{"as_of":"2026-08-08T20:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a3cf6fbd96ae950fe047951978ad9a6484ea170c5c24d86fa0ad43508ac81583","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":"2026-08-06T19:47:56.429862Z","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/2507.04992/citation-record","integrity":"/paper/2507.04992/integrity","json":"/paper/2507.04992/citation-record.json","paper":"/paper/2507.04992"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:47:56.794471Z","title":null,"venue":null,"work_id":"4a14b02d-440c-4d3f-895d-140efecd538d","year":1986},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.323817Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:1bbc9381458fd0af5ac35f24a46ad71750c396f8b3560edd30d19b19339957e4","observation_id":"d7a74204-ca8e-4e5c-9969-b84fc8eb711f","resolution":{"observed_at":"2026-08-06T19:47:56.798499Z","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":"2026-08-06T19:47:56.780065Z","title":null,"venue":null,"work_id":"e129c1c3-03ba-455d-a345-1cd909d89598","year":2023},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.329015Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:aa67f934dcd2132e237ae446061d81885e79de9c4e290a377bcf25d4fb1cdd24","observation_id":"0172089a-89e6-4c33-9004-b2d65e983f31","resolution":{"observed_at":"2026-08-06T19:47:56.784787Z","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":"2026-08-06T19:47:56.765740Z","title":null,"venue":null,"work_id":"dcdbed5b-3b9d-44a5-9511-634e694a9313","year":2017},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.334140Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:6e4621baa7518226423c98e8733380937486f4677d55402c097e0a0073078ae6","observation_id":"8d97f262-0a91-4ad8-b39c-8a52e799fcf4","resolution":{"observed_at":"2026-08-06T19:47:56.770258Z","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":"2026-08-06T19:47:56.751517Z","title":null,"venue":null,"work_id":"9e538501-c5be-49fc-a045-02dcd427d5ed","year":2017},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.338773Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:dc8a177e271e2e97e1cb80646718a8b810c018fe18641b3fae836f4798eee87f","observation_id":"aa0d579f-1e7e-4ad0-82df-f96cb19eb8e0","resolution":{"observed_at":"2026-08-06T19:47:56.756328Z","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":"2505.19303","last_updated":"2025-05-25T20:22:36Z","snapshot_observed_at":"2026-08-08T13:41:31.105719Z","submitted_at":"2025-05-25T20:22:36Z","title":"Dynamical Frames and Hyperinvariant Subspaces","version":1},"cited_work":{"arxiv_id":"2505.19303","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.19303","snapshot_observed_at":"2026-08-06T19:47:56.465220Z","title":"Dynamical Frames and Hyperinvariant Subspaces","venue":"math.FA","work_id":"d475aec4-46d0-43e2-aace-75a213490934","year":2025},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.343364Z"},"links":{"cited_paper":"/paper/2505.19303","citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:76f332ecbbd035c8d525dcfda36cfa6d622ba59c7f2cf36373ebbf470d34881f","observation_id":"69649e55-bde2-45ea-9bb9-aea2702dc5e1","resolution":{"observed_at":"2026-08-06T19:47:56.472278Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"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":"2026-08-06T19:47:56.736420Z","title":null,"venue":null,"work_id":"b583eb5d-b9a6-4230-8d0f-d82b6392e9de","year":1948},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.348028Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:8f140273f00876889c665289cbdeaedc2a3fad4b8706b9ff164415918924330a","observation_id":"adf36969-665d-4621-988a-89cec072d15c","resolution":{"observed_at":"2026-08-06T19:47:56.741137Z","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":"2026-08-06T19:47:56.722135Z","title":null,"venue":null,"work_id":"5392f83b-7d8c-4ff0-9efe-46345c262059","year":2003},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.353474Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:6df51a4a1db7bc41a5b7222162038f54c2151be2bae2fc6a800a39e10ca6d84c","observation_id":"1139e6c4-1184-488a-ac5b-62f0f2845847","resolution":{"observed_at":"2026-08-06T19:47:56.726726Z","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":"2026-08-06T19:47:56.705909Z","title":null,"venue":null,"work_id":"a2ac5d24-6138-43f1-a49a-fb1359520e02","year":2019},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.358286Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:bf032b7074248d2237a1494edde19c6b870a6296e0461e829265a05ebdcd8277","observation_id":"4588761c-a583-498a-bbd9-6c16bf51c016","resolution":{"observed_at":"2026-08-06T19:47:56.711220Z","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":"2026-08-06T19:47:56.691347Z","title":"B., A