{"as_of":"2026-07-11T19:36:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:90b0d037475cbaf1ba7320a205ca3c2d9753a1e95660d324bea08b21cfeb69de","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-09T23:00:14.881779Z","state":"measured"},{"denominator":35,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":35,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-07-11T06:31:22.384518+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-30T04:23:07.685564Z","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":"2026-07-01T15:15:47.454985Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"cited_work":{"arxiv_id":"2604.20330","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.20330","snapshot_observed_at":"2026-07-01T15:15:47.454985Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","venue":"math.CV","work_id":"92ff5e49-bcca-43d1-afea-2167bd88e4a6","year":2026},"citing_paper":{"arxiv_id":"2606.29969","last_updated":"2026-06-29T08:46:37Z","snapshot_observed_at":"2026-07-07T00:03:51.213896Z","submitted_at":"2026-06-29T08:46:37Z","title":"Compactness of composition operator on weighted Bergman spaces of the polydisc","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-30T04:23:07.685564Z"},"links":{"cited_paper":"/paper/2604.20330","citing_paper":"/paper/2606.29969"},"observation_digest":"sha256:d836119ee223566b3849d6a546b672e8e8a0e8f5a8f5835dfc91346a51065b11","observation_id":"5edbffa7-f73b-47aa-ab2b-bec87b7543e8","resolution":{"observed_at":"2026-07-01T15:15:47.456289Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2604.20330/citation-record","integrity":"/paper/2604.20330/integrity","json":"/paper/2604.20330/citation-record.json","paper":"/paper/2604.20330"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Agler and J","venue":null,"work_id":"71acd8f1-86e8-4174-bc9c-4a10db93ddec","year":2002},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:6ccdd8cb8ab2f56582dc19b1b3c0cae45bd2bb69f3534ca20b68f4c1844cba29","observation_id":"577b681f-665c-4297-8168-852647c58673","resolution":{"observed_at":"2026-05-23T13:45:40.117259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Agler and J","venue":null,"work_id":"f5c7b762-b2f8-43e7-b6aa-9a850cd21ff3","year":2005},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:78e5356b9ff8aba4d9377c8ab1c6688b9282c59d21442e4b3085e8fd661042fa","observation_id":"73d30d98-12aa-4ae7-a3be-d22abb185aa8","resolution":{"observed_at":"2026-05-23T13:45:40.109306Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Agler and J","venue":null,"work_id":"9e5eabeb-334b-4751-8592-0ab8ef006b1f","year":1999},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:ce4b31d802289aa9b14487b129c3ca69238dbbd4c6d28ff7101fcafd8205ac25","observation_id":"360176ff-3464-41c7-90cf-1881bfc9bcb3","resolution":{"observed_at":"2026-05-23T13:45:40.129472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d04da7a0-6047-4225-b4ab-eab1e78e9a18","year":2024},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:8fe6b2643ded05993d5ec6b08fbbc827b2a78883260c681c6427307c7488c9af","observation_id":"9fdc258e-f745-4504-8883-15bc6edfeddc","resolution":{"observed_at":"2026-05-23T13:45:40.145193Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bayart,Composition operators on the polydisk induced by affine maps, J","venue":null,"work_id":"5d6ebedb-1067-4673-b6de-76ef68d937be","year":2011},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:0fee37a17af4f0308d19f0bd2edf757f8db74a3f638387679281cf034fe22cdb","observation_id":"d76a8752-2bb9-4085-8893-979dbdb32a7a","resolution":{"observed_at":"2026-05-23T13:45:40.100683Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bayart,Composition operators on the Hardy space of the tridisc, to appear in Indiana Univ","venue":null,"work_id":"f6bf6292-2607-4c1a-ac5e-2fe93cf68913","year":null},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:51441af5ccefb710c8aef704cb1dd13509ce2831f1213d7d2f6b62c0b8d2a89f","observation_id":"e1329315-a779-4382-a9f4-3e9dab50119f","resolution":{"observed_at":"2026-05-23T13:45:40.105401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bayart and