{"as_of":"2026-08-08T09:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:01af6ec097c8ae3f63aff5f6bed87f2453bfe3719f533f6512188134a8539c87","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:40:18.835852Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2505.22136/citation-record","integrity":"/paper/2505.22136/integrity","json":"/paper/2505.22136/citation-record.json","paper":"/paper/2505.22136"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:23.027889Z","title":"Ai, Z.-Y","venue":null,"work_id":"ad20459b-e132-4b06-b08a-f53651b3c096","year":2023},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:16.352901Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:9e049646c714aa99e9d05c991c2c2ad274f3b5fdaaf0d37f250525f049852f5c","observation_id":"662ece54-7895-4412-a15d-8cab997093a6","resolution":{"observed_at":"2026-08-07T13:40:23.073959Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:22.900242Z","title":"Christensen, An introduction to frames and Riesz bases, Appl","venue":null,"work_id":"2ae002e7-8c96-434e-afcb-c9fb0dcd9f91","year":2003},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:16.513823Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:36e144be640aac56617b264b7fda641703891561a3bc181271de52c04b721a8e","observation_id":"71209a32-cc71-463a-95da-f14ad8216bc0","resolution":{"observed_at":"2026-08-07T13:40:22.948130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:22.766961Z","title":"Dai, Spectra of Cantor measures, Math","venue":null,"work_id":"1a36583f-0cdf-4bda-8078-68fb2000572c","year":2016},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:16.653949Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:30a4e38eeda6b558d56120490fb47fbec9ab79dbe88df6418aab04f13b801c93","observation_id":"f35cde30-d345-400e-b265-94734490c2a5","resolution":{"observed_at":"2026-08-07T13:40:22.831336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:22.627994Z","title":null,"venue":null,"work_id":"d7c2f112-0dca-4ccb-97c3-70f417b05321","year":2012},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:16.725658Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:8d4a5dc06d00da05587b8c6cee960d5ae9943dd74d119d04999f7525d75bcf60","observation_id":"78c4aeec-69cf-4d72-8518-3a82b23ddc0e","resolution":{"observed_at":"2026-08-07T13:40:22.681868Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:22.476985Z","title":null,"venue":null,"work_id":"087c7fac-c2d3-4a04-9d7f-a3acd3f0f6bc","year":2014},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:16.844435Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:e806fff3bd8a7d6f6b578282ef7cf5b94dd7bf76346e89db6b72bfc393581a50","observation_id":"5c9c081d-ebaf-48a8-a683-78157a4f01b0","resolution":{"observed_at":"2026-08-07T13:40:22.555381Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:22.326162Z","title":"Duffin,A","venue":null,"work_id":"509f930a-9a19-4e98-a7e6-378e2ce43617","year":1952},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:16.945338Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:b80841221d94201ff2cd47c43969b2983f3923fd1a0239bddc3f08a831d7836c","observation_id":"81b23d72-9c2d-4959-b88f-658cfe44adf8","resolution":{"observed_at":"2026-08-07T13:40:22.393422Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:22.174802Z","title":"Fan, S.-L","venue":null,"work_id":"90132712-bbd4-487f-8b87-b893bdabfe2f","year":2019},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:16.985708Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:bafdc7ab2aec6815634b8f03ed3882d9bb169fe341320fd6404dfd20978652ac","observation_id":"aef45270-9b83-440c-abfb-dcbeb5007997","resolution":{"observed_at":"2026-08-07T13:40:22.230594Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:22.023071Z","title":"Fuglede, Commuting self-adjoint partial differential operators and a group theoretic prob- lem, J","venue":null,"work_id":"f71c3394-1d78-4d43-abc0-b1f9d927e01e","year":1974},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.023353Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:4439f183f93ea935bb7ec837bfb2c1b6f06d422de4183821dbb288ba1701d484","observation_id":"8fbfd2c7-70a6-4491-b31f-c4166edcbe06","resolution":{"observed_at":"2026-08-07T13:40:22.092319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:21.891791Z","title":"Heil, A