{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EXR37IXN273WFBQHBIMNLJZZ5K","short_pith_number":"pith:EXR37IXN","schema_version":"1.0","canonical_sha256":"25e3bfa2edd7f76286070a18d5a739ea8a5593cf9f3391f815e3c55f9cc08d24","source":{"kind":"arxiv","id":"1310.5895","version":1},"attestation_state":"computed","paper":{"title":"Stable Recovery from the Magnitude of Symmetrized Fourier Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Peter Jung, Philipp Walk","submitted_at":"2013-10-22T12:39:35Z","abstract_excerpt":"In this note we show that stable recovery of complex-valued signals $x\\in\\mathbb{C}^n$ up to global sign can be achieved from the magnitudes of $4n-1$ Fourier measurements when a certain \"symmetrization and zero-padding\" is performed before measurement ($4n-3$ is possible in certain cases). For real signals, symmetrization itself is linear and therefore our result is in this case a statement on uniform phase retrieval. Since complex conjugation is involved, such measurement procedure is not complex-linear but recovery is still possible from magnitudes of linear measurements on, for example, $("},"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":"1310.5895","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-22T12:39:35Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"75a2dc9fc27ccb74e1c8f4b550e328c38057a9b97e31b30663482b3a4591ed22","abstract_canon_sha256":"eede9330aa242768fb2639b36d2ad049f589381174d97b116ae13dcc7863a743"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:24.252733Z","signature_b64":"qxM4E42UOSrbDcLbaayUpChN1o0LluaAQelQ5uU3I8aTX9UN+nHotFCjlJ53QD93I+F50lrrPrmHYKIcDviXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25e3bfa2edd7f76286070a18d5a739ea8a5593cf9f3391f815e3c55f9cc08d24","last_reissued_at":"2026-05-18T03:09:24.252002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:24.252002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable Recovery from the Magnitude of Symmetrized Fourier Measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Peter Jung, Philipp Walk","submitted_at":"2013-10-22T12:39:35Z","abstract_excerpt":"In this note we show that stable recovery of complex-valued signals $x\\in\\mathbb{C}^n$ up to global sign can be achieved from the magnitudes of $4n-1$ Fourier measurements when a certain \"symmetrization and zero-padding\" is performed before measurement ($4n-3$ is possible in certain cases). For real signals, symmetrization itself is linear and therefore our result is in this case a statement on uniform phase retrieval. Since complex conjugation is involved, such measurement procedure is not complex-linear but recovery is still possible from magnitudes of linear measurements on, for example, $("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5895","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":""},"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":"1310.5895","created_at":"2026-05-18T03:09:24.252080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.5895v1","created_at":"2026-05-18T03:09:24.252080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5895","created_at":"2026-05-18T03:09:24.252080+00:00"},{"alias_kind":"pith_short_12","alias_value":"EXR37IXN273W","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EXR37IXN273WFBQH","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EXR37IXN","created_at":"2026-05-18T12:27:43.054852+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/EXR37IXN273WFBQHBIMNLJZZ5K","json":"https://pith.science/pith/EXR37IXN273WFBQHBIMNLJZZ5K.json","graph_json":"https://pith.science/api/pith-number/EXR37IXN273WFBQHBIMNLJZZ5K/graph.json","events_json":"https://pith.science/api/pith-number/EXR37IXN273WFBQHBIMNLJZZ5K/events.json","paper":"https://pith.science/paper/EXR37IXN"},"agent_actions":{"view_html":"https://pith.science/pith/EXR37IXN273WFBQHBIMNLJZZ5K","download_json":"https://pith.science/pith/EXR37IXN273WFBQHBIMNLJZZ5K.json","view_paper":"https://pith.science/paper/EXR37IXN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.5895&json=true","fetch_graph":"https://pith.science/api/pith-number/EXR37IXN273WFBQHBIMNLJZZ5K/graph.json","fetch_events":"https://pith.science/api/pith-number/EXR37IXN273WFBQHBIMNLJZZ5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EXR37IXN273WFBQHBIMNLJZZ5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EXR37IXN273WFBQHBIMNLJZZ5K/action/storage_attestation","attest_author":"https://pith.science/pith/EXR37IXN273WFBQHBIMNLJZZ5K/action/author_attestation","sign_citation":"https://pith.science/pith/EXR37IXN273WFBQHBIMNLJZZ5K/action/citation_signature","submit_replication":"https://pith.science/pith/EXR37IXN273WFBQHBIMNLJZZ5K/action/replication_record"}},"created_at":"2026-05-18T03:09:24.252080+00:00","updated_at":"2026-05-18T03:09:24.252080+00:00"}