{"as_of":"2026-08-13T17:25:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3540552c580b23f436aeccedbcb4ebe952cd254c67d209e4e1ee405f7b43b497","coverage":[{"denominator":57,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":57,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T11:12:46.092251Z","state":"measured"},{"denominator":57,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":57,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2506.03783/citation-record","integrity":"/paper/2506.03783/integrity","json":"/paper/2506.03783/citation-record.json","paper":"/paper/2506.03783"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:12:46.801697Z","title":"Agmon, L","venue":null,"work_id":"5eaa4122-b32f-4dc4-8633-fa73c46fad91","year":1976},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.916238Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:f1393c14e477aaf8962e02e8805230207db34bfd297baada481df57c3a105ff5","observation_id":"fbd6df39-f2d9-43b2-8de9-130d06299285","resolution":{"observed_at":"2026-08-07T11:12:46.804635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.793314Z","title":null,"venue":null,"work_id":"5d084f47-ea9c-4b6c-9cd8-3038fec18567","year":2011},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.920057Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:80464df38c3d7a819dca40c3ef6152a7255302f06b6be5f062fa1ee7375d4090","observation_id":"2c11272c-b036-42fd-a413-98ce2df3c0cd","resolution":{"observed_at":"2026-08-07T11:12:46.796122Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.784454Z","title":"Baernstein, II and M","venue":null,"work_id":"4f6a00af-214b-40a2-b109-cff206596216","year":1997},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.923477Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:61ec6f13a6de5b5affa4ff718405e4f2795d7e9997a5936dfbb2ab780c92aed2","observation_id":"cdc77972-dc10-4b14-a6b6-6ec9f11dcaaf","resolution":{"observed_at":"2026-08-07T11:12:46.787703Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.775678Z","title":null,"venue":null,"work_id":"55e0a7df-4d8c-4029-a019-0a299bf5c0d3","year":2008},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.926980Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:6d5c6dff11c6e80a0f9769a1e3ac76d0efc593ec0d97534c9b652c423905ef1c","observation_id":"6e17811d-93fd-4056-8827-2f7a2362b643","resolution":{"observed_at":"2026-08-07T11:12:46.778558Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.766556Z","title":null,"venue":null,"work_id":"83fe27ee-8a01-4ece-88d8-f21013af01b4","year":1997},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.930396Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:cbcdb234831526e5b15e0238f4f61f5903abd6526748e195715677909b8243e2","observation_id":"a5db0326-e686-4c36-9eaf-e3bfd07c414f","resolution":{"observed_at":"2026-08-07T11:12:46.769628Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.756725Z","title":"Bennett, N","venue":null,"work_id":"82e67691-11ea-43b3-8477-b2cda4ae444d","year":2014},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.933812Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:9d27980fa4d642eade4c69cf6093720f6d45a70349a5f10f0e5967f2ed70739d","observation_id":"62176ad4-57ee-4b57-8c41-19116d506f14","resolution":{"observed_at":"2026-08-07T11:12:46.760008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.746601Z","title":"Bennett, A","venue":null,"work_id":"325ce5af-c785-4b6c-b0a9-84eb454a6415","year":2006},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.937545Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:6ef5b9e8ea639ef8f1cfa3b0322c502c82dd02dde72bca762d28ae0809bcdd7a","observation_id":"94834efe-a599-40c2-a6e2-272749e42cf1","resolution":{"observed_at":"2026-08-07T11:12:46.749637Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2406.14886","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T11:12:46.336239Z","title":"Bennett, S","venue":null,"work_id":"da9901f2-09e0-4d15-80ba-c1ec552734cf","year":null},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.940664Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:df7839e98ec794186021525de68c8363297f4383af5196924e27dcd4a05448f0","observation_id":"028ad6a4-9b47-4455-8815-b7ff249ec91f","resolution":{"observed_at":"2026-08-07T11:12:46.341767Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.737678Z","title":"Bennett, S","venue":null,"work_id":"bfc34598-a644-460c-b0f5-4b640b257358","year":2021},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.944006Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:a099ef2dcf427d086820f2ae1833b9d0780bb75ee9a06e2df8a527079f2822fd","observation_id":"2bcbb751-e6fa-4dc6-9dd5-e5c8e795be3f","resolution":{"observed_at":"2026-08-07T11:12:46.740677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.727654Z","title":"Bennett, S","venue":null,"work_id":"c4e52f3b-415c-456b-882b-563153fbd764","year":2024},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.947155Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:772fb1e1355d335221a3b155f465e10fb9b851c53203557b160da673558aef93","observation_id":"59bbea7f-f1cc-467d-84f5-68bffe31e31e","resolution":{"observed_at":"2026-08-07T11:12:46.731250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.718735Z","title":"Bennett, T","venue":null,"work_id":"c455b7d5-1c01-47bd-8b6d-252efe974054","year":2024},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.950220Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:dc0c68e60fb6f4b15d4d3a4f0eea11097a471ac969e16e024228ef16514d036a","observation_id":"bc78ce60-716f-46a4-9457-ca2295bf2463","resolution":{"observed_at":"2026-08-07T11:12:46.721712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.709667Z","title":null,"venue":null,"work_id":"891a1ebf-3342-4fb9-8f74-406596c5effb","year":2020},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.953412Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:6013743102a006469c4ac96545af4b001f0835f7e8e2e4630fb805555a38f0f4","observation_id":"4f93585e-0a89-4331-bc2d-ce3dc08ea4ca","resolution":{"observed_at":"2026-08-07T11:12:46.712522Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.06137","last_updated":"2025-03-12T13:44:52Z","snapshot_observed_at":"2026-08-10T23:50:33.615321Z","submitted_at":"2025-02-10T03:55:11Z","title":"A Counterexample to the Mizohata-Takeuchi Conjecture","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.06137","snapshot_observed_at":"2026-08-07T11:12:45.956734Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.956734Z"},"links":{"cited_paper":"/paper/2502.06137","citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:7ee2a8b07e202d75bbcb3f21f2442d19ee955942f6fe0837cfeb8f7361f2017c","observation_id":"cc62f8ed-556f-43d8-98e3-b73755f894f0","resolution":{"observed_at":"2026-08-07T11:12:45.956734Z","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":"2026-08-07T11:12:46.701125Z","title":"Carbery, M","venue":null,"work_id":"8ef87ae3-1cfe-463a-916a-02739d60380d","year":2024},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.960618Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:671943e75f29494d167d0192bcabc0cb63cbac3499b64223869cc3844979e224","observation_id":"3fc75597-d8cb-4ac7-a059-f030a9dce68d","resolution":{"observed_at":"2026-08-07T11:12:46.703950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.692496Z","title":"Carbery, F","venue":null,"work_id":"b3a57996-7c13-490d-b488-1b3d94a35358","year":1997},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.963826Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:3806240e6bf86629c7aa0d7da068ca45f775383776fd813f2179a21ca7909e32","observation_id":"e13c955f-55fb-4eae-b3df-1575e735c24f","resolution":{"observed_at":"2026-08-07T11:12:46.695355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.683517Z","title":"Castella, B","venue":null,"work_id":"b7a93b3b-c2ad-4d50-a17b-e99731532094","year":1996},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.966812Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:794648b6c11c4ad1a6372ba55e03d91776b0878d0cc31d55c5a7919fad05e6b8","observation_id":"c54e79ca-ea20-4117-939a-e3db142144d5","resolution":{"observed_at":"2026-08-07T11:12:46.686407Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.674790Z","title":null,"venue":null,"work_id":"fe704eda-0650-46f0-8841-ba7edd6a08f3","year":2017},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.969974Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:9347de1c234cb485c0f86436c466c2810ee4b8703ad75a