Basis Theory Primer, Expanded Edition","venue":null,"work_id":"8950bd74-070d-44ba-8f60-6a3c7d1f8051","year":2011},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.091202Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:323b15854a696ba997e36e88d23cac7d415cb5c3eaefb4490dd8741957806472","observation_id":"61b84bd9-4553-4e44-935b-dafa5d69578e","resolution":{"observed_at":"2026-08-07T13:40:21.948673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:21.714076Z","title":"Iosevich, N","venue":null,"work_id":"ea2d7ac6-d1de-4d2e-89ce-24dcb63b156f","year":2003},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.174651Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:363527aa105737cd2aeb4bc6092b618e54ce9be5d9f8ba7501a2010072ad7dfe","observation_id":"b52f07bb-e6ba-4472-b04c-930042f22f39","resolution":{"observed_at":"2026-08-07T13:40:21.802227Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:21.545817Z","title":"Iosevich, S","venue":null,"work_id":"55e37187-997a-4e5a-be33-6e84efb34f03","year":2000},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.278504Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:e8ed2fb9cf4f1359bc83489155443199910e414a31e5ae328e22597950f574b8","observation_id":"6b2f5774-cd13-4d04-a75e-4e5609f4a49e","resolution":{"observed_at":"2026-08-07T13:40:21.633326Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:21.367420Z","title":"Jorgensen, S","venue":null,"work_id":"5d8ed520-964c-4f7b-ad5b-4a060da221db","year":1998},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.344405Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:65031abfd614914def2e95485184336802e8c817544fc5f845e9f772b859160c","observation_id":"a8f66712-6bac-4eb7-a5d4-336a8b162883","resolution":{"observed_at":"2026-08-07T13:40:21.463285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:21.237457Z","title":null,"venue":null,"work_id":"8493259a-050e-4b63-8676-b086c14aa61a","year":2016},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.436404Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:8bb1dfe7a0c7da06b8ab5cd87d155a0d0490a6492fb9ec5b389e966ac1791fe2","observation_id":"f866516f-7e3a-42da-a0eb-bc60f4b84a0a","resolution":{"observed_at":"2026-08-07T13:40:21.275097Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:21.000162Z","title":null,"venue":null,"work_id":"df73652d-b1f6-4346-b242-4703b2b31044","year":2006},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.522999Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:01da27e8f189478e45435b69452487ab6841006d8da1b0da9cdee3fed70c1cda","observation_id":"1bca2f00-6db7-43e2-8541-19b09f3eef55","resolution":{"observed_at":"2026-08-07T13:40:21.133068Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.11367","last_updated":"2025-01-28T12:40:04Z","snapshot_observed_at":"2026-07-06T20:23:18.251842Z","submitted_at":"2025-01-20T09:56:13Z","title":"Spectrality of a measure consisting of two line segments","version":2},"cited_work":{"arxiv_id":"2501.11367","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.11367","snapshot_observed_at":"2026-08-07T13:40:18.986720Z","title":"Spectrality of a measure consisting of two line segments","venue":"math.CA","work_id":"0cd70fe3-e4be-4b80-be54-341ee80c3656","year":2025},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.636910Z"},"links":{"cited_paper":"/paper/2501.11367","citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:e1edd057edecc9a1f977a452135634bdf1c1e11b1891d3c586063d9a5c93afee","observation_id":"77a11f76-ebf7-4b9a-8dc8-922c65775f66","resolution":{"observed_at":"2026-08-07T13:40:19.068093Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:20.773257Z","title":"Laba, Fuglede’s conjecture for a union of two