{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:MUA7RZGU5AH7XED5656EWCG44F","short_pith_number":"pith:MUA7RZGU","schema_version":"1.0","canonical_sha256":"6501f8e4d4e80ffb907df77c4b08dce16fe13f1f9aaf9845b639e0ab22f36e4e","source":{"kind":"arxiv","id":"0908.0447","version":2},"attestation_state":"computed","paper":{"title":"Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Alexander Olevskii, Nir Lev","submitted_at":"2009-08-04T13:58:09Z","abstract_excerpt":"Wiener characterized the cyclic vectors (with respect to translations) in $l^p(Z)$ and $L^p(R)$, $p=1,2$, in terms of the zero set of the Fourier transform. He conjectured that a similar characterization should be true for $1<p<2$. Our main result contradicts this conjecture."},"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":"0908.0447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-08-04T13:58:09Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d103dbf5d2d52368bd7217428783e302633cc7f11e2d01cf1ba55aebad3a667e","abstract_canon_sha256":"900612802c13b93b9248dd8c7b76400efaf91821debc652af9b0050b788284c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:43.843369Z","signature_b64":"8F4b4n5XJhR4P/i8KlawiPcMtACb55wSjHHpENwJ4nL+7wRvyQHgX5g2Scsk9taRgsFHybXbhoG3CUIpXP4nAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6501f8e4d4e80ffb907df77c4b08dce16fe13f1f9aaf9845b639e0ab22f36e4e","last_reissued_at":"2026-05-18T04:18:43.842902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:43.842902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Alexander Olevskii, Nir Lev","submitted_at":"2009-08-04T13:58:09Z","abstract_excerpt":"Wiener characterized the cyclic vectors (with respect to translations) in $l^p(Z)$ and $L^p(R)$, $p=1,2$, in terms of the zero set of the Fourier transform. He conjectured that a similar characterization should be true for $1<p<2$. Our main result contradicts this conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0447","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0908.0447","created_at":"2026-05-18T04:18:43.842958+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.0447v2","created_at":"2026-05-18T04:18:43.842958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0447","created_at":"2026-05-18T04:18:43.842958+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUA7RZGU5AH7","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUA7RZGU5AH7XED5","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUA7RZGU","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F","json":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F.json","graph_json":"https://pith.science/api/pith-number/MUA7RZGU5AH7XED5656EWCG44F/graph.json","events_json":"https://pith.science/api/pith-number/MUA7RZGU5AH7XED5656EWCG44F/events.json","paper":"https://pith.science/paper/MUA7RZGU"},"agent_actions":{"view_html":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F","download_json":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F.json","view_paper":"https://pith.science/paper/MUA7RZGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.0447&json=true","fetch_graph":"https://pith.science/api/pith-number/MUA7RZGU5AH7XED5656EWCG44F/graph.json","fetch_events":"https://pith.science/api/pith-number/MUA7RZGU5AH7XED5656EWCG44F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F/action/storage_attestation","attest_author":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F/action/author_attestation","sign_citation":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F/action/citation_signature","submit_replication":"https://pith.science/pith/MUA7RZGU5AH7XED5656EWCG44F/action/replication_record"}},"created_at":"2026-05-18T04:18:43.842958+00:00","updated_at":"2026-05-18T04:18:43.842958+00:00"}