A","venue":null,"work_id":"ac29c995-0299-4460-b37b-c88bc0a26cff","year":null},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:3943d970fe3f15e30adaf0be06d71a55b0b79619c41c3bfd8375e5b635521ae8","observation_id":"f9961b4d-803d-43e7-9012-9c1edf855002","resolution":{"observed_at":"2026-05-23T13:45:40.096766Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2601.19308","doi":"10.48550/arxiv.2601.19308","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T12:15:01.137692Z","title":"MR unavailable","venue":null,"work_id":"d8dd8a7c-8942-4222-8f77-4b28dba3e904","year":2026},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:7310129debe5985d87b5948c145a51c6d54da0b6da805145c4e2c9b225167833","observation_id":"2c2b8ff8-8be0-4116-a30e-838537604a56","resolution":{"observed_at":"2026-05-09T23:04:17.408371Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/conop-2025-0018","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Beslikas,Characterizing the RIFs that induce bounded composition operators on the Bergman space of the bidisc, Concrete Operators13(2026), no","venue":null,"work_id":"e8c8c71d-b8d0-4614-9e16-a8e299f50e74","year":2026},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:5fb622d03fbaa5e5e90fbdb2a1257e95f10dea32289cc0c91762b3057b50e0d5","observation_id":"2a768795-f0fd-4441-abb1-9c78fbe8fba8","resolution":{"observed_at":"2026-05-09T23:04:17.410359Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Beslikas,Composition operators and rational inner functions on the bidisc, Proc","venue":null,"work_id":"89f51d64-1b70-4a6d-8a0c-ccbcd48aa57f","year":2025},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:a8dc30d67a6b3d2ea7f4aa2dd4b76272fc68d8ede5df43e5023c5b2e1060cd67","observation_id":"80ec3abe-e2a4-4091-a2b2-29e6dde85a56","resolution":{"observed_at":"2026-05-23T13:45:40.090798Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2512.17388","last_updated":"2026-04-16T13:16:33Z","snapshot_observed_at":"2026-07-06T22:39:33.919723Z","submitted_at":"2025-12-19T09:43:53Z","title":"On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type","version":2},"cited_work":{"arxiv_id":"2512.17388","doi":"10.48550/arxiv.2512.17388","metadata_source":"pith","pith_arxiv_id":"2512.17388","snapshot_observed_at":"2026-07-10T12:15:01.137692Z","title":"On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type","venue":"math.CV","work_id":"c152397d-eb0d-42f0-b963-5b062f5b288b","year":2025},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"cited_paper":"/paper/2512.17388","citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:e25aa57f2c12ad06b0fd00de3f4c886790ca1ea1df69d1f8cef50198ab98bc7d","observation_id":"be4ae0a6-28b2-4ce0-af51-737674fac525","resolution":{"observed_at":"2026-05-09T23:04:17.413221Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Beurling,On two problems concerning linear transformations in Hilbert space, Acta Math.81(1949), 239–255","venue":null,"work_id":"629c6c3f-0293-40f1-9542-f8dedfff4ce4","year":1949},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:8f455acd6038e53b60a20915d07d3b562723a70487dad7a615775462cd69d444","observation_id":"c634264b-3677-424b-89db-a8278010bf48","resolution":{"observed_at":"2026-05-23T13:45:40.094075Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9ad8ccf5-43a8-4c6d-8d73-36e47b1c6fd7","year":1979},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:405964c04b5627a713c4d0df4e6a3849875cb803aec16effdc65785c37f37e7d","observation_id":"73719645-0f09-4228-888b-ceb2c444970f","resolution":{"observed_at":"2026-05-23T13:45:40.113105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bickel, J","venue":null,"work_id":"011f0ebc-cd7b-41b6-a98f-3335c4cedcba","year":2024},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:8c1b54e5b693f79e525d7ac0b48f00afd1f61dfc4ec536539355178b96c29598","observation_id":"3a32ebcc-f17c-4dc2-8dd4-b0e7e78ec3b6","resolution":{"observed_at":"2026-05-23T13:45:40.121997Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bickel and