0879fbef49b288d5b2","observation_id":"4f35dfb4-8b0c-4da9-8fdd-adfcd5a66485","resolution":{"observed_at":"2026-08-07T11:12:46.677755Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.665446Z","title":null,"venue":null,"work_id":"6d5d27c9-7d99-49c4-9842-fb8b01c47d67","year":2018},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.973089Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:914226997a3d8a135fa02e32bcb67fe0cfad6822953449693ec57577e7df935d","observation_id":"f2b3bbb0-f72a-43a1-a83a-c615c5bd837f","resolution":{"observed_at":"2026-08-07T11:12:46.668474Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.655611Z","title":"Christ,Estimates for thek-plane Transform, Indiana U","venue":null,"work_id":"f6ee43a2-64fb-49ec-83a5-0f20fcff749c","year":1984},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.976252Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:0fa916154345e47ac2bfefedb76293bbb8016acd69cfdde56cc26c4ecc895ff6","observation_id":"8fd9a337-52a4-4f14-b10a-50ad78d742da","resolution":{"observed_at":"2026-08-07T11:12:46.658561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.646511Z","title":"Colton, R","venue":null,"work_id":"30e8d97c-3766-40c3-9958-89007278f26c","year":1992},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.979131Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:0d9eec484235b2691b52acd6191a48fa66eccf75de1eef77c8032975a33414a7","observation_id":"77b623d2-60d0-410d-b580-912749b705a7","resolution":{"observed_at":"2026-08-07T11:12:46.649635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.637016Z","title":"Dendrinos, A","venue":null,"work_id":"fc1c3b0d-95ff-441c-baeb-39b66afcfcf7","year":2025},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.982272Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:33614dec77ef63f99b8868a579d1c5946197d35664694186cd12d75a218c26e5","observation_id":"bf2a590e-405f-43d1-b0b5-8e3689bb85a4","resolution":{"observed_at":"2026-08-07T11:12:46.640500Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.627835Z","title":null,"venue":null,"work_id":"5dcd48b2-ef43-46f4-8e49-9005d6a26ebd","year":1983},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.985280Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:d0b8eec944fc441f632fe10d91dbc59c3097614b242ae09c31c2f2b0059672fd","observation_id":"86c1b0b0-bf75-4fb9-aa46-76ec3eda56ac","resolution":{"observed_at":"2026-08-07T11:12:46.630864Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.618537Z","title":null,"venue":null,"work_id":"ce2967c7-0822-49cc-a4f3-e5df0ee2af45","year":2021},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.988282Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:f898580e3a1a865b32b943fb7d8a3a73357c6cd2bb487ded3aed50d8b23ce03c","observation_id":"9d780012-d8fd-4fe6-9b40-cc01a14d4666","resolution":{"observed_at":"2026-08-07T11:12:46.621700Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.10951","last_updated":"2024-04-16T23:27:37Z","snapshot_observed_at":"2026-08-13T00:28:43.673649Z","submitted_at":"2024-04-16T23:27:37Z","title":"$L^p$ weighted Fourier restriction estimates","version":1},"cited_work":{"arxiv_id":"2404.10951","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.10951","snapshot_observed_at":"2026-08-07T11:12:46.248221Z","title":"$L^p$ weighted Fourier restriction estimates","venue":"math.CA","work_id":"4484bd57-cc8f-4fd2-b77b-fddcdad90899","year":2024},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.991256Z"},"links":{"cited_paper":"/paper/2404.10951","citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:49ae36dbd5ea7390e9c4937ee95288f21bfef8f7e4310736c5adedb449fe16b3","observation_id":"245e95f3-97a7-413e-a587-9b6f63382f26","resolution":{"observed_at":"2026-08-07T11:12:46.251974Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.04501","last_updated":"2023-09-08T03:49:03Z","snapshot_observed_at":"2026-08-13T10:18:08.347623Z","submitted_at":"2023-09-08T03:49:03Z","title":"Weighted refined decoupling estimates and application to Falconer distance set problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.04501","snapshot_observed_at":"2026-08-07T11:12:45.994608Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.994608Z"},"links":{"cited_paper":"/paper/2309.04501","citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:a96bb4265489384278f98c57d5bdcc6948cb53925084d14ebca1c4f6033666b4","observation_id":"d1928558-c877-4e97-8753-2de4c319a531","resolution":{"observed_at":"2026-08-07T11:12:45.994608Z","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":"2026-08-07T11:12:46.608659Z","title":null,"venue":null,"work_id":"2b5f68b7-657e-4d01-82f1-6b432b4a64f5","year":2019},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:45.997907Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:c90dc443cf1af3c88b3aacc047ba7be016bb3eeb58eca4b9ed3480c6c4da77ef","observation_id":"b12c11c6-a6c6-4964-afcc-795e6dbdeb5c","resolution":{"observed_at":"2026-08-07T11:12:46.612298Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.599455Z","title":null,"venue":null,"work_id":"719d72a9-b3f9-49b4-871b-3d35cb5ca657","year":1967},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.000671Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:cac12edd7107e88cc24c316b7aadd2b4d5af44b4425c46416feeb7cfd59949e0","observation_id":"4794be8d-af82-4531-ba03-d05f4e6c8816","resolution":{"observed_at":"2026-08-07T11:12:46.602584Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.590317Z","title":null,"venue":null,"work_id":"fbf26c75-cc83-489b-8f05-f6287893f7df","year":1968},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.003667Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:e27f9d4f9b2a653388ae70aea8e765b5438d25c127e8656484b4b934eed60177","observation_id":"6612461b-903a-444e-a484-663dc4f64c31","resolution":{"observed_at":"2026-08-07T11:12:46.593393Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.580955Z","title":"Fefferman, E","venue":null,"work_id":"4f32ec35-ea6f-4399-90fe-d1cb69bd820b","year":1972},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.006606Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:599b844e10f2f23ce85193e3a426e6339367e10391d2863c1f3f0b144f695836","observation_id":"e7bd4752-19ee-4d34-87d0-a78f4e2ccb42","resolution":{"observed_at":"2026-08-07T11:12:46.583979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.571912Z","title":null,"venue":null,"work_id":"cec3b5d6-1245-444b-9b53-c6d93f90feeb","year":1989},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.009548Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:a373dab2245cbc09901729966085c96351c8fe52674d11fb4138227328017327","observation_id":"f15f14f7-0b41-40f5-a321-aedafa3d7dbc","resolution":{"observed_at":"2026-08-07T11:12:46.574722Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.562336Z","title":"Forbes, M","venue":null,"work_id":"30d8a0d6-79f7-4a15-9cf3-7abf2a2104e4","year":2021},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.012494Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:1cca78903f7e977f22785f18d2be2d50486a45170d145efdd4325ff715f39e6a","observation_id":"bee3e7f1-1a6d-4533-954c-1a951ffcde7f","resolution":{"observed_at":"2026-08-07T11:12:46.565801Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.552930Z","title":null,"venue":null,"work_id":"6e4614ea-c321-4417-ae3c-7a8c350add56","year":2021},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.015539Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:3e68776646fcf3ba5bd5da6ceabad1ea0e86201a927bc8a838483c71239e8ae6","observation_id":"eff83d22-b946-453b-961d-0a0b3b9e7ad9","resolution":{"observed_at":"2026-08-07T11:12:46.555833Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.543938Z","title":null,"venue":null,"work_id":"6ba37b89-65c5-488a-b78c-b5654d3b2a0a","year":2014},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.019105Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:ad7436da6cd3cae5f5ea328d278c7877726567ccff2a6b47e62c0521047545d9","observation_id":"41c31bd9-9204-4698-ba30-53557bcfc89c","resolution":{"observed_at":"2026-08-07T11:12:46.546854Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.535010Z","title":null,"venue":null,"work_id":"b5adfa6d-646b-4eea-a2eb-2098b01a4b4b","year":2017},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.022409Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:016df253be2cf4ad7474ff60f9013e4705f835195c1c48f292a1d54e4aad1fcb","observation_id":"d1e049b7-19f1-4e0b-89be-46dfbca3e5e8","resolution":{"observed_at":"2026-08-07T11:12:46.537987Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.525740Z","title":"Frank