{"as_of":"2026-08-13T11:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5ae5e9074921c7b044bbd9aafe93a5b7310a611b1cac2137900b4194ab46a9a8","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T00:29:35.580669Z","state":"measured"},{"denominator":16,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":16,"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/2608.08190/citation-record","integrity":"/paper/2608.08190/integrity","json":"/paper/2608.08190/citation-record.json","paper":"/paper/2608.08190"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s12220-013-9423-8","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.709808Z","title":"Benedetto and Abdelkrim Bourouihiya, Linear independence of finite Gabor systems determined by behavior at infinity,J","venue":null,"work_id":"1777f614-7dc7-4105-ac37-25f9fde35463","year":2015},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.529287Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:feeec58edeb62beb4d6266c5964e1a549489b1f40ed10beebb30c8ecbed7db5a","observation_id":"369192c2-1414-41a1-bd3d-5c26cbd659b2","resolution":{"observed_at":"2026-08-12T00:29:35.713937Z","resolver_source":"doi","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":"10.1112/blms/bds119","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.697896Z","title":null,"venue":null,"work_id":"2e5f7701-77ef-4958-aeb4-969bcd57ce79","year":2013},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.533958Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:a413c267ff9765e489fcf281ca9362da7acf0cf111bc47b73e89513eec478081","observation_id":"5c973d77-3bee-43da-b582-45d91d299533","resolution":{"observed_at":"2026-08-12T00:29:35.702415Z","resolver_source":"doi","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":"10.4310/mrl.2010.v17.n4.a14","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.686246Z","title":null,"venue":null,"work_id":"7f5aa59f-19fc-473f-8359-57dc6f0adc14","year":2010},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.538307Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:6bea7b96ba68222b5a9257c6e223083dc762fce0bf2644a26c4d81adfd00d0aa","observation_id":"64ceb103-3618-4182-86c4-618590322a6e","resolution":{"observed_at":"2026-08-12T00:29:35.689523Z","resolver_source":"doi","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":"10.1016/j.jmaa.2011.11.030","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.675461Z","title":null,"venue":null,"work_id":"b1b68f2d-8ff8-4c07-bc4c-797e264d4cd2","year":2012},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.542035Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:14d0fe628fe445d4c467c66b21f78bd89bc7d07fba1c92526652642249e1cf5e","observation_id":"ff9e481d-5cd9-4fe5-8624-bedeec8e421d","resolution":{"observed_at":"2026-08-12T00:29:35.678774Z","resolver_source":"doi","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":{"arxiv_id":"2608.05044","last_updated":"2026-08-05T16:55:13Z","snapshot_observed_at":"2026-08-12T20:14:28.032145Z","submitted_at":"2026-08-05T16:55:13Z","title":"Linear dependence of time-frequency shifts of a Schwartz function","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2608.05044","snapshot_observed_at":"2026-08-12T00:29:35.546201Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.546201Z"},"links":{"cited_paper":"/paper/2608.05044","citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:62776532788babc9d1f31063a8d4ca09adec7bec22b56cebada1322f165d0a0f","observation_id":"1079f9ca-5550-4192-815e-67d774d36da9","resolution":{"observed_at":"2026-08-12T00:29:35.546201Z","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":"2026-08-12T00:29:35.822553Z","title":"Folland,Harmonic Analysis in Phase Space, Annals of Mathematics Studies, vol","venue":null,"work_id":"572ad78f-ad65-408d-b78c-63ce19dc4661","year":1989},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.549927Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:81bf946b2b962179d12410ec2a456fab816df6b5b1d0b6945bccf32a08e7e280","observation_id":"5a6214d3-cad2-4a29-99a1-b2bdbe7329fe","resolution":{"observed_at":"2026-08-12T00:29:35.825828Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.553201Z","title":"DOI: 10.1007/978-1-4612-0003-1","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.553201Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:15a51edf27fcbdb3d8c9d36102821c73534cbed26c60a1fe054d48fc10bcb436","observation_id":"92dfffa9-71bc-4183-8eea-a47bdb6aa69d","resolution":{"observed_at":"2026-08-12T00:29:35.553201Z","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":"10.1007/s00605-014-0637-z","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.655064Z","title":"Math.177(2015), no","venue":null,"work_id":"1d1af0a6-2e26-4b5b-bd8c-74a44b9bf407","year":2015},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.556099Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:8d2e0e9f9be54c9a47ea7281c21c3d4fb70b6fe96cb4a1d94e6a098001140694","observation_id":"7ed597e0-581c-4522-95f8-931f2817280b","resolution":{"observed_at":"2026-08-12T00:29:35.659239Z","resolver_source":"doi","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":{"arxiv_id":"2607.26878","last_updated":"2026-07-29T13:08:31Z","snapshot_observed_at":"2026-08-11T00:28:13.359202Z","submitted_at":"2026-07-29T13:08:31Z","title":"The