{"as_of":"2026-08-20T11:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:116f6103e3c71bcd42be26d0c24ae12c273e3c556c98827669ade8c96e298ec7","coverage":[{"denominator":96,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":96,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:27:47.357022Z","state":"measured"},{"denominator":96,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":96,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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/2506.08494/citation-record","integrity":"/paper/2506.08494/integrity","json":"/paper/2506.08494/citation-record.json","paper":"/paper/2506.08494"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:46.914082Z","title":"Anantharam, V","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.914082Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:9b5314618f29f28b8c249f05bd581e04f0090a574ddfb5821ef3de9039f33c3a","observation_id":"4eda2c40-7e3a-4f98-8606-b50843d5f862","resolution":{"observed_at":"2026-08-07T05:27:46.914082Z","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":"2026-08-07T05:27:46.918218Z","title":null,"venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.918218Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:1435db0f5fc310ce665c59ac7815ee1bd06a5b1f249c48a4e931c0d481984cee","observation_id":"a81747c9-8622-4667-bfd3-f6a946abcb3d","resolution":{"observed_at":"2026-08-07T05:27:46.918218Z","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":"2026-08-07T05:27:46.921949Z","title":"Ball : Volumes of sections of cubes and related problems","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.921949Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:fddb948db34dc06515a8ed42321960a8c9c3498787b4dfee53ac2ed4f9a8dd26","observation_id":"7eadbbbb-d003-4a45-ac38-7bca666ca513","resolution":{"observed_at":"2026-08-07T05:27:46.921949Z","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":"2026-08-07T05:27:46.926008Z","title":"Bennett, N","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.926008Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:1c75502d7f82cd9c02a4e59b782961dd8da1cb3cf3c579f9293bfd0ee50705bb","observation_id":"82e70899-19ce-46b3-b552-cfb81c4808a8","resolution":{"observed_at":"2026-08-07T05:27:46.926008Z","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":"2026-08-07T05:27:46.929486Z","title":"Barthe, D","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.929486Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:36bf89725798da14d86453b5fc7cfeb82ce4df9f6d3c0cda7dcce0e18e84eb8d","observation_id":"7c0aeca1-cc68-43e3-989a-108a91dd7795","resolution":{"observed_at":"2026-08-07T05:27:46.929486Z","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":"2026-08-07T05:27:46.933263Z","title":"Barthe, D","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.933263Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:bc04f88f57b32a6233d5c056acedb9e937641477af29a3f8411363a8bda241de","observation_id":"7f6d7f48-324b-4d89-9508-7d73b0ba15b3","resolution":{"observed_at":"2026-08-07T05:27:46.933263Z","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":"2026-08-07T05:27:46.936939Z","title":"Barthe : Optimal Young’s inequality and its converse: a simple proof","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.936939Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:df139fec7307d88b4428657daadf2d81a376b646dfb198715202a1089b0afef0","observation_id":"34860791-b34c-4b5f-95bc-c26f84ec9578","resolution":{"observed_at":"2026-08-07T05:27:46.936939Z","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":"2026-08-07T05:27:46.940239Z","title":"Barthe : On a reverse form of the Brascamp-Lieb inequality","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.940239Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:ca6e54f719b2d80370e417c25e438dad65e9f38a7b7a140b730da295275786cc","observation_id":"ebd1b938-c2ec-4ff6-8e79-779da9782dbd","resolution":{"observed_at":"2026-08-07T05:27:46.940239Z","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":"2026-08-07T05:27:46.944217Z","title":"Barthe, N","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.944217Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:9cb3a87458747e19939ed984b8240c1ebd3da957003f0c7838ab11a949d87c5a","observation_id":"cc076fdb-def6-43ea-be49-969923169501","resolution":{"observed_at":"2026-08-07T05:27:46.944217Z","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":"2026-08-07T05:27:46.947955Z","title":"Barthe, P","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.947955Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:cd0ae6cb6859de1a2ce05d4ac3435d55a712f104eb4fecb5aae0c7f24a419f29","observation_id":"84c3307a-64e3-4fa0-b447-3d4650089dd9","resolution":{"observed_at":"2026-08-07T05:27:46.947955Z","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":"2026-08-07T05:27:46.951714Z","title":"Beckner , Inequalities in Fourier Analysis , Ann.\\ of Math.\\ 102 (1975), no","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.951714Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:30f27b6975a7a168f6701b0927e5460502768f96135f1c06141696385832c193","observation_id":"5d31a053-0e4a-4f31-88c4-648c2632d060","resolution":{"observed_at":"2026-08-07T05:27:46.951714Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.16558","last_updated":"2023-07-14T18:26:04Z","snapshot_observed_at":"2026-08-16T15:20:14.688481Z","submitted_at":"2023-06-28T20:56:47Z","title":"Adjoint Brascamp-Lieb inequalities","version":2},"cited_work":{"arxiv_id":"2306.16558","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.16558","snapshot_observed_at":"2026-08-07T05:27:47.438466Z","title":"Adjoint Brascamp-Lieb