course in functional analysis Springer-Verlag, New York, (1990)","venue":null,"work_id":"5a5dfa5d-0a04-4853-8181-088669b1fc77","year":1990},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.363349Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:37aaae3624d277d236f4988b7b585d049ee6a438a34111099bd57ff9b0ca2791","observation_id":"35b67481-6fcf-47b3-b3f9-c740a0625ba9","resolution":{"observed_at":"2026-08-06T19:47:56.695981Z","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":"2026-08-06T19:47:56.676910Z","title":null,"venue":null,"work_id":"0994a544-13eb-4696-a0b7-2d0dfcd00cdc","year":1989},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.367777Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:aedad6c08d280eccfca67e336538703b0b628e13701bf7a48f3b30281e57b667","observation_id":"32bede03-c9e4-4a03-a18b-17006620b863","resolution":{"observed_at":"2026-08-06T19:47:56.681201Z","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":"2026-08-06T19:47:56.663031Z","title":null,"venue":null,"work_id":"a7f6e611-8970-457c-ac6d-28e044e89ed0","year":2000},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.372320Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:a0e71d9f204e9d453bfb4d85747473a9b58ca3a8f829defc31120f30807e059e","observation_id":"68665bce-f1e0-47b2-9287-77f35a975025","resolution":{"observed_at":"2026-08-06T19:47:56.667687Z","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":"2026-08-06T19:47:56.648513Z","title":null,"venue":null,"work_id":"cab72a09-b848-46ee-b312-98b3a5db042d","year":2001},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.376934Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:f7f3beced6f0a183266426f598d107eaac2b2107828a31dec9e25e3926fb870c","observation_id":"8601590d-b0c6-4687-b43d-892460debc91","resolution":{"observed_at":"2026-08-06T19:47:56.653373Z","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":"2026-08-06T19:47:56.634159Z","title":null,"venue":null,"work_id":"51a831a3-4018-4434-9c71-4c0c4a2e6f49","year":2016},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.381822Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:ffd20166259406a174847c923bde2a7bf05237807382498ed8024a99ab16ac52","observation_id":"48fab198-d6ab-4d72-9486-ea8208e1ea8c","resolution":{"observed_at":"2026-08-06T19:47:56.638474Z","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":"2026-08-06T19:47:56.619063Z","title":null,"venue":null,"work_id":"1ce2b1f3-d769-4a98-a122-f2a4aa7d1d9d","year":1988},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.386475Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:5b9eaaed1754f5e1ce22ace3cff2b8fac0b6eb3316610984585a6d068a8a333a","observation_id":"b15d5b1d-ffaa-41af-a786-c64bfa771c9d","resolution":{"observed_at":"2026-08-06T19:47:56.624374Z","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":"2026-08-06T19:47:56.604531Z","title":null,"venue":null,"work_id":"8a561d20-cd1c-4485-8ab1-891bd6ba0e64","year":2011},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.390827Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:18a5028a0c77a0790f8f783d451fe9ef9083565b8f46ec99b0d816f8eb0448a1","observation_id":"a3e115b9-9aa3-4a40-a295-5e601a720f07","resolution":{"observed_at":"2026-08-06T19:47:56.608998Z","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":"2026-08-06T19:47:56.590604Z","title":null,"venue":null,"work_id":"9678c15f-fdf1-4d74-9454-d1e24b241784","year":1988},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.395263Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