and J","venue":null,"work_id":"f4b6732f-d43e-4ad1-a6c4-29736eb340f1","year":2015},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.025205Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:e5e5a351687947463b21da3cc441fbb40af3da7c6ddcf0e97af34d40397547f4","observation_id":"7cd377d1-434e-4ad6-b0e4-3ee35b749d16","resolution":{"observed_at":"2026-08-07T11:12:46.529058Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.09924","last_updated":"2026-06-03T22:29:57Z","snapshot_observed_at":"2026-08-10T18:53:01.086612Z","submitted_at":"2025-03-13T00:42:46Z","title":"Velocity Averaging for the Wigner Kinetic Equation in the Semiclassical Regime","version":2},"cited_work":{"arxiv_id":"2503.09924","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.09924","snapshot_observed_at":"2026-08-07T11:12:46.219257Z","title":"Velocity Averaging for the Wigner Kinetic Equation in the Semiclassical Regime","venue":"math.AP","work_id":"f6f99183-360c-4730-9427-2834618d6207","year":2025},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.028198Z"},"links":{"cited_paper":"/paper/2503.09924","citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:21953b05a4288ffb9b7c0cba0b5f932aa35fc65428e6f224fa43c2994978f77f","observation_id":"5a3588fa-d030-47bf-9987-aa62978d6c5f","resolution":{"observed_at":"2026-08-07T11:12:46.224767Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.516512Z","title":"de Gosson, The Wigner Transform, Advanced Textbooks in Mathematics, World Scientific 2017","venue":null,"work_id":"b9491acc-028a-4e6a-be2a-0cd67273421c","year":2017},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.031684Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:2ed0a41fcaba2f67bfaef348b8960af3250f0c645c21aa686054e1552769f29b","observation_id":"558aee81-f11a-4e72-91ec-a92250cd7fb7","resolution":{"observed_at":"2026-08-07T11:12:46.519749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.507460Z","title":null,"venue":null,"work_id":"01ba5c72-7fad-486e-a758-add0c825b3cb","year":2024},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.034651Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:fc1446804ef0ee9b2270dcea5dd5ee4e47538a8ca847f426ac158afa4bc37393","observation_id":"9855aaf6-0d9f-4206-abef-9aa2f7f6dcf3","resolution":{"observed_at":"2026-08-07T11:12:46.510422Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.498594Z","title":null,"venue":null,"work_id":"8c84a38c-4057-42f1-b1b1-c3ea11049de9","year":2007},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.037595Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:534d3f1857e7225bc1f375d5ba63244f4c3f105421cc5ef6a1cdb21a2bb627af","observation_id":"e0080a7d-634a-47d7-80d6-2bb1c3e0b7bc","resolution":{"observed_at":"2026-08-07T11:12:46.501608Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.489046Z","title":"Hickman, J","venue":null,"work_id":"7cc6bf44-f0af-4f0a-bd54-813e5cd6a4fe","year":2024},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.040332Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:758dc3a490b32241eef0035ebb3bb24963f96bc8270cf8f7ce5849172647d114","observation_id":"7d53f661-189c-4332-8457-e4c642138574","resolution":{"observed_at":"2026-08-07T11:12:46.492523Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.479562Z","title":null,"venue":null,"work_id":"17e58ee2-6a2f-47bf-9acc-49a0950d59eb","year":1998},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.043104Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:f21e390680f15e1b12971e1bfc00d16fbe3346a5d9d009102eb6c8cef5abe47b","observation_id":"f77d6e33-eebf-42e2-86c0-b605105992f6","resolution":{"observed_at":"2026-08-07T11:12:46.482367Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.469216Z","title":null,"venue":null,"work_id":"a4c0da99-349b-4898-9104-c6c8fbebddd2","year":1998},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.045999Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:7b38628d19fd0a6e32a4a3d65fa4093510178fd78e6943555db15e59ef7dae7e","observation_id":"cf4f86b2-2860-4caf-8e42-75c5b5bec987","resolution":{"observed_at":"2026-08-07T11:12:46.472712Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.459656Z","title":null,"venue":null,"work_id":"23cbc4ab-f221-4fb8-b44c-731fdf53b600","year":1998},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.049000Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:58f736f568bae2ddd88ff4e32d74c3130c1dcebd7195c7d7bdb2b6c15debf2ff","observation_id":"fab1b4b3-a872-48f4-ade8-d6417003241e","resolution":{"observed_at":"2026-08-07T11:12:46.462576Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.450336Z","title":"Lerner,Integrating