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More precisely, we show that the operator $$ BHC_{[\\vec{a},\\vec{\\alpha}]}(f_1,f_2)(x) := \\sup_{\\lambda\\in\\mathbb{R}} \\left|\\,p.v.\\, \\int_{\\mathbb{R}} f_1(x - a_1 t^{\\alpha_1}) \\,f_2(x - a_2 t^{\\alpha_2}) \\,e^{i\\,\\lambda\\,a_3 \\,t^{\\alpha_3}} \\,\\frac{dt}{t}\\right|$$ obeys the bounds $$\\|BHC_{[\\vec{a},\\vec{\\alpha}]} (f_1,f_2)\\|_{L^r} \\lesssim_{\\vec{a} \\,\\vec{\\alpha},r,p_1,p_2} \\|f_1\\|_{L^{p_1}}\\,\\|f_2\\|_{L^{p_2}}$$ whenever "},"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":"2507.04467","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-07-06T17:11:44Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"383e0b91ba595fc1bd4d94bea2cacc73f5d842687bcf2a75d53d28bdac17d193","abstract_canon_sha256":"1746b42a8ba38d0fd3e4f4fe8a74473d7239dea9e2e188f9d08bbd5ef76ba03f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:48.574407Z","signature_b64":"2ktI/mLUNBmLWMJ7rf/50twyTikHyGEpHT6RZidZ3xGrLJSzjCkwzNqgGTO7wYTQS9hYZl4srrFAvJCuF408Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f7561af7919e9f3cf3b7f8434f7f795fa2fa3f6198f75672d1546ea05e07344","last_reissued_at":"2026-07-05T11:32:48.573895Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:48.573895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bilinear Hilbert-Carleson operator along curves. 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