{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PWXTJWDUEMK5PVXBVGY3LDVE4W","short_pith_number":"pith:PWXTJWDU","schema_version":"1.0","canonical_sha256":"7daf34d8742315d7d6e1a9b1b58ea4e5bd96ff768fccf863aef7d867b7469cff","source":{"kind":"arxiv","id":"1605.00574","version":1},"attestation_state":"computed","paper":{"title":"Variational estimates for the bilinear iterated Fourier integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Camil Muscalu, Christoph Thiele, Yen Do","submitted_at":"2016-05-02T17:29:57Z","abstract_excerpt":"We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator, the bilinear Hilbert transform, the variation norm Carleson operator, and the bi-Carleson operator. Terry Lyon's rough path theory allows for extension of our result to multilinear estimates. We consider our result a proof of concept for a wider array of similar estimates with possible applications to ordinary differential equations."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.00574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-02T17:29:57Z","cross_cats_sorted":[],"title_canon_sha256":"b6619b684d790b6c7092c6f6b5ff1ea180327b8409cb7c7280fe7c1b1940a6ec","abstract_canon_sha256":"f241f30bc4e90c5d5d1de7b88fdfe1172ff8bc661c1f69f72f0c957a9e2ffb9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:53.840657Z","signature_b64":"RRovbLJHBV2ho4/B5Mjy+oMbDWkGss56JcCnIH3ohsIjW7c7p6nczGW6ydewqlPXKY4G0jUgqjvuTmvVCN6sBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7daf34d8742315d7d6e1a9b1b58ea4e5bd96ff768fccf863aef7d867b7469cff","last_reissued_at":"2026-05-18T01:15:53.839938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:53.839938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variational estimates for the bilinear iterated Fourier integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Camil Muscalu, Christoph Thiele, Yen Do","submitted_at":"2016-05-02T17:29:57Z","abstract_excerpt":"We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator, the bilinear Hilbert transform, the variation norm Carleson operator, and the bi-Carleson operator. Terry Lyon's rough path theory allows for extension of our result to multilinear estimates. We consider our result a proof of concept for a wider array of similar estimates with possible applications to ordinary differential equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00574","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.00574","created_at":"2026-05-18T01:15:53.840044+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.00574v1","created_at":"2026-05-18T01:15:53.840044+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00574","created_at":"2026-05-18T01:15:53.840044+00:00"},{"alias_kind":"pith_short_12","alias_value":"PWXTJWDUEMK5","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PWXTJWDUEMK5PVXB","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PWXTJWDU","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W","json":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W.json","graph_json":"https://pith.science/api/pith-number/PWXTJWDUEMK5PVXBVGY3LDVE4W/graph.json","events_json":"https://pith.science/api/pith-number/PWXTJWDUEMK5PVXBVGY3LDVE4W/events.json","paper":"https://pith.science/paper/PWXTJWDU"},"agent_actions":{"view_html":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W","download_json":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W.json","view_paper":"https://pith.science/paper/PWXTJWDU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.00574&json=true","fetch_graph":"https://pith.science/api/pith-number/PWXTJWDUEMK5PVXBVGY3LDVE4W/graph.json","fetch_events":"https://pith.science/api/pith-number/PWXTJWDUEMK5PVXBVGY3LDVE4W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W/action/storage_attestation","attest_author":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W/action/author_attestation","sign_citation":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W/action/citation_signature","submit_replication":"https://pith.science/pith/PWXTJWDUEMK5PVXBVGY3LDVE4W/action/replication_record"}},"created_at":"2026-05-18T01:15:53.840044+00:00","updated_at":"2026-05-18T01:15:53.840044+00:00"}