{"as_of":"2026-08-12T23:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4f4e87a162f33a26d8d59d4dd81ac11a8548cb599d0c5ae3976be97ffd5501eb","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T07:34:21.417572Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T15:54:06.134420Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.12663","snapshot_observed_at":"2026-08-01T15:54:06.134420Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.18160","last_updated":"2026-07-22T17:48:18Z","snapshot_observed_at":"2026-08-06T17:56:08.821103Z","submitted_at":"2026-07-20T17:04:10Z","title":"Discrete analogues in harmonic analysis: Multi-parameter Radon averages","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-01T15:54:06.134420Z"},"links":{"cited_paper":"/paper/2606.12663","citing_paper":"/paper/2607.18160"},"observation_digest":"sha256:d27c5208a913c571558db45634dd25d5481c87464cd3e2eeb139830e38a21fdd","observation_id":"e4b7cb5d-bf51-4115-8e4e-b6b6bc7eabb1","resolution":{"observed_at":"2026-08-01T15:54:06.134420Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.12663/citation-record","integrity":"/paper/2606.12663/integrity","json":"/paper/2606.12663/citation-record.json","paper":"/paper/2606.12663"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:510c4b246dc6ba60344fe516e3fc72c55efc6256ac908b78f5e72ac8e90de2b6","observation_id":"b919342c-3cd3-4ac9-b3a4-17033ef8eaca","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Birkhoff","venue":null,"work_id":null,"year":1931},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:8dd3fd9f8b73b6ca4bd6ddeff09292a9d8ffe7a26643e9d76b0c7ac0dc16fe2d","observation_id":"4ae1b24f-e50d-4652-8eb5-24b9996d1ec0","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Bourgain","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:f9904151c7181590bea4f6fc71616ff1d5d64aed5a7badc68690808f0ae0e3b9","observation_id":"9c1a8989-908f-41e5-b689-f7324d34d648","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Bourgain","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:8814f689b12fa1fafebbb770637ecf16a0f69ec48e6de7322c1642cb1f7015d2","observation_id":"56034563-440a-4804-9685-bc1c5bb44c2e","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Bourgain","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:1ffebe3b103b37d9b65ac02e673af5fa11c576a94d66cb04820412e4e60fe41c","observation_id":"06eeaefd-41a5-4831-bdae-fae378296f0a","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Buczolich, R.D","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:bb60fa5b5b854faac2b88b3bff56ec4310c8ec9a0b2e810c6ac224530f303297","observation_id":"ac6a3bc6-5e7d-4df4-a35e-ea8776a2e8a1","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Calder\\' o n","venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:6ef042d4851cc7fc5f353b1ca592521a99a981508a04e53487cc754777a5539d","observation_id":"ff739b32-7086-4ba1-8489-4113a6e62509","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Duoandikoetxea, J.L","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:cffe95e289ad606449cbcb667a1d2cd1331edd77023b1e511139f74f747b5a21","observation_id":"b775d9a8-dc13-430f-9e96-dc639db4bac8","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Furstenberg","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:05a471cf69f6815f9abe1c381e45beed3277661d5312719dc82609cc1a433a39","observation_id":"f579cf4d-d28a-4064-ad94-53d0f7e5fee5","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Furstenberg","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:2105a5be47d8f8eac8e95563a2c7b153c58cea3906ccb1c399121ef6d1873e51","observation_id":"8165275a-906b-473a-8277-a64fe877e2e4","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Ionescu, S","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:3822455f1f5bdeb1b7a5f1492982db3335f7bcce48d5316028958a960d1f023e","observation_id":"393d9aeb-5512-44e8-a73a-e063ce8d7a75","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Iwaniec, E","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:fcae1c151857e0f13fb341e0c65eb59c1186e274440b0704be39974c642a3bb2","observation_id":"f89c58dc-6e59-4ada-8dad-22c9b89e247f","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Jones, A","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:5ef3f4e30ce30d3ef8318db12eb29e31d50136fbe0faf9ec7cbbcfd443c0ce54","observation_id":"559e3a77-dfd9-4f9d-ac21-c6488a3cfe67","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:895fdcee777235a572b144e6b4f6d6ed2f0e38f721af5dd9a69ce1d8c9266bd0","observation_id":"8993713d-fe55-4bcf-a699-3d9df102e27c","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","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":"2411.09478","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-03T13:48:20.805438Z","title":"A MULTIDIMENSIONAL SZEMER ´EDI THEOREM 31","venue":null,"work_id":"d151f36b-8e3a-482f-8f61-83c4dd29ecbf","year":null},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:600c0bf9ca8f985dd82d7ec904fcff72fc5d478adc3c5377dc0f9eab2caf0056","observation_id":"ab01b79d-3967-404c-b42e-2b5c07536df4","resolution":{"observed_at":"2026-07-03T13:48:20.806737Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"LaVictoire","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:91cf07545ac20f884bbfb5d5adf8ea4860ced19c69f4d2c3a0f71cbe77e6e3c2","observation_id":"272adab0-d2b1-4372-bf44-f3971a3b002f","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Magyar, E.M","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:43133e6cb207cd2d304af48d6887b6dd64d5e08275153d8879865a67e9686b84","observation_id":"0ea5fa9d-f697-4de8-ac35-1975fdb2f7c5","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:ccaa043c5c8a1a7ad1cbfb1dad74d96e32ff4c37cd57561613e11b0b1dea047f","observation_id":"a6af2309-5b98-47a6-9623-c4c0266645e4","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","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":"2602.11344","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-03T13:48:20.808369Z","title":"To