the Wigner distribution on subsets of the phase space, Mem","venue":null,"work_id":"b1a44295-044f-4408-8c2f-cf3d27bfbd9b","year":2024},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.052156Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:eaa536ef27b6118ae049f0fa4c1de9b9f3f895428fc717895ac2eddcfad88ec7","observation_id":"1a9997b2-1725-4de8-829a-0b01c654422b","resolution":{"observed_at":"2026-08-07T11:12:46.453516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.441177Z","title":"Lewin, J","venue":null,"work_id":"500f0b72-9c99-442f-aa27-3556bf569800","year":2015},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.055300Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:55add94a181a35cdae1caf6a24d3f91626e5777f0f4159146087d2d17adc9a04","observation_id":"3af0d32a-b2ab-4648-9f95-5da571df71c7","resolution":{"observed_at":"2026-08-07T11:12:46.444232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.431890Z","title":"Lewin, J","venue":null,"work_id":"ffc81d34-32d8-49ac-b95e-e9a1d10ac862","year":2014},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.058299Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:e7c9c583b02432be0600e219991c1b6d07eb5f34cca6d9b28576378db0ea5a72","observation_id":"ee9ecbb4-d652-49bf-aea9-76d4cbf3201b","resolution":{"observed_at":"2026-08-07T11:12:46.434891Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.422487Z","title":null,"venue":null,"work_id":"b04970cb-e2b3-4151-bb59-a3dc08746418","year":1990},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.061535Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:fe1a083ac908238f6e1f24b5eaf69046e7a1cd8925145297052012225311f149","observation_id":"df9e5008-9a5c-4d47-875e-68f04e61a00b","resolution":{"observed_at":"2026-08-07T11:12:46.425635Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.412735Z","title":null,"venue":null,"work_id":"1a996b83-ea3c-4bda-815c-471b73a0cf92","year":1975},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.064470Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:9dfc3fc26fef31af2c5c386f29fba97cbdb69fda3171893fe0b66ccbbb8e16da","observation_id":"d7782953-3b72-42bf-9646-c209f44d5d3e","resolution":{"observed_at":"2026-08-07T11:12:46.415966Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.05624","last_updated":"2025-06-05T22:57:16Z","snapshot_observed_at":"2026-08-07T10:11:27.413838Z","submitted_at":"2025-06-05T22:57:16Z","title":"Random Constructions for Sharp Estimates of Mizohata-Takeuchi Type","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.05624","snapshot_observed_at":"2026-08-07T11:12:46.067652Z","title":"Mulherkar,Random Constructions for Sharp Estimates of Mizohata–Takeuchi Type, arXiv:2506.05624","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.067652Z"},"links":{"cited_paper":"/paper/2506.05624","citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:9ef0c79894e6960bb03f711947ba929f60a7a5584b27d45f6c59990449313531","observation_id":"9f8d0313-591a-43da-9590-b8d1e29baf4c","resolution":{"observed_at":"2026-08-07T11:12:46.067652Z","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":"2026-08-07T11:12:46.403026Z","title":null,"venue":null,"work_id":"2045ecad-3105-41b4-9d3b-0299dcd3df18","year":1987},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.071580Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:f1e431a92d522ddc2b25803ac46cecc549f4131b99ef7a34c4a86b523fe91fe7","observation_id":"5b8e0403-0e1a-4bb7-805f-0042011d2ba7","resolution":{"observed_at":"2026-08-07T11:12:46.406586Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.074549Z","title":"Ortiz,A sharp weighted Fourier extension estimate for the cone inR 3 based on circle