inequalities","venue":"math.CA","work_id":"00d21f06-afe7-4a7e-ba40-55f98569ce45","year":2023},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.954998Z"},"links":{"cited_paper":"/paper/2306.16558","citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:84d91e1f0ba17338794a5c2e05eee25e35b7a3d5445898283f3a1cc3ed53d177","observation_id":"7f180c5b-cc72-49b2-8e0a-dbd923737c08","resolution":{"observed_at":"2026-08-07T05:27:47.443971Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:46.959105Z","title":"Bennett, T","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.959105Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:8bb258f73bfdef89ba1f5eeba12ee0ad44c2f035d819e983c118dfc1bbf6b2d7","observation_id":"7526830b-f6b4-41d1-99d9-19562771b46f","resolution":{"observed_at":"2026-08-07T05:27:46.959105Z","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":"2026-08-07T05:27:46.962392Z","title":"Brascamp, E.H","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.962392Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:1788f6482815ca7ab17fc087ee33f7aee3876343c551c6f414de8a2464e411fb","observation_id":"3e5b9b82-5b50-43ab-9666-a997a0cef5f1","resolution":{"observed_at":"2026-08-07T05:27:46.962392Z","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":"2026-08-07T05:27:46.965641Z","title":"Borell , Positivity improving operators and hypercontractivity , Math.\\ Z.\\ 180 (1982), no","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.965641Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:c110c09489361c38755f894af2034e1a6e8e7a5204337d3e35d69798259ed8c9","observation_id":"45e67aa1-82d0-4c8d-859f-58eaa93b6d49","resolution":{"observed_at":"2026-08-07T05:27:46.965641Z","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":"2026-08-07T05:27:46.969013Z","title":"Borell , Geometric bounds on the Ornstein-Uhlenbeck velocity process , Z.\\ Wahrsch.\\ Verw.\\ Gebiete 70 (1985), no","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.969013Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:448936a453e1101ea11bef48a84b6a781f9f1d5dd1d090e99dfdaf64073b8310","observation_id":"6feefa47-0e76-4c2d-8af4-c96ea0aa3dab","resolution":{"observed_at":"2026-08-07T05:27:46.969013Z","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":"2026-08-07T05:27:46.972487Z","title":"Bonami , Étude des coefficients de Fourier des fonctions de L^p(G) , Ann.\\ Inst.\\ Fourier 20 (1970), 335--402","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.972487Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:febef8051bedd5e230e7d4496c348c4a845234d31db5d49a80980cf38fff4a7d","observation_id":"a46f76c4-0a1f-4479-9f1a-1f4492e125b4","resolution":{"observed_at":"2026-08-07T05:27:46.972487Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:48.417603Z","title":null,"venue":null,"work_id":"3b5271ca-8565-498d-9a11-14d284939318","year":1976},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.976236Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:4ada2bb99bb4b9e774cec0ce4517eaf7bee673cda7a5ddabcd3a3bc605467059","observation_id":"1980bbb7-1757-4312-a242-12a5e535e030","resolution":{"observed_at":"2026-08-07T05:27:48.421983Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.405541Z","title":null,"venue":null,"work_id":"4867ac1b-f3c9-423c-aa3e-1e67f220be87","year":2007},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.979932Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:712068393c494f46377e46238b2be66b2cca5213f0966a845cf1b4c3249eba7b","observation_id":"9026b3d8-673e-4c51-83c6-274307bbb61e","resolution":{"observed_at":"2026-08-07T05:27:48.410331Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.389714Z","title":"Carlen, D","venue":null,"work_id":"64f5b9b3-1a9f-417b-a859-4b578628493e","year":2009},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.983954Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:c7c43b4dddb41cf5ebd94ce2c507776e1394a3cee44e275105df1ec91b0b87cd","observation_id":"ed19f5a4-0b62-453d-abfc-bded76179225","resolution":{"observed_at":"2026-08-07T05:27:48.396530Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.377409Z","title":"Carlen, E.H","venue":null,"work_id":"1653d9c5-5570-484b-9c2e-169dae356d7a","year":2004},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.987614Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:4b3327a36cc8bab186800a890c6ae7565d881653f099945845d30fa95d5812ac","observation_id":"b35387a1-a0fa-4a37-8a06-47f8d0470088","resolution":{"observed_at":"2026-08-07T05:27:48.382085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.364500Z","title":"older and reverse H\\","venue":null,"work_id":"955d09f8-d919-48b8-b6a0-be9b14e5b84a","year":2015},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.990855Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:ee1653bf2eaf103957a7a42efc1777c3e0f9bc14f48bdf45a29ad5e9ca8b6049","observation_id":"19101f92-b658-42a8-8aeb-94eee19599b2","resolution":{"observed_at":"2026-08-07T05:27:48.370066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.352611Z","title":"Courtade, J","venue":null,"work_id":"9d5cb5c6-bb7c-4f3c-bb08-42ad623afb0a","year":2021},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.993956Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:38dace0888ed505bc1662396a147001ac0a9c53fb13a4a301de7c8f76439df8d","observation_id":"eca33c2e-f1a6-4aaa-8455-17c455939d04","resolution":{"observed_at":"2026-08-07T05:27:48.357177Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1406.1210","last_updated":"2014-06-04T20:56:17Z","snapshot_observed_at":"2026-08-18T11:52:52.932031Z","submitted_at":"2014-06-04T20:56:17Z","title":"A sharpened Hausdorff-Young inequality","version":1},"cited_work":{"arxiv_id":"1406.1210","doi":null,"metadata_source":"pith","pith_arxiv_id":"1406.1210","snapshot_observed_at":"2026-08-07T05:27:47.420093Z","title":"A sharpened Hausdorff-Young