{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:VHGBTXI7P3OV7GIR6GICDUNSHP","short_pith_number":"pith:VHGBTXI7","schema_version":"1.0","canonical_sha256":"a9cc19dd1f7edd5f9911f19021d1b23bd2d3ac9c18cf7986093aed8be2e4e81e","source":{"kind":"arxiv","id":"2210.05851","version":2},"attestation_state":"computed","paper":{"title":"A dichotomy for H\\\"ormander-type oscillatory integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Hong Wang, Ruixiang Zhang, Shaoming Guo","submitted_at":"2022-10-12T01:25:11Z","abstract_excerpt":"In this paper, we first generalize the work of Bourgain and state a curvature condition for H\\\"ormander-type oscillatory integral operators, which we call Bourgain's condition. This condition is notably satisfied by the phase functions for the Fourier restriction problem and the Bochner-Riesz problem. We conjecture that for H\\\"ormander-type oscillatory integral operators satisfying Bourgain's condition, they satisfy the same $L^p$ bounds as in the Fourier Restriction Conjecture. To support our conjecture, we show that whenever Bourgain's condition fails, then the $L^{\\infty} \\to L^q$ boundedne"},"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":"2210.05851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-10-12T01:25:11Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0c4ea322ffed04c3c3b691d1d99770e806a835820be977504fd55d6e306401c3","abstract_canon_sha256":"308cc43403555fc29bf719c6dc49cccc066e630f927b9311ec9ec4cd7c034300"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:38:29.384648Z","signature_b64":"/p/eIwAECC2N/vmCBspNhkAq9MupRQ41KI4e/dOdSNSA3tPhbUzlQIIIuUja/AfvWYCuCjzUYdmgy3U0jqPsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9cc19dd1f7edd5f9911f19021d1b23bd2d3ac9c18cf7986093aed8be2e4e81e","last_reissued_at":"2026-07-05T05:38:29.384146Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:38:29.384146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A dichotomy for H\\\"ormander-type oscillatory integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Hong Wang, Ruixiang Zhang, Shaoming Guo","submitted_at":"2022-10-12T01:25:11Z","abstract_excerpt":"In this paper, we first generalize the work of Bourgain and state a curvature condition for H\\\"ormander-type oscillatory integral operators, which we call Bourgain's condition. This condition is notably satisfied by the phase functions for the Fourier restriction problem and the Bochner-Riesz problem. We conjecture that for H\\\"ormander-type oscillatory integral operators satisfying Bourgain's condition, they satisfy the same $L^p$ bounds as in the Fourier Restriction Conjecture. To support our conjecture, we show that whenever Bourgain's condition fails, then the $L^{\\infty} \\to L^q$ boundedne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.05851","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.05851/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2210.05851","created_at":"2026-07-05T05:38:29.384201+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.05851v2","created_at":"2026-07-05T05:38:29.384201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.05851","created_at":"2026-07-05T05:38:29.384201+00:00"},{"alias_kind":"pith_short_12","alias_value":"VHGBTXI7P3OV","created_at":"2026-07-05T05:38:29.384201+00:00"},{"alias_kind":"pith_short_16","alias_value":"VHGBTXI7P3OV7GIR","created_at":"2026-07-05T05:38:29.384201+00:00"},{"alias_kind":"pith_short_8","alias_value":"VHGBTXI7","created_at":"2026-07-05T05:38:29.384201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.08871","citing_title":"Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP","json":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP.json","graph_json":"https://pith.science/api/pith-number/VHGBTXI7P3OV7GIR6GICDUNSHP/graph.json","events_json":"https://pith.science/api/pith-number/VHGBTXI7P3OV7GIR6GICDUNSHP/events.json","paper":"https://pith.science/paper/VHGBTXI7"},"agent_actions":{"view_html":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP","download_json":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP.json","view_paper":"https://pith.science/paper/VHGBTXI7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.05851&json=true","fetch_graph":"https://pith.science/api/pith-number/VHGBTXI7P3OV7GIR6GICDUNSHP/graph.json","fetch_events":"https://pith.science/api/pith-number/VHGBTXI7P3OV7GIR6GICDUNSHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP/action/storage_attestation","attest_author":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP/action/author_attestation","sign_citation":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP/action/citation_signature","submit_replication":"https://pith.science/pith/VHGBTXI7P3OV7GIR6GICDUNSHP/action/replication_record"}},"created_at":"2026-07-05T05:38:29.384201+00:00","updated_at":"2026-07-05T05:38:29.384201+00:00"}