intervals, Proc","venue":null,"work_id":"d919375a-f82d-4058-bf51-2030d9ad16b0","year":2001},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.820573Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:10b84e7da1d01c273301073455b31b716f6f38c765c709a87f3cc58ce564d720","observation_id":"abf78cd6-520a-4fa3-9ffd-0e5e6844ae9c","resolution":{"observed_at":"2026-08-07T13:40:20.842737Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:20.510138Z","title":null,"venue":null,"work_id":"68979dab-426b-40c1-9713-02eb6074998b","year":2021},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:17.976103Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:54e86a5944536c13d766aa6bde83b64519b797fa72b4dc5c60f118616d1d82f5","observation_id":"835c9c3c-6d4e-4e39-b9c3-e25d10a89ede","resolution":{"observed_at":"2026-08-07T13:40:20.624064Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:20.342750Z","title":"Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math","venue":null,"work_id":"c357ade5-9794-4ee9-b042-6ee78b736d93","year":1967},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:18.033730Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:86ee542c98262a44ecd5429cf21685cff39cbaa7d614333ce74379ef1756cc5d","observation_id":"02ba3fd2-6327-489c-ab78-481ece4c5c95","resolution":{"observed_at":"2026-08-07T13:40:20.402136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:20.161270Z","title":"Lev and M","venue":null,"work_id":"2fef78ff-c384-425d-b2f3-940bfcb74066","year":2022},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:18.211727Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:6122cf424d53833d59376ee4a7197da7f4b7e3c8dc34b8463ea11418bffc426d","observation_id":"cc3e0198-5694-4097-806c-06fbbdebcadf","resolution":{"observed_at":"2026-08-07T13:40:20.203079Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:19.954519Z","title":"Matolcsi, Fuglede conjecture fails in dimension 4, Proc","venue":null,"work_id":"afbb8298-8c2d-48e2-83df-27fe9e2e7389","year":2005},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:18.339160Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:cb588ade5a9689c89a1e1e9ac9a264dc40d46888273c609044fa673670fd9fa1","observation_id":"af8c82b8-ec2e-46e8-8446-e3babb0e520f","resolution":{"observed_at":"2026-08-07T13:40:20.071310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:19.780413Z","title":"Lev, Fourier frames for singular measures and pure type phenomena, Proc","venue":null,"work_id":"bcb7c7f7-5de6-4b4a-acc0-e61453553047","year":2018},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:18.499249Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:125c223e0a0eea0fb230c3fd1349f395ea84bd200cc44f6e4aec7e1886d9c9f4","observation_id":"41000823-0bde-49a6-a2b5-6a6464c9a2b1","resolution":{"observed_at":"2026-08-07T13:40:19.858790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:19.554814Z","title":"Ortega-Cerd, K","venue":null,"work_id":"69101138-57bb-408a-9277-ed2e62fae994","year":2002},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:18.643795Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:d79b26c8c222c1f5ba399856a39d7b0dc7768e0af2dfc2e6648004a90a7c4580","observation_id":"59aeec10-7316-4a26-b21e-354727ded7b2","resolution":{"observed_at":"2026-08-07T13:40:19.661653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:40:19.289290Z","title":"Tao, Fuglede’s conjecture is false in 5 and higher dimensions, Math","venue":null,"work_id":"e9f1620b-b2dd-48ea-889b-d401c4f116a8","year":2004},"citing_paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T13:40:18.835852Z"},"links":{"citing_paper":"/paper/2505.22136"},"observation_digest":"sha256:0e0f2963e8383baded2efcd230c21ca9d01580cfb11898e149167f9699b5d21d","observation_id":"5838f9af-c740-4ed0-910a-4de746f7d697","resolution":{"observed_at":"2026-08-07T13:40:19.400634Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.22136","last_updated":"2025-05-28T09:00:01Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-08-07T13:12:11.377495Z","submitted_at":"2025-05-28T09:00:01Z","title":"Frame bound, spectral gap and Plus space"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":1,"verified_fuzzy":17},"total_outbound_references":23},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2505.22136."}