inequality","venue":"math.CA","work_id":"66da0bd8-2194-4794-8a57-194fbf4c5867","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:46.997638Z"},"links":{"cited_paper":"/paper/1406.1210","citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:ec22b8313b8518255dbd2053c510f072dd0fde51157d42fdd97a92452a1f3f58","observation_id":"5ed156d9-45c2-4f29-a437-388151afc75d","resolution":{"observed_at":"2026-08-07T05:27:47.426724Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.338097Z","title":null,"venue":null,"work_id":"80ac827f-e45a-46e4-be34-44a111878244","year":2016},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.001265Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:b89a5a3b0ddc0068077870d9823be330772520e1d95926d28286c7c3e0eb47f8","observation_id":"0649ab5d-1a6a-401d-a196-0d117056f63a","resolution":{"observed_at":"2026-08-07T05:27:48.343141Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.324523Z","title":null,"venue":null,"work_id":"f965e53e-5394-4d54-b7af-1c3b234cae50","year":1989},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.004397Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:57f86f04320e1f6e8e36d1bd5a4b32857d799eeb103f8e6d6d433a513ed0d279","observation_id":"357f98d5-6f0d-459b-967e-ff80277b4f23","resolution":{"observed_at":"2026-08-07T05:27:48.330667Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.309600Z","title":"Eskenazis, P","venue":null,"work_id":"5bc3a289-65a8-47d3-b3e9-521411d068ec","year":2020},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.008395Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:fd41142c34d7527052f84db68cffbd9e470040c141bfeb7a21b77452707a1adf","observation_id":"8edfe8f8-b7be-45af-adf8-0996068816e4","resolution":{"observed_at":"2026-08-07T05:27:48.316008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.294804Z","title":"Eskenazis, P","venue":null,"work_id":"dda5f118-0f37-4a85-aa96-31285315d06c","year":null},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.012847Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:947e4bce6e757fe803ce4396a5aafd12e572df555080e6af09ad30e4e18fa8ea","observation_id":"1c41693b-2929-4da3-84cd-ba25c4eca204","resolution":{"observed_at":"2026-08-07T05:27:48.300686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.282979Z","title":"Eskenazis, P","venue":null,"work_id":"bc43be0f-4805-4929-9040-efa69acc2cc5","year":2020},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.016284Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:e433209f8770eaeafbf272958e69eae433a3593bece43345c683fadab546582e","observation_id":"b0c19964-a14f-42b7-8524-d9da92715313","resolution":{"observed_at":"2026-08-07T05:27:48.287217Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.271469Z","title":"Gross , Logarithmic Sobolev inequalities , Amer.\\ J.\\ Math.\\ 97 (1975), 1061--1083","venue":null,"work_id":"ea53b30b-136f-4c7f-aedb-5a206e48b2c4","year":1975},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.019979Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:84fc208e6b154e3cc814efd845e6571f8eb420ea8c30d50b2795ff070842d1bc","observation_id":"8d16b472-1c02-4abc-845e-086a97224e02","resolution":{"observed_at":"2026-08-07T05:27:48.275851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.259678Z","title":"Hardy, J.E","venue":null,"work_id":"44c22a35-b329-42df-bcbb-611a361be03f","year":1952},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.024145Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:a2cee15d14e278dab1da74493e7987faf425f737eb02a98fb4e526c9b273c376","observation_id":"c5282333-0a27-40a8-9ec1-159b9b06c79e","resolution":{"observed_at":"2026-08-07T05:27:48.263834Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.247093Z","title":"Hariya , A unification of the hypercontractivity and its exponential variant of the Ornstein--Uhlenbeck semigroup , J.\\ Funct.\\ Anal.\\ 275 (2018), no","venue":null,"work_id":"dbc8ef78-7ca0-46b4-b584-f04fc906dbc1","year":2018},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.028192Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:8137c5a44a7572f806e5b318af037ac66398ca137296b9cc92bfc5a5566405c3","observation_id":"7d39057a-f187-48cb-9de6-b2ed0c19f64e","resolution":{"observed_at":"2026-08-07T05:27:48.252071Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.230976Z","title":"Hu , Analysis on Gaussian Spaces , World Scientific Publishing, Singapore, 2016","venue":null,"work_id":"4b27b434-950c-4ae8-959d-fbed940084cf","year":2016},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.034268Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:0dbfeea68c077b10f69f0b35ba4f05c68b616b387361fab8d9d68b21e5ed40be","observation_id":"7be10108-adac-4227-bca7-a61cdb17faf9","resolution":{"observed_at":"2026-08-07T05:27:48.238332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.216370Z","title":"Ivanisvili , Boundary value problem and the Ehrhard inequality , Studia Math.\\ 246 (2019), no","venue":null,"work_id":"000aec17-dfe5-426c-baf4-4f1bf19b5bce","year":2019},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.038996Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:eba3c6d290c3089462884028246ced8f51c95c40b75d6982b8067195c45bacc2","observation_id":"c5a6225b-8b1d-4413-b844-29e65c964627","resolution":{"observed_at":"2026-08-07T05:27:48.223115Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.203749Z","title":"Ivanisvili, F","venue":null,"work_id":"cdf2d1bc-cef4-49aa-9dd3-bbb0a0764ffd","year":2022},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.044191Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:ada12ea1d1116a91596d1ed41a0abbe1f98a69b8031a0b3a21a4ad1346d89726","observation_id":"709f2137-5c18-4ae5-8bc4-7f2ae388638b","resolution":{"observed_at":"2026-08-07T05:27:48.208552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.189576Z","title":"Ivanisvili, T","venue":null,"work_id":"dbe09c33-4834-4d0b-b28b-b70894649b76","year":2019},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.049056Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:f1852bff7a90f0713526af37f78dd097f3154ad29e8473e80e7aefa8afbfb9ab","observation_id":"489e98ce-100d-4cc1-867a-6a029d54e507","resolution":{"observed_at":"2026-08-07T05:27:48.195797Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.178183Z","title":"Ivanisvili, A","venue":null,"work_id":"a371ec52-132f-4e09-9a31-dd61fb7ed6c8","year":2019},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.054062Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:17e32b2f22c0cb3b98f67cd8aae55933d17c4b3df4ad43a2ab8c8335e4e72bb0","observation_id":"5f48e95c-704a-4a4c-83a3-7e1152386900","resolution":{"observed_at":"2026-08-07T05:27:48.182405Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.18053","last_updated":"2024-07-25T14:06:34Z","snapshot_observed_at":"2026-08-16T13:31:05.082065Z","submitted_at":"2024-07-25T14:06:34Z","title":"$(P,Q)$ complex hypercontractivity","version":1},"cited_work":{"arxiv_id":"2407.18053","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.18053","snapshot_observed_at":"2026-08-07T05:27:47.400388Z","title":"$(P,Q)$ complex hypercontractivity","venue":"math.FA","work_id":"8f251901-e850-4eaf-bca3-70e557147a83","year":2024},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.058690Z"},"links":{"cited_paper":"/paper/2407.18053","citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:a0a258938e89f511ccc5e25715e5204cd850fdb44a49ec424ae5fec4ee5a3733","observation_id":"fda964e9-a8dd-42d9-be3c-90e55dcf82c8","resolution":{"observed_at":"2026-08-07T05:27:47.407314Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.166907Z","title":"Ivanisvili, A","venue":null,"work_id":"d4ed4bf8-2fdf-4b25-a6c7-ccc149df2c07","year":2015},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.071227Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:e86f48d8498274cf5f4f5351bb0d315f3885b07815ad5f02cbf69b01d75e2a31","observation_id":"ef0d562b-46ff-4d2a-ac35-924bd1bd312b","resolution":{"observed_at":"2026-08-07T05:27:48.171419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.152726Z","title":"Janson , On complex hypercontractivity , J.\\ Funct.\\ Anal.\\ 151 (1997), no","venue":null,"work_id":"607e5c64-69b4-4a87-8d0e-0c5229b32da9","year":1997},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.076664Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:03bb3c4b0253248df21d5d0a4bcb066eebba97767bf1a2942d692b838c6a0a4f","observation_id":"ed543e91-94cf-405c-831b-26b40f128b09","resolution":{"observed_at":"2026-08-07T05:27:48.159009Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.140024Z","title":null,"venue":null,"work_id":"0714c7d5-cae8-4a82-a476-839dbd92b15f","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.081739Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:f34b7194c51b0aa0eab5d0024b64befc86a3ef27ea6d3c8c429e25a9693410db","observation_id":"db5ae153-16f7-4354-b2be-24409746651d","resolution":{"observed_at":"2026-08-07T05:27:48.144947Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.125969Z","title":"Lehec : Short probabilistic proof of the Brascamp-Lieb and Barthe theorems","venue":null,"work_id":"fa19eff1-0101-4e3b-aa87-ab8c3e82c3ec","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.086910Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:ab6e6b231a4cdcc5ae32307d3142bcee340c690f24b404b2ad0161ebcfc05324","observation_id":"ca2b1b92-56f2-4a74-b1e2-3e246f8ad596","resolution":{"observed_at":"2026-08-07T05:27:48.132320Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.113240Z","title":"Lieb , Gaussian kernels have only Gaussian maximizers , Invent.\\ Math.\\ 102 (1990), no","venue":null,"work_id":"cd15f9eb-3398-44df-81a3-d49832bf8cbb","year":1990},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.091656Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:4f6c8f15f2587ddfe7471929b7dc99abf0562d15e19993019f83985282a31d96","observation_id":"684ed211-a7b9-4af1-9041-e13d065a31ce","resolution":{"observed_at":"2026-08-07T05:27:48.118238Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.098454Z","title":"Mendel, A","venue":null,"work_id":"a55ebae9-d75d-4b6b-98eb-de20dbdb8353","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.097046Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:abd422efea0ef57796e33552e2d628a5690e3975f8097a2ac10b1a4991ca493b","observation_id":"c529db82-a4a2-49a0-8e5b-386f31254446","resolution":{"observed_at":"2026-08-07T05:27:48.103273Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.085553Z","title":"Mossel, R","venue":null,"work_id":"fe5a1e98-0ded-43cb-9f7a-4119cc35efed","year":2010},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.102193Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:37a74b9adef43e16235409e169a4db7226d3498119e86804ac48b020cb5e2080","observation_id":"819ad626-6fab-4942-9a98-e008317060b3","resolution":{"observed_at":"2026-08-07T05:27:48.090479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.073733Z","title":"Mossel, J","venue":null,"work_id":"fe9e7259-ef29-4f9a-aa35-f5d39f3355fc","year":2015},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.107274Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:e14a95801bb162d23a653190096af45ad87cac02b9f2bc6823eb38b99848331e","observation_id":"4f9ff65c-1999-4f70-b55b-d79cb6e4c241","resolution":{"observed_at":"2026-08-07T05:27:48.077905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.059473Z","title":"Neeman , A multidimensional version of noise stability , Electron.\\ Commun.\\ Probab.\\ 19 (2014), no","venue":null,"work_id":"6850e976-494e-4485-b4de-7bdc25e9ba39","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.112599Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:794fd62984b58598f244ebabdd1d7e96c368dd2adde66e3bd28d018d005d9b04","observation_id":"f2462bf0-8817-4a5b-9d73-b7291d78dc7d","resolution":{"observed_at":"2026-08-07T05:27:48.065943Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.046572Z","title":"Neeman, G","venue":null,"work_id":"502c4df3-1d59-4831-ab4c-f4e623ee5a44","year":2016},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.119627Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:42e961d0dd239bec9d4d5c9f33aa5e3c82c74176787b5031e2dc4b9582a63ddc","observation_id":"8a0985be-4695-47f9-86d0-3d33ee4ae3cf","resolution":{"observed_at":"2026-08-07T05:27:48.051521Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.033995Z","title":"Nelson , The free Markoff field , J.