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Montes-Rodr\\'iguez on Heisenberg Uniqueness Pairs for perturbed lattice crosses.\n  The first of them deals with a complete characterization of $\\beta>0$ for which, for a fixed $\\theta \\in \\mathbb{R},$ the translated lattice cross $\\Lambda_{\\beta}^{\\theta} = ((\\mathbb{Z} + \\{\\theta\\}) \\times \\{0\\}) \\cup (\\{0\\} \\times \\beta \\mathbb{Z})$ satisfies that $(\\Gamma,\\Lambda_{\\beta}^{\\theta})$ is a Heisenberg Uniqueness Pair, where $\\Gamma$ is the hyperbola in $\\mathbb{R}^2$ with axes as asymptotes. We show that $(\\Gamma,\\Lambda_{\\beta}^{"},"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":"2410.04557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-06T17:25:52Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"83c73047175d81311d4922da44de8d91955651e0815437766a7783a6d791e4be","abstract_canon_sha256":"5dacd5cd3de010edcdf082b9c4fc06ce11c73aaaa13982fc5f78604933755fe6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:16:35.995597Z","signature_b64":"CmrrjffRIhLELkx3uF09nyyijJW/l6KYMAkxXfRJmxZsg/BnSeBT0xCCqPjDIdgIeEPeuw1s46/Rxd3mWZerBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c2ac9e79caf4d6e23f6827189608d1b8f399ac23a44fd3a40d5c7c70991bab2","last_reissued_at":"2026-07-05T09:16:35.995073Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:16:35.995073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbed lattice crosses and Heisenberg uniqueness pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Danylo Radchenko, Jo\\~ao P. G. Ramos","submitted_at":"2024-10-06T17:25:52Z","abstract_excerpt":"This work focuses on two questions raised by H. Hedenmalm and A. Montes-Rodr\\'iguez on Heisenberg Uniqueness Pairs for perturbed lattice crosses.\n  The first of them deals with a complete characterization of $\\beta>0$ for which, for a fixed $\\theta \\in \\mathbb{R},$ the translated lattice cross $\\Lambda_{\\beta}^{\\theta} = ((\\mathbb{Z} + \\{\\theta\\}) \\times \\{0\\}) \\cup (\\{0\\} \\times \\beta \\mathbb{Z})$ satisfies that $(\\Gamma,\\Lambda_{\\beta}^{\\theta})$ is a Heisenberg Uniqueness Pair, where $\\Gamma$ is the hyperbola in $\\mathbb{R}^2$ with axes as asymptotes. 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