tangencies, arXiv:2307.11731","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.074549Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:03d3e67ded4444e77f1d24aaa04c756653662f86daf502f481d43ffc2b8540f0","observation_id":"eebaa5e5-d8ad-479f-986d-3fddcecbe5a7","resolution":{"observed_at":"2026-08-07T11:12:46.074549Z","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":"2026-08-07T11:12:46.392080Z","title":"Sabin,The Hartree equation for infinite quantum systems, Journ´ ees ´ equations aux d´ eriv´ ees partielles, (2014), Exp","venue":null,"work_id":"f27981bb-9b4a-4ec4-b972-742423a001ab","year":2014},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.077552Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:632619b44b941dac9facdaa721ce2f192fc1fd5f643466e99b3e039825beec00","observation_id":"d951b277-4b3f-4e78-98c6-7ad5f8f91274","resolution":{"observed_at":"2026-08-07T11:12:46.395804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.380430Z","title":"Shayya,Mizohata–Takeuchi estimates in the plane, Bull","venue":null,"work_id":"354ed3c0-64ba-4e2a-b17d-9837808c9e9b","year":2023},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.080695Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:021110f1b5114f82af8517b6e10d81d0ad5c87c2c0f30f80aa094e7df07cbca6","observation_id":"8853f34a-5ae5-4f75-8a2e-aabb5911c54f","resolution":{"observed_at":"2026-08-07T11:12:46.384031Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.369915Z","title":"Stovall,Waves, Spheres, and Tubes","venue":null,"work_id":"77c4a66b-621e-414b-9359-616e8eaaff4a","year":2019},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.083688Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:b8496de61bde4bc7b3e8c477d6b3d9de0649303b0ad75992628d59d0c6740cc0","observation_id":"021a96f9-f3c1-4640-b293-031ea4675cd8","resolution":{"observed_at":"2026-08-07T11:12:46.373387Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.359237Z","title":null,"venue":null,"work_id":"c15133b9-b578-4c50-a312-e2a21ff2e904","year":1981},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.086730Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:3db663e7c49b36bfa2b21eb85b6b7542f6ae8f84d6f45f2bfb7fe55f5f47b11d","observation_id":"cca3a42e-7543-4471-8254-2c0c8bb50007","resolution":{"observed_at":"2026-08-07T11:12:46.362904Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-07T11:12:46.348599Z","title":"Wigner,On the Quantum Correction For Thermodynamic Equilibrium, Phys","venue":null,"work_id":"f8324291-9b40-4406-8ac8-62b9aeda8638","year":1932},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.089403Z"},"links":{"citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:f4b3c388d6cb1596861623764e002610374a26894fe5e852b3032e11f6d4b68f","observation_id":"289d3e22-c1e6-4a7b-90e3-0349a4f405fb","resolution":{"observed_at":"2026-08-07T11:12:46.351811Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.02650","last_updated":"2025-06-03T09:02:12Z","snapshot_observed_at":"2026-08-09T05:14:27.050909Z","submitted_at":"2025-06-03T09:02:12Z","title":"Weighted $L^2$ estimates with applications to $L^p$ problems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.02650","snapshot_observed_at":"2026-08-07T11:12:46.092251Z","title":"Wu,WeightedL 2 estimates with applications toL p problems, arXiv:2506.02650","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems","version":3},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T11:12:46.092251Z"},"links":{"cited_paper":"/paper/2506.02650","citing_paper":"/paper/2506.03783"},"observation_digest":"sha256:56b3e6cbb4671c99459b6230e41ca5e7f1b58f269d5e17fa1832799a2f582258","observation_id":"52903d7b-25a6-436b-9069-07c84818e6d2","resolution":{"observed_at":"2026-08-07T11:12:46.092251Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2506.03783","last_updated":"2026-07-20T14:39:44Z","latest_version":3,"primary_category":"math.CA","snapshot_observed_at":"2026-08-13T05:50:13.642463Z","submitted_at":"2025-06-04T09:44:17Z","title":"Mizohata-Takeuchi inequalities for orthonormal systems"},"reference_resolution":{"displayed":57,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":29,"verified_exact":3,"verified_fuzzy":25},"total_outbound_references":57},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2506.03783."}