{"as_of":"2026-08-08T23:29:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b52a56a80335312a4001a8ef3cef202ac1213682fcdc1616122fa5ae9fe7aaef","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T17:52:54.420074Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T00:25:59.153414Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-05T00:24:15.646393Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"cited_work":{"arxiv_id":"2606.00850","doi":null,"metadata_source":"pith","pith_arxiv_id":"2606.00850","snapshot_observed_at":"2026-08-05T00:24:15.646393Z","title":"A Toeplitz corona theorem for the pentablock and applications","venue":"math.CV","work_id":"0c6b5dc2-bb57-4d71-bc08-92e08ca63ff1","year":2026},"citing_paper":{"arxiv_id":"2608.00819","last_updated":"2026-08-01T18:52:49Z","snapshot_observed_at":"2026-08-08T04:12:14.700190Z","submitted_at":"2026-08-01T18:52:49Z","title":"Function theory of the hexablock and applications to the tetrablock and Euclidean biball","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-05T00:24:15.586276Z"},"links":{"cited_paper":"/paper/2606.00850","citing_paper":"/paper/2608.00819"},"observation_digest":"sha256:245effd50859dc6b0ee43e3e63a5d3458669393b2e1cf40bbdbc7f4afc40db47","observation_id":"4815d1c3-7ab0-4310-9e2b-6f500f49d997","resolution":{"observed_at":"2026-08-05T00:24:15.653150Z","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":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.00850","snapshot_observed_at":"2026-08-05T00:25:59.153414Z","title":"Pal and N","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.00827","last_updated":"2026-08-01T19:06:07Z","snapshot_observed_at":"2026-08-06T23:21:13.324745Z","submitted_at":"2026-08-01T19:06:07Z","title":"Function theoretic aspects of the symmetrized polydisc and generalization","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-05T00:25:59.153414Z"},"links":{"cited_paper":"/paper/2606.00850","citing_paper":"/paper/2608.00827"},"observation_digest":"sha256:b78b60493a0efaf6864cad125722c90bda3348b25e1cfec43063c8ef0a1a24ea","observation_id":"572eac09-26be-46e1-ba95-f7f9d084d7aa","resolution":{"observed_at":"2026-08-05T00:25:59.153414Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.00850/citation-record","integrity":"/paper/2606.00850/integrity","json":"/paper/2606.00850/citation-record.json","paper":"/paper/2606.00850"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:299026c8f270ea9261ce1daaf5c5990a9166dc75e0b2091481449475d7c36b63","observation_id":"8e388073-0040-4c0c-b083-690f30d66f5a","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Agler, Z","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:bc04a2440553204d1a247b295936f5483196aeb1d1a00ec8a3adc0c51d71e49a","observation_id":"9b0323e7-ae16-4320-a8e9-e1dbe8202bf9","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Agler and J","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:9748e5f3e411108827bb03151b8873310f6be9c7ce722eae92d13758028facbf","observation_id":"d58afc55-7035-4204-a46c-4fa2e04e14a4","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Agler and J","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:ae24a9bdc7f733fe892c2374fdb844bf5ad9a6abadad9f37aac02257c72122fe","observation_id":"dcaecf3b-ed2d-41d8-b41d-5bfa5ea190f7","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Agler and N","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:7298648aba0a12d1c5e3a4a752e3e2b7d0b8505caf2ed7e7ec9267f81cf66706","observation_id":"1029f768-ab37-46c5-a554-4e9ce29ef755","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Agler and N","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:3f69221ac652e4a4f6e85a7b8662c18b5fe4ec2484e11ac6297c2ef4e3771ecd","observation_id":"4b5181fc-f827-45b0-baa4-d1c6183c84c1","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Agler and N","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:7eb6b6ce140c16524ed6bb7f3da87cbc30ce456dd1c8b5342652820c1066c276","observation_id":"ddd142b3-a76e-48cf-96d8-c1cbaaa32450","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Amar,On the Toeplitz corona problem, Publ","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:cea89a8881407e7519128a07d90eb9f634b4711d15dbe2899cceed46ed190460","observation_id":"ef05819d-1ee9-4a02-86f0-310cbfb2b981","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Ambrozie,Remarks on the operator-valued interpolation for multivariable bounded analytic functions, Indiana Univ","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:5c166eff434f01bab2c9c833d45f7d1cb8c1069c228e9863abc8881813afba14","observation_id":"9e41b912-2c98-4b21-aa51-56dfacf102f3","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"And ˆo,On a pair of commutative contractions, Acta Sci","venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:e458be3a8de352e286871af4572cff45e36c4f538f3f7505f3d1f705715c23d4","observation_id":"c3056fc4-3e30-417f-8b5a-87c6416f1e47","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Arveson,Interpolation problems in nest