{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TQNQLQNR2YCJ5GSCJSZQ4IF2RU","short_pith_number":"pith:TQNQLQNR","schema_version":"1.0","canonical_sha256":"9c1b05c1b1d6049e9a424cb30e20ba8d1f99b3d38cab40b3cbb96a04c42513ce","source":{"kind":"arxiv","id":"1505.03882","version":1},"attestation_state":"computed","paper":{"title":"A polynomial Carleson operator along the paraboloid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"L. B. Pierce, Po-Lam Yung","submitted_at":"2015-05-14T20:37:33Z","abstract_excerpt":"In this work we extend consideration of the polynomial Carleson operator to the setting of a Radon transform acting along the paraboloid in $\\mathbb{R}^{n+1}$ for $n \\geq 2$. Inspired by work of Stein and Wainger on the original polynomial Carleson operator, we develop a method to treat polynomial Carleson operators along the paraboloid via van der Corput estimates. A key new step in the approach of this paper is to approximate a related maximal oscillatory integral operator along the paraboloid by a smoother operator, which we accomplish via a Littlewood-Paley decomposition and the use of a s"},"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":"1505.03882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-14T20:37:33Z","cross_cats_sorted":[],"title_canon_sha256":"9c3dfe5aa7e07ffeee8fc161590cbcf43645ac602c27ec712e040cb276ffe8e4","abstract_canon_sha256":"f2f06a3421b0715558fb8f8ff5d2d2b539d2788a70392cf83487997f2422b7de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:00.889291Z","signature_b64":"QPGVLeCVj411pEO6jjKjw9/5Q/kmppwKgE6QutKZUpC8zp3W5bHE5ib8ICTTUUJZBQmekeugBZ5DXMx0Fh/TCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c1b05c1b1d6049e9a424cb30e20ba8d1f99b3d38cab40b3cbb96a04c42513ce","last_reissued_at":"2026-05-18T02:04:00.888404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:00.888404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A polynomial Carleson operator along the paraboloid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"L. B. Pierce, Po-Lam Yung","submitted_at":"2015-05-14T20:37:33Z","abstract_excerpt":"In this work we extend consideration of the polynomial Carleson operator to the setting of a Radon transform acting along the paraboloid in $\\mathbb{R}^{n+1}$ for $n \\geq 2$. Inspired by work of Stein and Wainger on the original polynomial Carleson operator, we develop a method to treat polynomial Carleson operators along the paraboloid via van der Corput estimates. A key new step in the approach of this paper is to approximate a related maximal oscillatory integral operator along the paraboloid by a smoother operator, which we accomplish via a Littlewood-Paley decomposition and the use of a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03882","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":"1505.03882","created_at":"2026-05-18T02:04:00.888556+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03882v1","created_at":"2026-05-18T02:04:00.888556+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03882","created_at":"2026-05-18T02:04:00.888556+00:00"},{"alias_kind":"pith_short_12","alias_value":"TQNQLQNR2YCJ","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TQNQLQNR2YCJ5GSC","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TQNQLQNR","created_at":"2026-05-18T12:29:42.218222+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/TQNQLQNR2YCJ5GSCJSZQ4IF2RU","json":"https://pith.science/pith/TQNQLQNR2YCJ5GSCJSZQ4IF2RU.json","graph_json":"https://pith.science/api/pith-number/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/graph.json","events_json":"https://pith.science/api/pith-number/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/events.json","paper":"https://pith.science/paper/TQNQLQNR"},"agent_actions":{"view_html":"https://pith.science/pith/TQNQLQNR2YCJ5GSCJSZQ4IF2RU","download_json":"https://pith.science/pith/TQNQLQNR2YCJ5GSCJSZQ4IF2RU.json","view_paper":"https://pith.science/paper/TQNQLQNR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03882&json=true","fetch_graph":"https://pith.science/api/pith-number/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/graph.json","fetch_events":"https://pith.science/api/pith-number/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/action/storage_attestation","attest_author":"https://pith.science/pith/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/action/author_attestation","sign_citation":"https://pith.science/pith/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/action/citation_signature","submit_replication":"https://pith.science/pith/TQNQLQNR2YCJ5GSCJSZQ4IF2RU/action/replication_record"}},"created_at":"2026-05-18T02:04:00.888556+00:00","updated_at":"2026-05-18T02:04:00.888556+00:00"}