{"as_of":"2026-08-13T07:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0c4f61fb65f8d00b81ff7217cd2fa903a01a94aa951ece31cff9578936c4606a","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T10:13:04.405320Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2411.19562/citation-record","integrity":"/paper/2411.19562/integrity","json":"/paper/2411.19562/citation-record.json","paper":"/paper/2411.19562"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:13:05.317977Z","title":"Agora, J","venue":null,"work_id":"238323b0-caee-48f9-bb03-a3692ed205a4","year":2015},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.148959Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:f26751464168fde85a01ed03e11d9db4a8dbeef9b1bc8aeb596f192ff207c5c4","observation_id":"84ae6f69-e9dd-4575-9f0d-3fe9b5e2c036","resolution":{"observed_at":"2026-08-12T10:13:05.329872Z","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":"2026-08-12T10:13:05.283725Z","title":"Agora, J","venue":null,"work_id":"6d9757ff-e216-4162-b741-d6439be3cf3c","year":2019},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.162498Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:24c383ab2a3a35f7498a5b25798487b6a35a4f006becfe58a631c5cd6a9dc605","observation_id":"dad1feca-15eb-4017-b0a0-8dc3165bf664","resolution":{"observed_at":"2026-08-12T10:13:05.297065Z","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":"2026-08-12T10:13:05.239704Z","title":"Antezana and M","venue":null,"work_id":"fd54535f-e219-411d-9457-d6b0897ff8b3","year":2022},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.171311Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:79255d198f9e5490fcf58ec02d2c2912a5585bc21a45be7fa2e8cafc47044e80","observation_id":"6bfb5f6e-6c54-46f0-9181-483a3817ac9a","resolution":{"observed_at":"2026-08-12T10:13:05.254128Z","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":"2026-08-12T10:13:05.207403Z","title":"Balan, P","venue":null,"work_id":"7d0665af-74cb-4a2c-8d06-035266111b10","year":2011},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.182263Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:54ba598f53091927c79984eac13616dd7a2391fb6754f7bf6598f851a3bea50e","observation_id":"9e99ce05-2497-4df7-ac08-9f4fb882dde1","resolution":{"observed_at":"2026-08-12T10:13:05.215515Z","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":"2026-08-12T10:13:05.179889Z","title":"Batson, D","venue":null,"work_id":"82b14880-9bef-47d5-850f-c06f2abae2c9","year":2014},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.204173Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:5c5ca727f2ccfcbd2d31501d9c9e4cb88c26cd82fd5009d691f8ed71b9cbfee6","observation_id":"b736c171-c65e-4ef6-8f18-f4adf6effd22","resolution":{"observed_at":"2026-08-12T10:13:05.186276Z","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":"2405.18235","last_updated":"2024-05-28T14:45:54Z","snapshot_observed_at":"2026-08-12T23:56:05.838378Z","submitted_at":"2024-05-28T14:45:54Z","title":"Selector form of Weaver's conjecture, Feichtinger's conjecture, and frame sparsification","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.18235","snapshot_observed_at":"2026-08-12T10:13:04.215652Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.215652Z"},"links":{"cited_paper":"/paper/2405.18235","citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:8284bd53a694f3e2e8915c0e84166ca59b3854f7e4bd83c879bc0fdbff7af479","observation_id":"3696687a-19e9-4f1d-87f4-df5e47e73a06","resolution":{"observed_at":"2026-08-12T10:13:04.215652Z","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":"2026-08-12T10:13:05.156767Z","title":"Bownik and