algebras, J","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:4acaea737a6969646fa4bb67dad42cfe15ed2a6306eb758b9999062487cadd91","observation_id":"ca71a77f-aadf-49a6-96ee-2c157cb0dd79","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Bhattacharyya and H","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:0101bfe0e2889f1d571cc35165d0ee99f30ddc66d59b0fec00d0c9b4aaa72e82","observation_id":"54a75d20-43ec-47f6-92e5-d493f47b2ffa","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Carleson,Interpolations by bounded analytic functions and the corona problem, Ann","venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:7d214411c431ef6dd86c62b502d626364c9581dfa4a07e918dcd1fd33f3bef0c","observation_id":"aeaaf6d3-d0bd-49f8-838c-25d9f2662036","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":null,"venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:351b47f4288e0535d2e4fabb811832d26bc8f4e2b21c6f24c64a3eef5cd41217","observation_id":"b97a8c14-06f9-4509-b8cb-91a9826c75d9","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":null,"venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:0b93d7e5888be9b6d88a7b55993701f64b69534e00a8404f6e74e3bfd13689f7","observation_id":"db02e276-5b4b-4de6-8291-788f80ee5fa8","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Eschmeier and M","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:7aed637acc1e3dc6bbc3959be5d410d132f6e30e8811120a1a2b2cf402f8023a","observation_id":"905b50cc-f099-4d0d-b0ae-e6c6cf12015c","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":null,"venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:a5927bca8afe1fa63247f4b76792c6a401a50b9d93d30d3d679b25704a224024","observation_id":"9dc6c638-da1d-4862-b72b-357bb8037f37","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"H ¨ormander,Generators for some rings of analytic functions, Bull","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:4a0f0c76f157e296449bec4a11e4327b96d3506ab5a62722b73c5d66de9a9b3e","observation_id":"bdbb18e6-555f-40b6-88b2-12866d1dc014","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.23492","last_updated":"2025-08-27T13:45:23Z","snapshot_observed_at":"2026-08-07T12:42:36.750087Z","submitted_at":"2025-05-29T14:42:50Z","title":"Function Theory on Tetrablock: Realization, Interpolation, Extension and Toeplitz Corona Theorem","version":2},"cited_work":{"arxiv_id":"2505.23492","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.23492","snapshot_observed_at":"2026-07-01T20:46:13.181010Z","title":null,"venue":null,"work_id":"61d287ab-19b9-4114-88ee-ab99838dbc5d","year":null},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"cited_paper":"/paper/2505.23492","citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:254abceff51358d8acd38ba5d1c7de89769c89f33d54d7c5af0395080c557a50","observation_id":"15100e43-4d04-4df4-bdda-e3c643a4b7cc","resolution":{"observed_at":"2026-06-28T18:02:27.353197Z","resolver_source":"arxiv_id","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Sz.-Nagy and C","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:926e3b4a40a733ca6f96583df64a74e1806ee965d44f4c78ac97e1c8ed93fd10","observation_id":"ff505991-ddce-4fa7-9d03-fd00a43a03e3","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Pal and N","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:3287c655ad88b81039c904da43ae86fe06c870c86268b254f07cc0b6f22a04f0","observation_id":"4db01aa7-894a-4521-8166-a32912a48c47","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":"submit/7657754","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T18:02:27.352485Z","title":"Pal and N","venue":null,"work_id":"7ebef9e4-38de-4b3c-b292-4cd79c1297b2","year":null},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:53d854177ed619cbdf9cb8697e482d5792da517b80464947730a09dbfcc2ef3a","observation_id":"d2b934f7-8656-406e-801d-6f7498d290df","resolution":{"observed_at":"2026-06-28T18:02:27.353963Z","resolver_source":"arxiv_id","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":"Rosenblum,A corona theorem for countably many functions, Integral Equations Operator Theory, 3 (1980), 125 – 137","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:63c3d8c000d3f2995ead935d29190df3e9878f322aaf1b87d37627b8b6aaa534","observation_id":"eed06889-a0ad-4d44-a90f-90e9a7445703","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T17:52:54.420074Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-28T17:52:54.420074Z"},"links":{"citing_paper":"/paper/2606.00850"},"observation_digest":"sha256:66c0e7346432a6a8699fa3ed170edcd8301eeb963a714c2164fdb6df20401c32","observation_id":"803a2f1a-15a0-43d5-8bc5-1249dcd1dd2f","resolution":{"observed_at":"2026-06-28T17:52:54.420074Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.00850","last_updated":"2026-05-30T18:49:19Z","latest_version":1,"primary_category":"math.CV","snapshot_observed_at":"2026-08-08T05:48:09.826442Z","submitted_at":"2026-05-30T18:49:19Z","title":"A Toeplitz corona theorem for the pentablock and applications"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":24},"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 24 of 24 outbound references and 2 inbound Pith citation observations for arXiv:2606.00850."}