{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:S3P7PAYPQBXPS3CCTD2SSR25KL","short_pith_number":"pith:S3P7PAYP","schema_version":"1.0","canonical_sha256":"96dff7830f806ef96c4298f529475d52f3d83908a02f3c39a6c9d9ac94006c75","source":{"kind":"arxiv","id":"1511.04948","version":2},"attestation_state":"computed","paper":{"title":"Multiple Vector Valued Inequalities via the Helicoidal Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Camil Muscalu, Cristina Benea","submitted_at":"2015-11-16T13:12:28Z","abstract_excerpt":"We develop a new method of proving vector-valued estimates in harmonic analysis, which we like to call \"the helicoidal method\". As a consequence of it, we are able to give affirmative answers to some questions that have been circulating for some time. In particular, we show that the tensor product $BHT \\otimes \\Pi$ between the bilinear Hilbert transform $BHT$ and a paraproduct $\\Pi$ satisfies the same $L^p$ estimates as the $BHT$ itself, solving completely a problem introduced in a paper of Muscalu, Pipher, Tao and Thiele. Then, we prove that for \"locally $L^2$ exponents\" the corresponding vec"},"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":"1511.04948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-11-16T13:12:28Z","cross_cats_sorted":[],"title_canon_sha256":"c64befb412423aeab68038d9ef4482fe0d7e6b50f4ec530926faa631947bc335","abstract_canon_sha256":"5d2ea840d486029e1106921a425df85a1c533c9bafccd8538874be21b7a76fe9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:09.570443Z","signature_b64":"jdxHpBRUGdFga62vlVq/VdKheRPAJd9vg/6WYGyNZ1CzhLK7Peminpzx1s54pjrlsBOwoB+sJRiNQv1zi/00CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96dff7830f806ef96c4298f529475d52f3d83908a02f3c39a6c9d9ac94006c75","last_reissued_at":"2026-05-18T00:52:09.569860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:09.569860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple Vector Valued Inequalities via the Helicoidal Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Camil Muscalu, Cristina Benea","submitted_at":"2015-11-16T13:12:28Z","abstract_excerpt":"We develop a new method of proving vector-valued estimates in harmonic analysis, which we like to call \"the helicoidal method\". As a consequence of it, we are able to give affirmative answers to some questions that have been circulating for some time. In particular, we show that the tensor product $BHT \\otimes \\Pi$ between the bilinear Hilbert transform $BHT$ and a paraproduct $\\Pi$ satisfies the same $L^p$ estimates as the $BHT$ itself, solving completely a problem introduced in a paper of Muscalu, Pipher, Tao and Thiele. Then, we prove that for \"locally $L^2$ exponents\" the corresponding vec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04948","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":""},"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":"1511.04948","created_at":"2026-05-18T00:52:09.569932+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.04948v2","created_at":"2026-05-18T00:52:09.569932+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04948","created_at":"2026-05-18T00:52:09.569932+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3P7PAYPQBXP","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3P7PAYPQBXPS3CC","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3P7PAYP","created_at":"2026-05-18T12:29:39.896362+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/S3P7PAYPQBXPS3CCTD2SSR25KL","json":"https://pith.science/pith/S3P7PAYPQBXPS3CCTD2SSR25KL.json","graph_json":"https://pith.science/api/pith-number/S3P7PAYPQBXPS3CCTD2SSR25KL/graph.json","events_json":"https://pith.science/api/pith-number/S3P7PAYPQBXPS3CCTD2SSR25KL/events.json","paper":"https://pith.science/paper/S3P7PAYP"},"agent_actions":{"view_html":"https://pith.science/pith/S3P7PAYPQBXPS3CCTD2SSR25KL","download_json":"https://pith.science/pith/S3P7PAYPQBXPS3CCTD2SSR25KL.json","view_paper":"https://pith.science/paper/S3P7PAYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.04948&json=true","fetch_graph":"https://pith.science/api/pith-number/S3P7PAYPQBXPS3CCTD2SSR25KL/graph.json","fetch_events":"https://pith.science/api/pith-number/S3P7PAYPQBXPS3CCTD2SSR25KL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3P7PAYPQBXPS3CCTD2SSR25KL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3P7PAYPQBXPS3CCTD2SSR25KL/action/storage_attestation","attest_author":"https://pith.science/pith/S3P7PAYPQBXPS3CCTD2SSR25KL/action/author_attestation","sign_citation":"https://pith.science/pith/S3P7PAYPQBXPS3CCTD2SSR25KL/action/citation_signature","submit_replication":"https://pith.science/pith/S3P7PAYPQBXPS3CCTD2SSR25KL/action/replication_record"}},"created_at":"2026-05-18T00:52:09.569932+00:00","updated_at":"2026-05-18T00:52:09.569932+00:00"}