:cc6f870f99b8a926932e60fbae0f6662152f0487b9c0d9dad6b244213fba3e25","observation_id":"3b426fac-86a4-47fb-9f69-9ba9be4c2e90","resolution":{"observed_at":"2026-08-06T19:47:56.594752Z","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":"2026-08-06T19:47:56.576889Z","title":null,"venue":null,"work_id":"ec1f88c2-e746-4a56-882b-d8d1f3066957","year":2007},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.400958Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:4a20614fbbfc0b0163cb5e5fba5d215cfdedef28a564edf00e321a57b8e56711","observation_id":"58bac4ff-7203-4115-953e-6191741142de","resolution":{"observed_at":"2026-08-06T19:47:56.581090Z","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":"2026-08-06T19:47:56.561494Z","title":", New York, (2003)","venue":null,"work_id":"5444d422-79eb-4998-afe8-a78a36e11eb7","year":2003},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.405672Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:d8734416184daa0813a4f700373de0e952e9baa4235cb244c049755f2b45d2f3","observation_id":"76f085a7-af96-4664-9690-620a70c04384","resolution":{"observed_at":"2026-08-06T19:47:56.566521Z","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":"2026-08-06T19:47:56.545256Z","title":null,"venue":null,"work_id":"b9369d52-d818-41a7-bd37-f61353f0e2f3","year":1969},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.410798Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:0a5065834a8081a80a5c5103c568c6c0e4a1789e1049406022155f25cd56bc61","observation_id":"d67bc9a6-e013-43a6-b7cd-62816d69c770","resolution":{"observed_at":"2026-08-06T19:47:56.550511Z","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":"2026-08-06T19:47:56.529635Z","title":null,"venue":null,"work_id":"8eafa55c-fad4-4ce8-8580-2f1e2622653c","year":1985},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.415669Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:fdaf1bc0f1ba209acee59df4fc150b8d3c8d86defd7c72babbde4369d843dbe7","observation_id":"03ba6b82-f736-4913-9a99-cb176da5533a","resolution":{"observed_at":"2026-08-06T19:47:56.534890Z","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":"2026-08-06T19:47:56.513843Z","title":null,"venue":null,"work_id":"15eedd06-2bd8-49fe-acd7-3aa12f540703","year":2015},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.420873Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:772848587b6a43c09b45c2b8eabc02f14d9ed35a6d6dfd766744fe4cb15aecb9","observation_id":"d6a866de-30e6-4a65-9d9b-c02e4a405d7d","resolution":{"observed_at":"2026-08-06T19:47:56.518750Z","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":"2026-08-06T19:47:56.497829Z","title":null,"venue":null,"work_id":"d9dab8e3-28b4-4fd0-9bfb-0c6c8194c518","year":1952},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.425513Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:8e1a9dcb118b575ab8efe631ea0d8b92328b7731a06c9b5b72b0d33b060739b1","observation_id":"95f058fc-655b-496d-b27a-e6484ed7ecd6","resolution":{"observed_at":"2026-08-06T19:47:56.502960Z","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":"2026-08-06T19:47:56.483599Z","title":"Luis Santal´o","venue":null,"work_id":"01e44402-7965-47f5-be24-cc1f657daec4","year":2019},"citing_paper":{"arxiv_id":"2507.04992","last_updated":"2025-07-08T22:05:02Z","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T19:47:56.429862Z"},"links":{"citing_paper":"/paper/2507.04992"},"observation_digest":"sha256:b8328e9b4211e16825ce1d1c2f94012562f33bcc3fa4ed6aeeaf5d909759abd3","observation_id":"db12cd8e-3cb4-4b76-accf-46a06f4d44c5","resolution":{"observed_at":"2026-08-06T19:47:56.488131Z","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":"2507.04992","last_updated":"2025-07-08T22:05:02Z","latest_version":2,"primary_category":"math.FA","snapshot_observed_at":"2026-08-08T13:41:58.444775Z","submitted_at":"2025-07-07T13:31:22Z","title":"Submodules of $H^2(\\mathbb{T}^2)$ and Frames by Pairs of Bounded Commuting Operators"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":19,"verified_exact":0,"verified_fuzzy":3},"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:2507.04992."}