\\ Funct.\\ Anal.\\ 12 (1973), 211--227","venue":null,"work_id":"fd93e6e2-fe9c-4e21-ac39-a70f019bb2ac","year":1973},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.124626Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:c246ed74f064dc92903e4f35ebe15b236f60ffcf2f8ca81b94880ae83eddd9ce","observation_id":"862c4e38-4fed-41ad-94cf-ba8db844cbb5","resolution":{"observed_at":"2026-08-07T05:27:48.039102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.019636Z","title":"Weissler , Two-point inequalities, the Hermite semigroup and the Gauss--Weierstrass semigroup , J.\\ Funct.\\ Anal.\\ 32 (1979), 102--121","venue":null,"work_id":"02871de4-47a4-4557-9ae4-7fef9899f067","year":1979},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.130017Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:1ffccd980f58f2c10906a0c8379cd7da08bdfeb75dd5ef8cb4d8fdb3c67c1013","observation_id":"64afa8e9-7f85-4006-9aa4-b3e0f0e05736","resolution":{"observed_at":"2026-08-07T05:27:48.026965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:48.005092Z","title":"Anantharam, V","venue":null,"work_id":"436bc6f6-5418-4722-95b7-b12d14ff9c52","year":2022},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.137188Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:746baf548bc45126345291ae0eeef7dfc714e0fa0a235eab3738e514d3657d53","observation_id":"6be2efad-7455-4829-a712-c69757c27442","resolution":{"observed_at":"2026-08-07T05:27:48.011862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.989745Z","title":"Barthe : On a reverse form of the Brascamp-Lieb inequality","venue":null,"work_id":"a15cf59c-1055-405a-b23c-3ddb344b30c5","year":1998},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.142177Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:cb859aaef8da3e7279af0ab2ce90b686308693e1903a8dd88750fa0b73977734","observation_id":"584b8df3-6846-43cd-9fa3-8ee33385df5b","resolution":{"observed_at":"2026-08-07T05:27:47.997007Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.978335Z","title":null,"venue":null,"work_id":"1da582d9-7b2e-472b-b081-1858a2ef9493","year":1961},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.146593Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:b5811af57932d731d36ab7497182d106d81e9ddf44f72ee0dc87379db5873f5e","observation_id":"8bada225-96f2-403f-8b84-7987c52b8d69","resolution":{"observed_at":"2026-08-07T05:27:47.982690Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.966658Z","title":"Barthe, D","venue":null,"work_id":"7060f92a-2dd7-4276-b630-69878f144f60","year":2004},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.150979Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:2d30f6e3c18ae82dd012f3202c03ef642c015e03592da607b876a17c0c5dcc99","observation_id":"2a16fc79-ead0-4d65-8899-c16b1e4a81ec","resolution":{"observed_at":"2026-08-07T05:27:47.971180Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.955114Z","title":"Barthe, D","venue":null,"work_id":"022c29d0-5fd2-47bc-bc94-5d2982e81e58","year":2011},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.155790Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:0908738abf2da18478cd4974ac0152a7b7cbcb9e25d87ed31f3ff5afe0fca83e","observation_id":"5520dfe0-e850-46b5-8bdd-914c7dc30c32","resolution":{"observed_at":"2026-08-07T05:27:47.959622Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.943268Z","title":"Barthe, N","venue":null,"work_id":"6ddd4d91-4694-49b1-b872-15a0f4709055","year":2009},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.160630Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:b0580c792e634dca73297ef1ca4206e6e219ae0933751b62ff89e19668f46de4","observation_id":"c1a2591d-2b33-48cb-b0a1-25cfc2d48e30","resolution":{"observed_at":"2026-08-07T05:27:47.947653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.932239Z","title":"Barthe, P","venue":null,"work_id":"a7f2bee4-284b-438b-b66e-fa861280c22f","year":2022},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.166076Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:928d58da2368b1ea6d16e63f2f5ba19244cbfa0d049c7fbbcb98a7af4a99a0f8","observation_id":"1004feaf-d2d4-4b1d-94cb-5c15ee433a2f","resolution":{"observed_at":"2026-08-07T05:27:47.936486Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.918323Z","title":"Bannett, T","venue":null,"work_id":"69c4a2c7-aecc-4ef4-acb9-6ae1332c86cb","year":2008},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.172145Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:620f2f243e254a54d4eeca631d640b137e1cc8d8c82449e311cec59840239b07","observation_id":"cf73c70a-24df-406f-9352-75f0de2e902a","resolution":{"observed_at":"2026-08-07T05:27:47.924860Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.906289Z","title":"Borell , Positivity improving operators and hypercontractivity , Math","venue":null,"work_id":"aab028a5-1e4e-4d6a-9d0e-ef692f492a50","year":1982},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.176609Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:a9be9307790373d54ed1d9190d5ce208b213ff1c6157d86365942df2a22c99a8","observation_id":"749f72e5-1912-4352-8a35-3ae3f0044344","resolution":{"observed_at":"2026-08-07T05:27:47.910907Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.892110Z","title":"Borell , Geometric bounds on the Ornstein-Uhlenbeck velocity process , Z","venue":null,"work_id":"a0ce27d8-c992-443d-8ef4-408c79f60fa4","year":1985},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.181389Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:8f6c59f44eec6fe95da1f204f58550b65303388d38c6dbcbb3fedcb1e90c59de","observation_id":"a8252260-f34a-409d-8038-60d25b82412b","resolution":{"observed_at":"2026-08-07T05:27:47.896941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.880063Z","title":"Beckner , Inequalities in Fourier Analysis , Ann","venue":null,"work_id":"f19469de-ddc6-44cc-8d76-42db36f00a99","year":1975},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.185936Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:0c1cdb6e3b6e0e03862577590b8a631cf4198dddcdfcbc5eccd85f5f582878cf","observation_id":"622ba0f8-1723-427a-8bd7-215addc2228a","resolution":{"observed_at":"2026-08-07T05:27:47.884559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.868973Z","title":"Bennett, N","venue":null,"work_id":"e7049752-e9ee-4b6f-a623-dc6c9c6f9a2b","year":2009},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.190631Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:3d60a71d8a0d9a689a5296a28c288ab21ec540843de5d6c938b567f54a3cf1c3","observation_id":"f858993f-a8a8-428a-810c-abd78ea30ecb","resolution":{"observed_at":"2026-08-07T05:27:47.873150Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.858690Z","title":"Bennett, T","venue":null,"work_id":"da8f87dc-a14d-44ad-8942-186461248a4e","year":2008},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.195106Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:fe50b84afd698e5746ca2b04e5fc47368be91ec26a04db6f8e5e00e717318ea2","observation_id":"c2672c8b-d1fa-4921-a87c-74cef8243dd0","resolution":{"observed_at":"2026-08-07T05:27:47.862537Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.847274Z","title":"Brascamp, E.H","venue":null,"work_id":"ebeefc12-3361-4794-a501-946da91a0c73","year":1976},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.199286Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:0b21b7faa0bb4f62b7141a9eec705f99803091ef5940f6243d9f96179d92de5b","observation_id":"cfaaf57b-4945-4a8a-aaa7-6362a9997ec8","resolution":{"observed_at":"2026-08-07T05:27:47.851635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.834248Z","title":"Bonami , \\'Etude des coefficients de Fourier des fonctions de L^p(G) , Ann","venue":null,"work_id":"8ce25a2b-fc76-4c4c-b8b8-a881df02b51e","year":1970},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.204691Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:99588a50a527570efa1b9c11de161b4ee34a2fad953b9568abba3b9fd550462f","observation_id":"fc868bde-bf40-4000-a567-2af8ba7adc05","resolution":{"observed_at":"2026-08-07T05:27:47.839196Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.822923Z","title":null,"venue":null,"work_id":"1ac06372-24a1-429f-902f-f6342a8a8992","year":1976},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.209683Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:8cb983135406ba482b585da0181059b45846dd502d1c3a0b512f494a21e94a08","observation_id":"0d8202c2-574f-4093-b1c4-7ad4f2d352bc","resolution":{"observed_at":"2026-08-07T05:27:47.827445Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.809226Z","title":null,"venue":null,"work_id":"cbe64611-5d9a-4c1f-85f9-e9dd262b940a","year":2007},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.215321Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:705901047e01ef6a0084c7a6242a9742fc8ded4cbfc38300af519be41b6e5071","observation_id":"e3318ddb-ca8d-48b8-8a8b-c7ab07b5d556","resolution":{"observed_at":"2026-08-07T05:27:47.815718Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.797260Z","title":null,"venue":null,"work_id":"3235d1af-c761-43c7-9949-0b6cc3fc6dd3","year":2009},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.220813Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:1fd5169249049bf5e7a29516ec38c93b0f3b337e50bbf97776ed622673d7ec17","observation_id":"8dc45818-d180-4b43-9944-4b0cc865c6ff","resolution":{"observed_at":"2026-08-07T05:27:47.801812Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.784959Z","title":"Carlen, E.H","venue":null,"work_id":"f1c246e9-bf9c-4c9f-8ea0-b1e7941ad17b","year":2004},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.226275Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:48344e42f15ae76408bc90838ecf3f6487d0f3f1c34d543999e68df49b2a7ca5","observation_id":"e973c85d-f4fb-4e5d-9838-a952857db6be","resolution":{"observed_at":"2026-08-07T05:27:47.789475Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.773221Z","title":"older and reverse H\\","venue":null,"work_id":"32cf9636-1a8d-4581-97ab-93f1589fc554","year":2015},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.231446Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:0971c31157a7be3b736856f9c5dbc63d05f94d6af616ff7517dc56cdf8bd79ba","observation_id":"40e615b7-3926-43d6-bd0d-93bcc04b544a","resolution":{"observed_at":"2026-08-07T05:27:47.777777Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.759767Z","title":"Courtade, J","venue":null,"work_id":"9e709f98-000a-43db-a9bd-f363028a5a98","year":2021},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.236864Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:4da784f06ce2195442875785ebf37dbdc12e38e13929298174ce9932e19e7229","observation_id":"07ef2325-c5cc-4c27-bcf8-a999e4d97c60","resolution":{"observed_at":"2026-08-07T05:27:47.765985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.747055Z","title":null,"venue":null,"work_id":"082a0e68-afe2-4deb-8fb4-9196797b9994","year":2016},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.241833Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:542b320754d8b0f1bfa7ef87318bdd4d417b6691f448f96dfc66983eafe14d79","observation_id":"355fd077-7759-4ffe-9951-08f490272e51","resolution":{"observed_at":"2026-08-07T05:27:47.751463Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.734903Z","title":null,"venue":null,"work_id":"dbd3491c-c0c4-4c28-a317-cc9770663472","year":1989},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.246142Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:6988fd2f38981983aa778be35c407732cef1aff78dbbbc1c49d9ba8989ef100e","observation_id":"8f403f34-3f5f-40e9-ad54-368ce53ba341","resolution":{"observed_at":"2026-08-07T05:27:47.739972Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.721073Z","title":"Eskenazis, P","venue":null,"work_id":"d24952e0-a485-456a-9b7d-167fc2dabe1a","year":2020},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.251578Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:dc054bbb114217df7198704302c1c1db18c2a6c41debb209d97fe3c43eeaa37c","observation_id":"5a5d673f-c817-4d64-996e-6bcc2f11bb8c","resolution":{"observed_at":"2026-08-07T05:27:47.726540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.708275Z","title":"Eskenazis, P","venue":null,"work_id":"66dd32a7-acd7-4c08-9ebd-a30522a1d880","year":null},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.257525Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:74e53ff50f0edfb7b301c737a2d2d71282ea20247471a3c9bcb644a8c321e9fa","observation_id":"28d259a4-d368-43c1-be97-bddb88fe2399","resolution":{"observed_at":"2026-08-07T05:27:47.713092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.695871Z","title":"Eskenazis