{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3UVDUG2ZKUW625OMTTBYRYIYPP","short_pith_number":"pith:3UVDUG2Z","canonical_record":{"source":{"id":"1312.6236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-21T10:59:24Z","cross_cats_sorted":[],"title_canon_sha256":"ebff92bec7e45aaabcc8cba3e75fa88b4c981b6e52157767f0bb38c581323377","abstract_canon_sha256":"397bf02f79fc6bbd1d732f8862731c9df28854b16d6a127d120490d2db3588be"},"schema_version":"1.0"},"canonical_sha256":"dd2a3a1b59552ded75cc9cc388e1187be3a7ba57063686a9dc1f2fc547720520","source":{"kind":"arxiv","id":"1312.6236","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6236","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6236v2","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6236","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"3UVDUG2ZKUW6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3UVDUG2ZKUW625OM","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3UVDUG2Z","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3UVDUG2ZKUW625OMTTBYRYIYPP","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-21T10:59:24Z","cross_cats_sorted":[],"title_canon_sha256":"ebff92bec7e45aaabcc8cba3e75fa88b4c981b6e52157767f0bb38c581323377","abstract_canon_sha256":"397bf02f79fc6bbd1d732f8862731c9df28854b16d6a127d120490d2db3588be"},"schema_version":"1.0"},"canonical_sha256":"dd2a3a1b59552ded75cc9cc388e1187be3a7ba57063686a9dc1f2fc547720520","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:46.516864Z","signature_b64":"G0ZxvQBiGnNzeR25jaMwya/0JIMoDejqHhwoEocCp0NS1iBZNt6lYqk69ep4wiRykcGkPbAYxigdQPhkOW/PDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd2a3a1b59552ded75cc9cc388e1187be3a7ba57063686a9dc1f2fc547720520","last_reissued_at":"2026-05-18T02:48:46.516127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:46.516127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6236","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LikItpTcfVZEPzza9uVpPuUQ2yZl9c6ruNuPs6s/YPc+zY3rxH9kfz3u4HRzF53cYHjcKT6nb7UsbZOIiy10Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:44:27.342432Z"},"content_sha256":"c088cec9b50f8f31f25ad15213d30201fcb7f9d48325728b278b5a3706726194","schema_version":"1.0","event_id":"sha256:c088cec9b50f8f31f25ad15213d30201fcb7f9d48325728b278b5a3706726194"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3UVDUG2ZKUW625OMTTBYRYIYPP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A dynamical system approach to Heisenberg Uniqueness Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Karim Kellay (IMB), Philippe Jaming (IMB)","submitted_at":"2013-12-21T10:59:24Z","abstract_excerpt":"Let $\\Lambda$ be a set of lines in $\\mathbb{R}^2$ that intersect at the origin. For $\\Gamma\\subset\\mathbb{R}^2$ a smooth curve, we denote by $\\mathcal{A}\\mathcal{C}(\\Gamma)$ the subset of finite measures on $\\Gamma$ that are absolutely continuous with respect to arc length on $\\Gamma$. For such a $\\mu$, $\\widehat{\\mu}$ denotes the Fourier transform of $\\mu$. Following Hendenmalm and Montes-Rodr\\'iguez, we will say that $(\\Gamma,\\Lambda)$ is a Heisenberg Uniqueness Pair if $\\mu\\in\\mathcal{A}\\mathcal{C}(\\Gamma)$ is such that $\\widehat{\\mu}=0$ on $\\Lambda$, then $\\mu=0$. The aim of this paper is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6236","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xlGoCq3Ac9JgN6yJ6VSxd9wPd7dEIYDK2TlbMwUWULYb+Ci8+XaS2CL7UXWNlmeApsgDCaQL2UjI9HRa+MeaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:44:27.342895Z"},"content_sha256":"bf052309162ffa2754aa92fce0c7a3cb2e2cc9c10cd3d9e84ff9025675cabb2b","schema_version":"1.0","event_id":"sha256:bf052309162ffa2754aa92fce0c7a3cb2e2cc9c10cd3d9e84ff9025675cabb2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UVDUG2ZKUW625OMTTBYRYIYPP/bundle.json","state_url":"https://pith.science/pith/3UVDUG2ZKUW625OMTTBYRYIYPP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UVDUG2ZKUW625OMTTBYRYIYPP/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":"2026-06-25T23:44:27Z","links":{"resolver":"https://pith.science/pith/3UVDUG2ZKUW625OMTTBYRYIYPP","bundle":"https://pith.science/pith/3UVDUG2ZKUW625OMTTBYRYIYPP/bundle.json","state":"https://pith.science/pith/3UVDUG2ZKUW625OMTTBYRYIYPP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UVDUG2ZKUW625OMTTBYRYIYPP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3UVDUG2ZKUW625OMTTBYRYIYPP","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":"397bf02f79fc6bbd1d732f8862731c9df28854b16d6a127d120490d2db3588be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-21T10:59:24Z","title_canon_sha256":"ebff92bec7e45aaabcc8cba3e75fa88b4c981b6e52157767f0bb38c581323377"},"schema_version":"1.0","source":{"id":"1312.6236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6236","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6236v2","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6236","created_at":"2026-05-18T02:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"3UVDUG2ZKUW6","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3UVDUG2ZKUW625OM","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3UVDUG2Z","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:bf052309162ffa2754aa92fce0c7a3cb2e2cc9c10cd3d9e84ff9025675cabb2b","target":"graph","created_at":"2026-05-18T02:48:46Z","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"},"paper":{"abstract_excerpt":"Let $\\Lambda$ be a set of lines in $\\mathbb{R}^2$ that intersect at the origin. For $\\Gamma\\subset\\mathbb{R}^2$ a smooth curve, we denote by $\\mathcal{A}\\mathcal{C}(\\Gamma)$ the subset of finite measures on $\\Gamma$ that are absolutely continuous with respect to arc length on $\\Gamma$. For such a $\\mu$, $\\widehat{\\mu}$ denotes the Fourier transform of $\\mu$. Following Hendenmalm and Montes-Rodr\\'iguez, we will say that $(\\Gamma,\\Lambda)$ is a Heisenberg Uniqueness Pair if $\\mu\\in\\mathcal{A}\\mathcal{C}(\\Gamma)$ is such that $\\widehat{\\mu}=0$ on $\\Lambda$, then $\\mu=0$. The aim of this paper is ","authors_text":"Karim Kellay (IMB), Philippe Jaming (IMB)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-21T10:59:24Z","title":"A dynamical system approach to Heisenberg Uniqueness Pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6236","kind":"arxiv","version":2},"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:c088cec9b50f8f31f25ad15213d30201fcb7f9d48325728b278b5a3706726194","target":"record","created_at":"2026-05-18T02:48:46Z","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":"397bf02f79fc6bbd1d732f8862731c9df28854b16d6a127d120490d2db3588be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-21T10:59:24Z","title_canon_sha256":"ebff92bec7e45aaabcc8cba3e75fa88b4c981b6e52157767f0bb38c581323377"},"schema_version":"1.0","source":{"id":"1312.6236","kind":"arxiv","version":2}},"canonical_sha256":"dd2a3a1b59552ded75cc9cc388e1187be3a7ba57063686a9dc1f2fc547720520","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd2a3a1b59552ded75cc9cc388e1187be3a7ba57063686a9dc1f2fc547720520","first_computed_at":"2026-05-18T02:48:46.516127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:46.516127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G0ZxvQBiGnNzeR25jaMwya/0JIMoDejqHhwoEocCp0NS1iBZNt6lYqk69ep4wiRykcGkPbAYxigdQPhkOW/PDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:46.516864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c088cec9b50f8f31f25ad15213d30201fcb7f9d48325728b278b5a3706726194","sha256:bf052309162ffa2754aa92fce0c7a3cb2e2cc9c10cd3d9e84ff9025675cabb2b"],"state_sha256":"09ecb9d097a3c7707bfef14631dc61d3ce4c4c29d39a98843aefb751ac2a4484"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOJAObazieVKYv8dvgoTgWN0tgKZ5uWNBCaPVtdouTbmE8CdONycRRBS0RjLiZXuRFYEH3IU3i+LtEY8FlHOAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:44:27.345397Z","bundle_sha256":"74dc5769792f1cc67957fe2e0c74bb58679948cdb36edc8dc4a2a80b60036746"}}