4d3b-be8e-00d7b1770b90","resolution":{"observed_at":"2026-08-16T12:08:36.211478Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.147186Z","title":null,"venue":null,"work_id":"b2582716-b769-49c2-867a-f61b65ead534","year":2000},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.489278Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:7c4aecf930030b703cc70e6e6784cde5b7ea1a4b82c2e883995e95ff8d917fe4","observation_id":"cd4808af-6138-45f8-ba8b-d3f50234da8d","resolution":{"observed_at":"2026-08-16T12:08:36.152217Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:36.134940Z","title":"Norms of randomiz ed circulant matrices","venue":null,"work_id":"643556f8-0b89-4eb6-8e2c-49d7daecc596","year":2022},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.572014Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:5669d8f7ecb8940d8c816ad950b050fefd314a52b9f939a3d38604b92c2dbf1e","observation_id":"ff28ca4f-65b7-4943-ace7-31ea6cf70a05","resolution":{"observed_at":"2026-08-16T12:08:36.138575Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.988858Z","title":"Diameters of r andom circulant graphs","venue":null,"work_id":"aac23050-1ec0-44e7-ad53-89a068ae69a0","year":2013},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.576163Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:25cefd7a5613e154022b6ff171cdddc4a4c155a4fad8545470d4b96c3f72de0e","observation_id":"dfc8e576-8338-41e2-9cab-26ea2a51608e","resolution":{"observed_at":"2026-08-16T12:08:36.083335Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.976321Z","title":null,"venue":null,"work_id":"378ee4d9-e8bf-4f53-8ed9-60ff6183d24e","year":1967},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.580250Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:97ff96f57777dfb1eaf2da9ad0e9f2c7104f0558b510b83b6addb900ed244b12","observation_id":"eb06bc67-9377-4c17-ba17-2b859e4358d2","resolution":{"observed_at":"2026-08-16T12:08:35.980575Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.962952Z","title":null,"venue":null,"work_id":"a0d0cedd-6661-465b-92cb-3d1d8589323d","year":2009},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.585099Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:904f58de1f4e321c5baff0afb9674af2fe742b8ff06a1bbcdc389c6b6c2f686e","observation_id":"916a3f22-a30c-431d-8f30-b0f262ffc669","resolution":{"observed_at":"2026-08-16T12:08:35.967135Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.821223Z","title":null,"venue":null,"work_id":"35dd1f49-6bc4-4ca3-81fd-ec26a294446b","year":2012},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.590137Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:22346c29eb0d00144ad002effbf0221911be04c07b490cac5943a381774ce226","observation_id":"9a1c5728-33a1-4bbd-80dc-c3311e377576","resolution":{"observed_at":"2026-08-16T12:08:35.896121Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.764604Z","title":"Ein Beitrag zur analytischen Zahlenthe orie","venue":null,"work_id":"b76c8818-e3ed-47ad-bea1-0cb90dc77b84","year":null},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.594156Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:26affe1f50a57d8637cda28e3708e1b620f1b3ada02e9704ab40a72b3ac2ba66","observation_id":"ca463979-9460-45b8-a281-70cf137a5c1b","resolution":{"observed_at":"2026-08-16T12:08:35.796201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.690380Z","title":"One-point concentration of the clique a nd chromatic numbers of the random Cayley graph on Fn 2","venue":null,"work_id":"63848c60-29ad-4322-9585-8b8ebe82945d","year":2017},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.598617Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:ff0878b8f869177a2b28cbfb18fd0bba3cba0979f37d98082f45bb53c151214d","observation_id":"b0a3ee93-8068-47f7-9540-c46dd222eaf8","resolution":{"observed_at":"2026-08-16T12:08:35.721739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.615654Z","title":"Unsolved Problems: How Small Can a Sum o f Roots of Unity Be? Amer","venue":null,"work_id":"dbde045c-34ce-49dc-b95b-a907697d925e","year":1986},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.602963Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:23279015294b18e75495caba2aa6d1dca413bd05d388ff168ef8e491764aae07","observation_id":"992cf0eb-a93f-46e4-9bb8-d42965bf3604","resolution":{"observed_at":"2026-08-16T12:08:35.679582Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.17635","last_updated":"2025-06-30T18:32:48Z","snapshot_observed_at":"2026-08-20T05:37:17.206297Z","submitted_at":"2023-10-26T17:51:53Z","title":"The limiting spectral law for sparse iid