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Furthermore, we compute the Fourier dimension of the multiplicative $\\psi$-well approximable set $$M_2^{\\times}(\\psi)=\\left\\{(x_1,x_2)\\in [0,1]^{2}\\colon \\|qx_1\\|\\|qx_2\\|<\\psi(q) \\text{ for infinitely many } q\\in \\N\\right\\},$$ where $\\psi\\colon\\N\\to [0,\\frac{1}{4})$ is a positive function satisfying $\\sum_q\\psi(q)\\log\\frac{1}{\\psi(q)}<\\infty.$ As a corollary, we show that the set $M_2^{\\times}(q\\mapsto q^{-\\tau})$ is non-Salem for $\\tau>1.$"},"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":"2409.12557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-19T08:25:43Z","cross_cats_sorted":[],"title_canon_sha256":"5ae46944a666f9b4dc982206e5980817339d9d00994aaa8d87f72fc40998d1ae","abstract_canon_sha256":"9d50df8be7a22e212a54d4acc62f81fd54c4a8f203dadc9019f4af962f439b5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:08.794165Z","signature_b64":"9AeAUQrKqB8VWg8+mpBeQ6OOCylgO1uYbBevB7OnNHT4swOg6wJUO6Jp1ksE3B9DcCGUgkJ/ZLw6fuBuReMVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3178c1eb7ee068b98018c47c39f88bf91fc94bec8ca0f1326d0f4dd0a56cf1e7","last_reissued_at":"2026-07-05T09:09:08.793655Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:08.793655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Salem sets in multiplicative Diophantine approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bo Tan, Qing-Long Zhou","submitted_at":"2024-09-19T08:25:43Z","abstract_excerpt":"In this paper, we answer a question of Cai-Hambrook in (arXiv$\\colon$ 2403.19410). 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