G","venue":null,"work_id":"bc79be6c-6a29-4eef-a74b-f1d2201f084e","year":2013},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:793db1168dec7e4b792c095f4be1773bf5de8a4114f294f122b20c06138bfff0","observation_id":"f178652e-28fd-482f-8675-983cc1cc3699","resolution":{"observed_at":"2026-05-23T13:45:40.125669Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bickel, G","venue":null,"work_id":"18950ad7-222a-4f99-9dfd-864b7f0bb5e8","year":2024},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:6ba3f5e0f98d46ae1e53278fc3eebc3a96a4a10ef56bdefaf94774930cf60752","observation_id":"f5d45789-45da-4628-93cf-d50c286dda94","resolution":{"observed_at":"2026-05-23T13:45:40.133330Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bickel, J","venue":null,"work_id":"af40bd80-ac51-443e-9543-8bd51ef30e09","year":2018},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:8b0595aebc60dc7be3bb95878f3b7d2979b45bbb1451f3669a39fabce96424a5","observation_id":"803ef724-9d5f-400f-bc6c-e623330b6812","resolution":{"observed_at":"2026-05-23T13:45:40.084406Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bickel, J","venue":null,"work_id":"8e18e152-1cb8-4933-8c57-524df403fdc6","year":2020},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:026ea7de2909b1b01adc629e144ab4340b4fbc3f0f9ce5f8ea4716c4ffda49df","observation_id":"13e14c91-4515-4bc0-876f-6fa69afe3281","resolution":{"observed_at":"2026-05-23T13:45:40.087128Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Bickel, J","venue":null,"work_id":"92659a6a-2b1e-4f62-9b97-c90dc8e07f63","year":2022},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:81923a2ac7e261eaed1fa9bf03ef9960a17a3a85880cc85bc54f7bc1b033a30c","observation_id":"7ed21d4a-6c66-441b-9530-4bc366ecbfcc","resolution":{"observed_at":"2026-05-23T13:45:40.069665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ccfaa7da-381e-43f1-bea8-3760fd31724c","year":2025},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:a01491f0035cfeedace7b44cefa61eefb1c9faea2fa7f91354b02f1d920f3fe8","observation_id":"1f2c809e-3a8e-4967-a1ad-9d5f9d06e14f","resolution":{"observed_at":"2026-05-23T13:45:40.073102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Fulton,Algebraic curves, Advanced Book Classics, Addison–Wesley Publishing Company, Advanced Book Program, Redwood City, CA","venue":null,"work_id":"931981e2-1033-4eca-a69b-80a99a173dad","year":1989},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:eb113fedc011e924e417f536e9cd1cce254c90597ca58f5f3831df12daf36ffa","observation_id":"80bed8d8-92b9-440d-8709-ec8cc45918b2","resolution":{"observed_at":"2026-05-23T13:45:40.077120Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Hedenmalm, B","venue":null,"work_id":"3fe6d8bb-ad26-4edb-adc0-033280eaa174","year":2000},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:c29d438c34e3bcd01b12dcc3acb4f3a5092595a548fcd7cdf0475b6a84590943","observation_id":"b7c3e409-4716-4d7c-ae6f-c50b9411a5f5","resolution":{"observed_at":"2026-05-23T13:45:40.065918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Jafari,On bounded and compact composition operators in polydiscs, Can","venue":null,"work_id":"6858f62a-0659-466b-9d3a-48f935fbad23","year":1990},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:74880f59dce5762c91d37c5675cf96c69644567760ab13196b45f5cb804d0f4d","observation_id":"fc1e4ecc-ea6b-4b1a-b28b-61b58c9ea8e7","resolution":{"observed_at":"2026-05-23T13:45:40.137435Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Knese,Rational inner functions in the Schur–Agler class of the polydisk, Publ","venue":null,"work_id":"8cf5aaa9-d4f5-4f0a-8d36-ade816d44cc5","year":2011},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:b352c20b44a445024125f53db1aa1b2fac6f87b265d610b9aaa84b56170d49de","observation_id":"98e1ab3f-7cf4-4587-8236-3f6a22fb42c3","resolution":{"observed_at":"2026-05-23T13:45:40.141402Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Knese,Integrability and regularity of rational functions, Proc","venue":null,"work_id":"b224e321-8456-4b2e-bad5-4b1752bcee14","year":2015},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:c16fdc2da7c5b4df5cab925781f05373f8eb0d2561906ccd6dfc8de009dff970","observation_id":"7cb7a40a-2f89-4bda-906a-ef0ca59099ab","resolution":{"observed_at":"2026-05-23T13:45:40.089250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2404.05042","doi":"10.48550/arxiv.2404.05042","metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-10T06:15:00.866473Z","title":"Knese,Boundary local integrability of rational functions in two variables,to appear in