HRT Conjecture for Symmetric Configurations and Real-Valued Functions","version":1},"cited_work":{"arxiv_id":"2607.26878","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.26878","snapshot_observed_at":"2026-08-12T00:29:35.800889Z","title":"The HRT Conjecture for Symmetric Configurations and Real-Valued Functions","venue":"math.FA","work_id":"7752e325-5c5c-4256-a2bb-77cf6d597cd2","year":2026},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.559137Z"},"links":{"cited_paper":"/paper/2607.26878","citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:c3b10a8a9db89e83b48eb2ddda3313b11ee15967f2efbbbd0ba8a67667a2e454","observation_id":"dd31da22-4dc5-4495-9eec-5315e34c8d84","resolution":{"observed_at":"2026-08-12T00:29:35.805703Z","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":"10.1007/0-8176-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.643122Z","title":null,"venue":null,"work_id":"f59c320f-4b11-4760-980e-8c56fa4c7ea8","year":2006},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.562647Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:34b501412a7cd3bcb3f88a7781b874a5a7b043a2769e28f954b6c2b25af32b23","observation_id":"1f99957d-09c4-4e4a-b3b2-95881964834a","resolution":{"observed_at":"2026-08-12T00:29:35.645954Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"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":"10.1090/s0002-9939-96-03346-1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.632881Z","title":null,"venue":null,"work_id":"a6e26c10-dec3-4511-aace-6f679700add1","year":1996},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.566573Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:aa8fe99a1b8fa4c33da768f5f3c84bcee0f1bdceb226ac56a1b2200fbf86e73d","observation_id":"2258e8e1-383a-4671-b6f9-984b60c82f69","resolution":{"observed_at":"2026-08-12T00:29:35.636176Z","resolver_source":"doi","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.569473Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.569473Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:8438740894192a08dc184b29f6d907e53f26e0b2ccd94536b486d15ca3501a57","observation_id":"f844b2d4-db65-4ef5-99dd-136e6cd05677","resolution":{"observed_at":"2026-08-12T00:29:35.569473Z","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":"10.1090/s0002-9939-99-05102-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.623252Z","title":"Linnell, Von Neumann algebras and linear independence of translates,Proc","venue":null,"work_id":"4101b6b5-a909-4b6f-80af-a24f3b1f8984","year":1999},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.572285Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:c140603701d783e8f590ba537b8e30b823e70339f65d7738331b19ae8db527c3","observation_id":"3f58f359-c1ec-4861-9363-89b2f50e3c82","resolution":{"observed_at":"2026-08-12T00:29:35.626390Z","resolver_source":"doi","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":"10.1007/s00041-018-9628-0","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.613280Z","title":"Fourier Anal","venue":null,"work_id":"73c4f478-89f0-48db-a465-1f28bbb22d91","year":2019},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.575307Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:55950793b135bb223e2242415b0bfda1b6ece67a0dc112efa61967dd67aeb938","observation_id":"7ae02a6d-7920-46fd-9208-d4b3a6604ff0","resolution":{"observed_at":"2026-08-12T00:29:35.616689Z","resolver_source":"doi","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":"10.1007/s00041-018-09661-x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T00:29:35.599916Z","title":"Okoudjou, Extension and restriction principles for the HRT conjecture,J","venue":null,"work_id":"f23cf5b0-9800-4f07-b763-44c5695c66b6","year":2019},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.577996Z"},"links":{"citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:3ebd1fe2dd5c2689adbe474003df44c0c26c884d5b0e70c4fc813aa88630eec6","observation_id":"3fbfcc18-cf28-4c50-b449-039676c648ae","resolution":{"observed_at":"2026-08-12T00:29:35.605748Z","resolver_source":"doi","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":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.21228","snapshot_observed_at":"2026-08-12T00:29:35.580669Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.580669Z"},"links":{"cited_paper":"/paper/2604.21228","citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:d8331d2c37b31f1948d815198ceac06581d3a5a5f131fc9bf464d474fd60d284","observation_id":"489123ea-0c3e-485f-a65c-db4b2665059f","resolution":{"observed_at":"2026-08-12T00:29:35.580669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-08-13T10:12:08.676964Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":10,"verified_fuzzy":1},"total_outbound_references":16},"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 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2608.08190."}