and P","venue":null,"work_id":"17c21eeb-8472-42a5-887c-34a3b29bb0af","year":2020},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.262198Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:dbf5e9e37fb6cbeb80f6bbdfb861e17f53b3d55ba56c95687f7384efc474cf5e","observation_id":"4e6d9a92-06af-451b-acdb-e4f1497d9d3d","resolution":{"observed_at":"2026-08-07T05:27:47.700871Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.683149Z","title":"Gross , Logarithmic Sobolev inequalities , Amer","venue":null,"work_id":"5f6b4f6d-7d96-4bdd-9dc2-6a823d911a48","year":1975},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.266412Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:9f638f59c7bda7f03f2fc75f1e8939356efa61d5e562eb0f3a2404845c150126","observation_id":"1b53bb82-8a07-497b-8dd3-ff95271c2a33","resolution":{"observed_at":"2026-08-07T05:27:47.687823Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.671771Z","title":"Hardy, J.E","venue":null,"work_id":"8bcad6fc-2b9c-43e9-ae78-9ba750651b27","year":1952},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.269975Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:a7e77f75110e2c92c2bed13aba97be4d27c103627950b1a535f694ff34da45e7","observation_id":"a60e0ad2-10a5-47ca-bdb7-9bf140f4a2dd","resolution":{"observed_at":"2026-08-07T05:27:47.676223Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.657510Z","title":null,"venue":null,"work_id":"f6bc7814-a373-4a6f-96e8-5e213f0225a4","year":2018},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.275577Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:dc676909ca4159472b9e2d9d3a8d0d816ce2b85e7ea46b3efe89e1f58caa1696","observation_id":"48a3199b-e330-4edc-ae6e-f19e9861a4ad","resolution":{"observed_at":"2026-08-07T05:27:47.664101Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.645503Z","title":"Ivanisvili , Boundary value problem and the Ehrhard inequality , Studia Math., 246 (2019), no","venue":null,"work_id":"7a2c7bd7-f0d5-4b29-b526-52beb2b619dc","year":2019},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.279722Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:df3c5ee93a0fdd1afe003c496f2f6c34e4297232d733e5cf4e9e168d24161df0","observation_id":"e338beb7-0c32-4d59-a324-828e273bcbf2","resolution":{"observed_at":"2026-08-07T05:27:47.649988Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.632017Z","title":"Ivanisvili, F","venue":null,"work_id":"38be0e93-cb7c-40ad-8186-7a06149e316f","year":2022},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.283631Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:288c896e8484079c5e0d64855f4a68faa71a79684087431e3fdcbbd5e8aa9fe9","observation_id":"87bb20de-b220-4392-9388-b4360e1bcfaf","resolution":{"observed_at":"2026-08-07T05:27:47.638448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.619361Z","title":"Ivanisvili, T","venue":null,"work_id":"8b452350-f7dd-4f94-828c-6c8d4a3daded","year":2018},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.288306Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:e4a59ebcc818867ceddba3677086366612384c6f48e4a8d199a08e3f0abb00a9","observation_id":"c229d4bd-ecc5-4014-b920-53f3ced7408d","resolution":{"observed_at":"2026-08-07T05:27:47.624371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.607440Z","title":"Ivanisvili, A","venue":null,"work_id":"1e2aeb51-a8a5-4217-af31-26a632a2d24a","year":2019},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.293561Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:6fdf1e56f3a5323b3bddbf396276a93de90edab04d468acf3360aeec3690fc28","observation_id":"2201e2f5-83c3-400e-9a1d-d0b5cb215741","resolution":{"observed_at":"2026-08-07T05:27:47.612090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1506.03409","last_updated":"2015-08-13T14:07:12Z","snapshot_observed_at":"2026-08-18T00:30:18.774532Z","submitted_at":"2015-06-10T17:54:24Z","title":"Bellman partial differential equation and the hill property for classical isoperimetric problems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1506.03409","snapshot_observed_at":"2026-08-07T05:27:47.298354Z","title":"Ivanisvili and A","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.298354Z"},"links":{"cited_paper":"/paper/1506.03409","citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:62572c89fdcebb847d35756144743b4a52fc2278f28693d6e499c3ea55ef8a6c","observation_id":"b38a2f2b-9c20-4a25-b60a-7b3e5059244e","resolution":{"observed_at":"2026-08-07T05:27:47.298354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:27:47.595338Z","title":"Ivanisvili and A","venue":null,"work_id":"c2e35aa1-2648-4996-b58f-b356d70c8700","year":2015},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.302554Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:e91a102cf7772ec3332be4e5279983be05e76f8e2d665f15ad35b6a90204ef48","observation_id":"64605c7d-6bdf-40c6-94ff-23b4c377f02a","resolution":{"observed_at":"2026-08-07T05:27:47.599853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.580920Z","title":"Janson , On complex hypercontractivity , J","venue":null,"work_id":"bf88ab11-b847-4dc9-ad7a-b52cd67e362a","year":1997},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.307472Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:f94609999ef7515aa0495e4f87cf6936844a2e900ee698b1e9fd1aec74d511ca","observation_id":"9cda2978-39a8-453f-a4e3-5935d9901ed5","resolution":{"observed_at":"2026-08-07T05:27:47.586920Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.568689Z","title":"Ledoux , Remarks on Gaussian noise stability, Brascamp--Lieb and Slepian inequalities , Geometric Aspects of Functional Analysis, Lecture Notes in Math., 2116 , Springer, 2014, pp","venue":null,"work_id":"84779831-d5ae-4aa2-b73e-4f8d08d15d19","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":88,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.312520Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:4bdbbbca8be0637c80fc5586e0b9e24e69b6915f3b8ddb09c8f7e8978d486a86","observation_id":"cbf127fb-d993-4c4f-8e3d-3f4251fa82b6","resolution":{"observed_at":"2026-08-07T05:27:47.573710Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.556285Z","title":"Lehec : Short probabilistic proof of the Brascamp-Lieb and Barthe theorems","venue":null,"work_id":"05bb7d90-75d4-4847-8c45-80b0884732f4","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":89,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.316725Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:873aec84adc4ea3599a740d5412be295761e306255f1d3651b72f44f4adcdfd1","observation_id":"f6feb621-112e-4ec8-9fd2-c2d587f4d87d","resolution":{"observed_at":"2026-08-07T05:27:47.560808Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.544147Z","title":null,"venue":null,"work_id":"026b6a49-4188-4156-92d5-307db98a3b76","year":1990},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":90,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.321885Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:c7f69b97f2b9e4bb553c5e694897ba143fbca9ca128e755819beb69186cd6487","observation_id":"d1cfa39d-d4a5-481d-9025-c1cb148942bf","resolution":{"observed_at":"2026-08-07T05:27:47.548810Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.529581Z","title":"Mendel, A","venue":null,"work_id":"269d1eab-f413-45f2-9486-fd4c137ed711","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":91,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.326770Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:41d876d1910f75dd6d4c099e007ff4379c38e00051c9e523a493f81dda2f1c63","observation_id":"1e67a6d6-1737-432a-a254-da21e17cbcce","resolution":{"observed_at":"2026-08-07T05:27:47.536351Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.516904Z","title":"Mossel, R","venue":null,"work_id":"264bfe9a-6405-44ce-9173-8bfe9ef15da5","year":2010},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":92,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.331904Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:6d5ac85e01ec73fdf5769e71b87c33e71a02f6ede42aeb12afbb2af1268baf9c","observation_id":"eed5ecb3-b127-48b4-9993-d032cc2a77ed","resolution":{"observed_at":"2026-08-07T05:27:47.521692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.504212Z","title":"Mossel and J","venue":null,"work_id":"5e4ef823-c71e-4181-89f9-6cdbb7212148","year":2015},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":93,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.337783Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:3c73171ce671cfb44f6203327c0c8c0d9d554d984b67c4ff765e1cfcafdcd908","observation_id":"e2172390-6a3f-4512-9037-0832c4d135c0","resolution":{"observed_at":"2026-08-07T05:27:47.509228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.491649Z","title":"Neeman , A multidimensional version of noise stability , Electron","venue":null,"work_id":"727da7ad-f505-4860-ad37-07ce1c0e2988","year":2014},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":94,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.342516Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:e6ab04440ea3d4db866d7ecc19305cf07933b95f1d66f91f66b4e229554a0d79","observation_id":"1cba2322-b313-486c-ba84-0bd02e742a11","resolution":{"observed_at":"2026-08-07T05:27:47.496582Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.478207Z","title":"Neeman and G","venue":null,"work_id":"8dd9d6bc-2a9f-4205-9591-be3d9804d414","year":2016},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":95,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.347521Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:ecc8a802643edfa6e72f1000ecc550f1bda156d0ca8823fa4905cdc84bf5bae5","observation_id":"4e52f07c-a338-4cc5-bae8-843153562215","resolution":{"observed_at":"2026-08-07T05:27:47.483347Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.464418Z","title":"Nelson , The free Markoff field , Journal of Functional Analysis, vol","venue":null,"work_id":"be304ce9-fb5b-4ff6-a714-a6c8dc3f8c19","year":1973},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":96,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.352119Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:d44f539d33aa4538820afba1d17b7804f0ce5e1654b8f83b0ba469b52fe1406a","observation_id":"12734c48-2fcc-40e9-a136-28aa41133910","resolution":{"observed_at":"2026-08-07T05:27:47.469790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-07T05:27:47.451800Z","title":null,"venue":null,"work_id":"6d2d7dd5-45e8-4e2c-a7ff-b304c23c13fe","year":1979},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":97,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.357022Z"},"links":{"citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:0e941f49c545d57eff1d656d9f0bb0a6edb908c7253f9e728298b9baa0068408","observation_id":"6960ca7a-9908-421c-8b72-cb1d3785e4f7","resolution":{"observed_at":"2026-08-07T05:27:47.456368Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality"},"reference_resolution":{"displayed":96,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":31,"verified_exact":3,"verified_fuzzy":62},"total_outbound_references":96},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 96 of 96 outbound references and 0 inbound Pith citation observations for arXiv:2506.08494."}