J","venue":null,"work_id":"a767caff-c21f-4594-b86e-eee88980a5ca","year":2021},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.233535Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:d0816ac90914db100b263cca20e5b11092ba3b474e7147e675e9d8d8405607c3","observation_id":"483dfdf3-61d2-4f10-8955-1f2cc3bdae97","resolution":{"observed_at":"2026-08-12T10:13:05.163978Z","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":"2026-08-12T10:13:05.115390Z","title":null,"venue":null,"work_id":"7632a1aa-acb5-41f7-96f4-a8b9cedd7f76","year":1968},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.242240Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:5e3e056b1f7354ed63e4378cb347d2816e87009ea4eea4edd2929c28cb6cf1f8","observation_id":"ecf33288-2b4e-4ae0-a216-df1398a3004e","resolution":{"observed_at":"2026-08-12T10:13:05.126115Z","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":"2026-08-12T10:13:05.071696Z","title":"Enstad and S","venue":null,"work_id":"f11392d9-1d03-42d8-8942-036adc83197b","year":1975},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.257144Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:e8653a3679d2e21e40c92b78bc31bc8a43d2663536d97a9cd70f046ec0074916","observation_id":"e2737dcf-b795-4250-8785-1b3b78393950","resolution":{"observed_at":"2026-08-12T10:13:05.086352Z","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":"2026-08-12T10:13:05.022359Z","title":null,"venue":null,"work_id":"f757b2b2-1b59-456c-8f27-0c043447f104","year":2016},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.276726Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:59fe5368b1e50b989c6c98656cb94c3f2d61c2157b83babea3420f00cc12249e","observation_id":"4cd1a348-eaf6-4108-ba2d-2ee5c44d4967","resolution":{"observed_at":"2026-08-12T10:13:05.043077Z","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":"2026-08-12T10:13:05.001545Z","title":"Friedland and P","venue":null,"work_id":"9cfe966e-6eb2-4267-81c5-07bf0cf9a664","year":2019},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.290474Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:99a507cb0329a313e30e1bd0980c00825e554d0510d33f5be65ffed3e04f2324","observation_id":"28c2b948-0217-4d9f-8811-1b39f6a901bb","resolution":{"observed_at":"2026-08-12T10:13:05.008488Z","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":"2026-08-12T10:13:04.969139Z","title":"Gr¨ ochenig, G","venue":null,"work_id":"95b85292-c775-4511-9080-cff184cf95de","year":2008},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.305790Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:fc0656ded8a6961624d6533d0be6f96f8d690d035af4b253dd96255325c6ec6c","observation_id":"a49bda7a-34d5-4308-bacc-c6a1047c40a8","resolution":{"observed_at":"2026-08-12T10:13:04.981711Z","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":"2026-08-12T10:13:04.940410Z","title":"Hewitt and K","venue":null,"work_id":"8e899e47-ec18-4c53-b4c7-80f63897d1f8","year":1963},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.318755Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:9a80f57d0fb30811b088ec3897efb06dd4d0a5b37f24c0b9fedb1920587a1121","observation_id":"ee9b7138-88b9-4207-ac98-85523719b0f0","resolution":{"observed_at":"2026-08-12T10:13:04.948826Z","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":"2026-08-12T10:13:04.911604Z","title":null,"venue":null,"work_id":"ab049f4d-7976-43c2-a778-156dcfc3d911","year":1967},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.328519Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:38ef0891a49a9fae7b443d9ec74fef560800d0197a82be2087be0b41056f099e","observation_id":"21959fc7-d87c-4636-b272-b99889dd2428","resolution":{"observed_at":"2026-08-12T10:13:04.918633Z","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":{"arxiv_id":"math/0601288","last_updated":"2006-01-12T14:26:32Z","snapshot_observed_at":"2026-07-07T05:54:14.935197Z","submitted_at":"2006-01-12T14:26:32Z","title":"Riesz basis of exponentials for a union of cubes in R^{d}","version":1},"cited_work":{"arxiv_id":"math/0601288","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0601288","snapshot_observed_at":"2026-08-12T10:13:04.489200Z","title":"Riesz basis of exponentials for a union of cubes in