Trans","venue":null,"work_id":"6ec00b9c-bbef-48e4-a026-98b684989ccb","year":null},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:1b69beb6a2f884abf58a1d9db59dfd2bf13da9d7771a7644c8186fc0c42d1546","observation_id":"491ab116-00c7-4104-bad4-0d5fd0a6254d","resolution":{"observed_at":"2026-05-09T23:04:17.405476Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"0bff3f8b-22f2-4506-bae4-39f3867070ae","year":2008},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:b6b1d7b790a824ae1c7f4ee6b3c80afdcb4294765112a6b12fc8f2fb59c568d4","observation_id":"d2d671f1-0e90-4071-b786-d3109900d797","resolution":{"observed_at":"2026-05-23T13:45:40.081204Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Kosi´ nski,Three-point Nevanlinna–Pick problem in the polydisc, Proc","venue":null,"work_id":"1956a41e-523d-41c8-9a31-efa2237c04ed","year":2015},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:f31da666be914fc498d626b9aebe9035b3619a234edbead783ef88c3ea8fafaa","observation_id":"61398a1a-ada7-43dc-acce-789ecbb1f42d","resolution":{"observed_at":"2026-05-23T13:45:40.070530Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Kosi´ nski,Composition operators on the polydisc, J","venue":null,"work_id":"05849f40-c758-4ae7-805b-7fa9ac08c042","year":2023},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:68a84962e681c277677abdb4b11854717a49e6655769b7a5fd600366f08919e6","observation_id":"bd8d5499-31f5-463d-97be-d71f6c12984c","resolution":{"observed_at":"2026-05-23T13:45:40.039255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Kummert,Synthesis of two-dimensional losslessm-ports with prescribed scattering matrix, Circuits Syst","venue":null,"work_id":"aeb58769-37ad-4ef5-90df-60426f29b541","year":1989},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:61a0c6cccb82e2fa027a0ec6d4c058bc6c3fc179e1b9caa38c567d9297d88858","observation_id":"31c34a2e-49e6-41d0-9d2a-6d69b0a0d6ae","resolution":{"observed_at":"2026-05-23T13:45:40.048463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Pfister, ¨Uber das Koeffizientenproblem der beschr¨ ankten Funktionen von zwei Ver¨ anderlichen, Math","venue":null,"work_id":"60c735d9-0221-4df8-af80-a20b73f45dc9","year":1962},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:429e0b111ea38782ce146cca534b69bfa5a775e0ecdf1a9a323b08875618d793","observation_id":"cc4dd8c9-dcef-490c-a107-0899f15089d2","resolution":{"observed_at":"2026-05-23T13:45:40.031255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":"Rudin,Function theory in polydiscs, W","venue":null,"work_id":"f7f330c8-715d-4d78-8f94-acd527bb5381","year":1969},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:e731332b732c4748d0af64614855a075eeaec5507958cc9fe1dff4d054ac0f2b","observation_id":"a10933dc-794b-474d-93d5-1532299d8313","resolution":{"observed_at":"2026-05-23T13:45:40.043326Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f35eaed0-6981-456f-a503-e4c20e2e4fb0","year":null},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:596a8a72286db23387f9d38ef0f4792d9fa6735308f3fba4ac2a15e7c45cfa91","observation_id":"6ed8e36e-8770-4406-9076-6bf00355f7ac","resolution":{"observed_at":"2026-05-23T13:45:40.027141Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4064/ap211108-28-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"29ff8212-5f19-4b0b-a7db-51754b78cb05","year":2022},"citing_paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-09T23:00:14.881779Z"},"links":{"citing_paper":"/paper/2604.20330"},"observation_digest":"sha256:7112260bd145b69470abadcff87103b64295f04f96a0a335f77fc18cbc9b6e83","observation_id":"9424c479-63b0-41b6-9327-c379e008bd19","resolution":{"observed_at":"2026-05-09T23:04:17.402389Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-11T06:31:22.384518+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.20330","last_updated":"2026-04-22T08:24:15Z","latest_version":1,"primary_category":"math.CV","snapshot_observed_at":"2026-07-06T23:06:49.210284Z","submitted_at":"2026-04-22T08:24:15Z","title":"Composition operators and Rational Inner Functions on the bidisc: A geometric approach"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":5,"verified_fuzzy":29},"total_outbound_references":34},"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":"2026-07-11T06:31:22.384518+00:00","source":"crossref"},{"observed_at":"2026-07-11T06:31:17.797779+00:00","source":"retraction_watch"}],"thesis":"As of 11 July 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2604.20330."}