appear in theProceedings of the International Congress of Mathematicians","venue":null,"work_id":"ee068886-cc50-4956-b9a9-46963ca993ca","year":null},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:8581545456e49607ae7cb9bb9b1b163efba57ad91691e7c7c0a2c80f82efd313","observation_id":"7eb3c448-0700-4128-a623-314535a59e68","resolution":{"observed_at":"2026-07-03T13:48:20.809872Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Mirek, W","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:f6e9e0d2dbe1a51d2a46fa6ccd833fe7706f0338fa713f758294045139b4f70e","observation_id":"771d4466-b2d4-4ead-94b8-1bf722fd8b1d","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Mirek, E.M","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:ca8d6800f88d96b4ed9835e0a227948b9318c77fc2cc46a045f4c53fb5be8a72","observation_id":"07b7feb9-4e82-4aa7-8c2f-2831bb184970","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Mirek, E.M","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:7a5cda70d82eb2d8dd9f0a34f0e3f9849040ce9124c3dc94ff5691723042f6c4","observation_id":"8c6d9843-0581-49b0-af31-57987ad8d616","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Mirek, E.M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:8f72d7d85f07b3540fb61571b658d47335b0ad913411ab20bf857cd0a473916d","observation_id":"b3874e5e-9c79-4a8f-ab43-fababbd10c89","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Mirek, E.M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:06bee350dbf0dc066ae8c77fda39c800a2f194db1c1bc2c47d2101b777403259","observation_id":"cb8d77db-ae2b-4168-9d8e-aef6ed6dbb21","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Mirek, E.M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:e59a4f3c4991f6ef14ee6236e369dcf85dd8f13dcde89925bb6c00c99b7739fe","observation_id":"ee3879b6-c741-4fe2-91b0-08e36b751131","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Nathanson","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:2ab5e2d651ad374f022c2145c059233d57821c488ad25848d68f7ea9dbd95f16","observation_id":"c84d7810-bde6-48d0-b308-8606c21cc663","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:3ff0a0ad00b4dca923b92b28546ca61f42c38a1981f6eb3b66b1f229da750864","observation_id":"5875fb80-d7dc-4275-a97d-6dc95e76d866","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Rosenblatt, M","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:5232be5827ec7132dc099f9cfbfd6bd3f913ada3d9c3a099e012e5d89b02c603","observation_id":"863ca192-4be6-4d59-92e7-292388776a4d","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:5ea5837ca253c7d5c97af0f0b5c625646a24b14bf9c015a6e8a5e9a74418f52d","observation_id":"de83b66e-b1dc-4fd8-a08f-6064a3308876","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:65b897051729b1afb0c9fc4050010eae247ee621c23a3847fcdad4ea9dc392a3","observation_id":"d2c2b625-a6c1-401e-a3dc-774e46bd631d","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:de40deddc84a271239af80e6a233b50c5e4571706172b6cad3ad8734c46e2c60","observation_id":"552dcdfc-bea4-4519-acbc-5c8d6f09b09f","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:7838fa4f6acb251d093d54ed10177338bc38f292e08fadf3a3b36384be9734dc","observation_id":"620c1d12-3dc0-4b38-80ad-c05c2cc94db5","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:7a403a731783ca520112f69bb221b60d3cd9712838a021d2f62f0a6ac0f39626","observation_id":"a808d295-bdb7-4060-82b3-7559349ee1b6","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"Vinogradov","venue":null,"work_id":null,"year":1954},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:9033440add2b8d33310d9326dc95fed5491f1f31ad9e655f433d8392beff97a7","observation_id":"e18d5760-7293-4f99-8509-f1fb7adcb9bd","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":"von Neumann","venue":null,"work_id":null,"year":1932},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:e2d063a64719fd33c628d923fd243fccc3bbc9ef6bf19ccdf0a0f4a0994f3d8f","observation_id":"01db9e27-dc1e-4305-b50f-117f35849e38","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":1916},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:ee7aa358e8cd59b5a45bd4248fd109dd572460394aa435fca54846f693199fe5","observation_id":"199c8bd2-5713-4aa4-8cf2-a64ac606c7e1","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T07:34:21.417572Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-06-27T07:34:21.417572Z"},"links":{"citing_paper":"/paper/2606.12663"},"observation_digest":"sha256:bea622830310e564389b97fc7bc6a2ad5f490b82f4a2110848b32e2a9ea69f23","observation_id":"504b6972-ff5e-409b-813a-d95633ea9766","resolution":{"observed_at":"2026-06-27T07:34:21.417572Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.12663","last_updated":"2026-06-10T20:45:53Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-06T22:09:00.855342Z","submitted_at":"2026-06-10T20:45:53Z","title":"Remarks on the Ionescu-Wainger multiplier theorem"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":35,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":37},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2606.12663."}