{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DQVMTZ44V5GW4I7WQJYYSYENDO","short_pith_number":"pith:DQVMTZ44","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"},"canonical_sha256":"1c2ac9e79caf4d6e23f6827189608d1b8f399ac23a44fd3a40d5c7c70991bab2","source":{"kind":"arxiv","id":"2410.04557","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.04557","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"2410.04557v1","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.04557","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"DQVMTZ44V5GW","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"pith_short_16","alias_value":"DQVMTZ44V5GW4I7W","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"pith_short_8","alias_value":"DQVMTZ44","created_at":"2026-07-05T09:16:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DQVMTZ44V5GW4I7WQJYYSYENDO","target":"record","payload":{"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"},"canonical_sha256":"1c2ac9e79caf4d6e23f6827189608d1b8f399ac23a44fd3a40d5c7c70991bab2","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"},"source_kind":"arxiv","source_id":"2410.04557","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5i/8EXKpCyNAaETVnRy7t3o06O8tdWfBUCTyFEKwgIsZaRjzHbiFyOqAR26uUN0rpRzoINvZeWvY42Tw8BtlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T20:47:42.244845Z"},"content_sha256":"9b4273fa4bb44e6179ef59dd917bbbbc84f21dab54903e0fc6da818333c35e87","schema_version":"1.0","event_id":"sha256:9b4273fa4bb44e6179ef59dd917bbbbc84f21dab54903e0fc6da818333c35e87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DQVMTZ44V5GW4I7WQJYYSYENDO","target":"graph","payload":{"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. We show that $(\\Gamma,\\Lambda_{\\beta}^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.04557","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.04557/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T/ePxHzvyrjijJy+iMPkTcEiJkJCSREtM61v4cteNPG/CU7Wi72qonyZ7oRgL36UQ+q7GJ0ZRhQQSJrIBzTiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T20:47:42.245370Z"},"content_sha256":"2e2e5048e35c9492c1c69e466e702b3bc2ad4ff14a052b5ae923f282729f0c09","schema_version":"1.0","event_id":"sha256:2e2e5048e35c9492c1c69e466e702b3bc2ad4ff14a052b5ae923f282729f0c09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQVMTZ44V5GW4I7WQJYYSYENDO/bundle.json","state_url":"https://pith.science/pith/DQVMTZ44V5GW4I7WQJYYSYENDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQVMTZ44V5GW4I7WQJYYSYENDO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-19T20:47:42Z","links":{"resolver":"https://pith.science/pith/DQVMTZ44V5GW4I7WQJYYSYENDO","bundle":"https://pith.science/pith/DQVMTZ44V5GW4I7WQJYYSYENDO/bundle.json","state":"https://pith.science/pith/DQVMTZ44V5GW4I7WQJYYSYENDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQVMTZ44V5GW4I7WQJYYSYENDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DQVMTZ44V5GW4I7WQJYYSYENDO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5dacd5cd3de010edcdf082b9c4fc06ce11c73aaaa13982fc5f78604933755fe6","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-06T17:25:52Z","title_canon_sha256":"83c73047175d81311d4922da44de8d91955651e0815437766a7783a6d791e4be"},"schema_version":"1.0","source":{"id":"2410.04557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.04557","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"2410.04557v1","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.04557","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"DQVMTZ44V5GW","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"pith_short_16","alias_value":"DQVMTZ44V5GW4I7W","created_at":"2026-07-05T09:16:35Z"},{"alias_kind":"pith_short_8","alias_value":"DQVMTZ44","created_at":"2026-07-05T09:16:35Z"}],"graph_snapshots":[{"event_id":"sha256:2e2e5048e35c9492c1c69e466e702b3bc2ad4ff14a052b5ae923f282729f0c09","target":"graph","created_at":"2026-07-05T09:16:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.04557/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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. We show that $(\\Gamma,\\Lambda_{\\beta}^{","authors_text":"Danylo Radchenko, Jo\\~ao P. G. Ramos","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-06T17:25:52Z","title":"Perturbed lattice crosses and Heisenberg uniqueness pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.04557","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9b4273fa4bb44e6179ef59dd917bbbbc84f21dab54903e0fc6da818333c35e87","target":"record","created_at":"2026-07-05T09:16:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5dacd5cd3de010edcdf082b9c4fc06ce11c73aaaa13982fc5f78604933755fe6","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-06T17:25:52Z","title_canon_sha256":"83c73047175d81311d4922da44de8d91955651e0815437766a7783a6d791e4be"},"schema_version":"1.0","source":{"id":"2410.04557","kind":"arxiv","version":1}},"canonical_sha256":"1c2ac9e79caf4d6e23f6827189608d1b8f399ac23a44fd3a40d5c7c70991bab2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c2ac9e79caf4d6e23f6827189608d1b8f399ac23a44fd3a40d5c7c70991bab2","first_computed_at":"2026-07-05T09:16:35.995073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:16:35.995073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CmrrjffRIhLELkx3uF09nyyijJW/l6KYMAkxXfRJmxZsg/BnSeBT0xCCqPjDIdgIeEPeuw1s46/Rxd3mWZerBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:16:35.995597Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.04557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b4273fa4bb44e6179ef59dd917bbbbc84f21dab54903e0fc6da818333c35e87","sha256:2e2e5048e35c9492c1c69e466e702b3bc2ad4ff14a052b5ae923f282729f0c09"],"state_sha256":"30ce5f061c15ba6c5f49fc5e09101ddf016bb7293de28f9577feb5acda963933"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N2OoLLPt95hXdyf1fmqxIS7dXi1FYUxM09q3B3K3bBEB73n9M3h7dQHHCKyNiuYJ1lZu1E0tUt1TUS3RUxToDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T20:47:42.250090Z","bundle_sha256":"a1d3fd4af8f8579ceaf8fded1eec06967447a80e3faf4f8b36fe3f106616c84d"}}