R^{d}","venue":"math.FA","work_id":"e0771686-1218-4473-997b-b937582c4641","year":2006},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.340780Z"},"links":{"cited_paper":"/paper/math/0601288","citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:3d3d9db273f1fe5ef9c0cb90750c12cab0e274f8a29174f769a645a4599e07ef","observation_id":"91051b0f-3ae0-4f00-a9b1-b27b50aecce1","resolution":{"observed_at":"2026-08-12T10:13:04.499438Z","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":"2026-08-12T10:13:04.891732Z","title":null,"venue":null,"work_id":"9d0f5db3-d3bf-4bc2-bcf9-c19dd8876cef","year":2010},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.352522Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:b2e09ad4bbd0c074c433dd68e4cafe7ada626c2b55ffcea0afbc05b33236cbc0","observation_id":"76cc57bf-494c-4fa9-8dca-8cdb0aacb443","resolution":{"observed_at":"2026-08-12T10:13:04.898325Z","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":"2026-08-12T10:13:04.841577Z","title":"Nitzan, A","venue":null,"work_id":"c7eef6b5-7d07-48a9-9b22-3cca84af8411","year":2013},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.362115Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:8247d4bf5a60c0de32934cde9675946dae5e1f766796d86bf37b68e4e618dc2d","observation_id":"3bbe5971-0b7c-4f3c-a5ba-b708bae8b226","resolution":{"observed_at":"2026-08-12T10:13:04.856422Z","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":"2026-08-12T10:13:04.808006Z","title":"Nitzan, A","venue":null,"work_id":"9a59c3f5-3246-41da-9ebf-e29181f9caaa","year":2016},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.371012Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:0c9116163c359fff031c64c33bba8b39daefbc4085f25eccb70b68f84baa2152","observation_id":"5503bae4-22bc-474a-a94e-fe4194108973","resolution":{"observed_at":"2026-08-12T10:13:04.820627Z","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":"2026-08-12T10:13:04.747077Z","title":null,"venue":null,"work_id":"abbd0ec3-1482-4cec-b9f5-102e26fd3990","year":1988},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.378042Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:ae43f3e98ac29a0b0edfc6c441057827be2931b688ddb696149227f2c3567ae9","observation_id":"da2b5672-1b2e-4764-bf46-1794d9b7b492","resolution":{"observed_at":"2026-08-12T10:13:04.778131Z","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":"2026-08-12T10:13:04.712719Z","title":"Pogorzelski, C","venue":null,"work_id":"f6bd963a-6b3e-4df1-ae16-76de26546b39","year":2022},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.387315Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:af39c250c649330e62d2cb68ca3bd4daa85862d82dbad89c80b94ed6e5435393","observation_id":"1adb383b-b04e-4985-8dc2-61019348c495","resolution":{"observed_at":"2026-08-12T10:13:04.720474Z","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":"2026-08-12T10:13:04.623039Z","title":"Reiter and J","venue":null,"work_id":"ced9c40f-2bdb-4c9b-b8fb-1162d61d67dd","year":2000},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.397091Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:6fc6e007dfe92e4bc46fc78d513f55f8256b0c898a922b09091232236982fe2f","observation_id":"1e380e9d-992a-46e8-bd3c-a71e8ad728ec","resolution":{"observed_at":"2026-08-12T10:13:04.659550Z","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":"2026-08-12T10:13:04.581119Z","title":"Richard and C","venue":null,"work_id":"24d562cf-191e-40ff-a88e-f41e0c46a40c","year":2020},"citing_paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T10:13:04.405320Z"},"links":{"citing_paper":"/paper/2411.19562"},"observation_digest":"sha256:3b1bee1d2d537d6261315969385d474667a40885c8ce49c14b3c6840616815e5","observation_id":"9217d316-bbc3-4654-a245-996a8d22966b","resolution":{"observed_at":"2026-08-12T10:13:04.589603Z","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"}}],"paper":{"arxiv_id":"2411.19562","last_updated":"2025-04-15T07:26:55Z","latest_version":3,"primary_category":"math.CA","snapshot_observed_at":"2026-08-12T10:01:56.249338Z","submitted_at":"2024-11-29T09:15:00Z","title":"On exponential frames near the critical density"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":1,"verified_fuzzy":15},"total_outbound_references":22},"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 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2411.19562."}