matrices","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.17635","snapshot_observed_at":"2026-08-16T12:08:34.606934Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.606934Z"},"links":{"cited_paper":"/paper/2310.17635","citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:3afd71cb5873666e4b8d2686f9dd2ab6ea2fc5bc074aa0edd3de60ff615419f0","observation_id":"f9c0e9b6-b0a9-4554-a0e8-2061493839d2","resolution":{"observed_at":"2026-08-16T12:08:34.606934Z","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":"2026-08-16T12:08:35.472489Z","title":"How small can a sum of a few roots of unity be? https://mathoverflow.net/questions/46068/how-small- can-a-sum-of-a-few-roots-of-unity-be","venue":null,"work_id":"6eb28123-8874-406a-94ac-ff3e7cb47f5b","year":null},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.667256Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:925a4e3db4048d1310eb34f82282c2ea8716a89b6a69160e52dba616945d9d0b","observation_id":"697b354c-fb7f-45dd-a332-aeec5c158d48","resolution":{"observed_at":"2026-08-16T12:08:35.476682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.317832Z","title":"Topics in random matrix theory , volume 132 of Graduate Studies in Mathematics","venue":null,"work_id":"9b25942d-1eba-4a40-aa6e-b01b77c9508b","year":2012},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.755167Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:524a5fe3c28582e3580141795698b64e9f502297058b399774005c9432bcff40","observation_id":"1b26ab63-7383-4e5c-a2ae-26a0081202c8","resolution":{"observed_at":"2026-08-16T12:08:35.463655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.303175Z","title":"Additive combinatorics, volume 105 of Cambridge Studies in Advanced Mathematics","venue":null,"work_id":"964f2fd4-0ef7-44f3-9158-aa6970b4fc23","year":2006},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.790844Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:e67bc8aa57a2404534820e9ea53d6aaee05e9ae5b34a3b695a1091fd2fca2f7a","observation_id":"f6e92ea0-0a4e-4616-ae60-6958eb22b832","resolution":{"observed_at":"2026-08-16T12:08:35.307832Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.036918Z","title":"Random matrices: the circular la w","venue":null,"work_id":"912e8810-fbaf-4a78-ad33-537563a169b1","year":2008},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.796914Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:b7bdc84d113719d94f24402d6c999f2d005eb60af61d661a3f53e2d8f9bdaaf6","observation_id":"55063c74-78f8-415e-ac29-5a7df96cd878","resolution":{"observed_at":"2026-08-16T12:08:35.145647Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-16T12:08:35.018958Z","title":"Random matrices: universality o f ESDs and the circular law","venue":null,"work_id":"b60501c6-b530-4c2b-96d3-99aeb6e7627a","year":2023},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.801390Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:d49fcf8fe9d56afc423cfd76562adc2e28a508124e000ef270f93a72f58d8236","observation_id":"c1312046-f151-4702-98f0-bc7d8a397b03","resolution":{"observed_at":"2026-08-16T12:08:35.024632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2206.00601","last_updated":"2022-06-01T16:15:08Z","snapshot_observed_at":"2026-08-20T04:53:00.595680Z","submitted_at":"2022-06-01T16:15:08Z","title":"Quantitative invertibility of non-Hermitian random matrices","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.00601","snapshot_observed_at":"2026-08-16T12:08:34.805664Z","title":"Tikhomirov","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.805664Z"},"links":{"cited_paper":"/paper/2206.00601","citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:cee081cea24945d16e6b536055703a99fdea8bd246a2bcb3048e0fa29a7958d7","observation_id":"da9e4a55-cb59-4ccd-a352-e727b68e08aa","resolution":{"observed_at":"2026-08-16T12:08:34.805664Z","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":"2026-08-16T12:08:34.882026Z","title":null,"venue":null,"work_id":"ab8ecde3-21c5-4c40-a6cd-efe57a17c512","year":1958},"citing_paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-16T12:08:34.811086Z"},"links":{"citing_paper":"/paper/2504.13833"},"observation_digest":"sha256:b0abb3b9ae4f992700e8b6e74d529feac6829c9b3d98b933b8350d26999e0c89","observation_id":"57655a9e-7fd9-44ca-86fa-f974a3b5541a","resolution":{"observed_at":"2026-08-16T12:08:34.964830Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.13833","last_updated":"2025-04-18T17:58:42Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-19T20:06:27.202367Z","submitted_at":"2025-04-18T17:58:42Z","title":"Limiting spectral laws for sparse random circulant matrices"},"reference_resolution":{"displayed":48,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":0,"verified_fuzzy":38},"total_outbound_references":48},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 1 inbound Pith citation observation for arXiv:2504.13833."}