{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Q4EK4MKSNCYZVZKSICGKTKPDQI","short_pith_number":"pith:Q4EK4MKS","schema_version":"1.0","canonical_sha256":"8708ae315268b19ae552408ca9a9e382042f2a34a8363254dd63de1b26c2c436","source":{"kind":"arxiv","id":"1502.04241","version":1},"attestation_state":"computed","paper":{"title":"PhaseLift is robust to a constant fraction of arbitrary errors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Paul Hand","submitted_at":"2015-02-14T20:32:35Z","abstract_excerpt":"Consider the task of recovering an unknown $n$-vector from phaseless linear measurements. This task is the phase retrieval problem. Through the technique of lifting, this nonconvex problem may be convexified into a semidefinite rank-one matrix recovery problem, known as PhaseLift. Under a linear number of exact Gaussian measurements, PhaseLift recovers the unknown vector exactly with high probability. Under noisy measurements, the solution to a variant of PhaseLift has error proportional to the $\\ell_1$ norm of the noise. In the present paper, we study the robustness of this variant of PhaseLi"},"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":"1502.04241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-14T20:32:35Z","cross_cats_sorted":[],"title_canon_sha256":"e22816e94d450f54db8fb05462f7128668f84c8dbd4e18e7890788f59f309182","abstract_canon_sha256":"09645b46c05a7d4733e7e741f5f657265ad341db59b2f0df9000fc29235883f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:00.157852Z","signature_b64":"YMD+MMtrG4qht3yuGQfCqKKpPqriMt+RwsIMBwo+NwpbXIgkJZW3nE+IxLtowbvwCGhilznn2unk7cOjXp1xCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8708ae315268b19ae552408ca9a9e382042f2a34a8363254dd63de1b26c2c436","last_reissued_at":"2026-05-18T02:27:00.157453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:00.157453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"PhaseLift is robust to a constant fraction of arbitrary errors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Paul Hand","submitted_at":"2015-02-14T20:32:35Z","abstract_excerpt":"Consider the task of recovering an unknown $n$-vector from phaseless linear measurements. This task is the phase retrieval problem. Through the technique of lifting, this nonconvex problem may be convexified into a semidefinite rank-one matrix recovery problem, known as PhaseLift. Under a linear number of exact Gaussian measurements, PhaseLift recovers the unknown vector exactly with high probability. Under noisy measurements, the solution to a variant of PhaseLift has error proportional to the $\\ell_1$ norm of the noise. In the present paper, we study the robustness of this variant of PhaseLi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04241","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":"1502.04241","created_at":"2026-05-18T02:27:00.157516+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04241v1","created_at":"2026-05-18T02:27:00.157516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04241","created_at":"2026-05-18T02:27:00.157516+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q4EK4MKSNCYZ","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q4EK4MKSNCYZVZKS","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q4EK4MKS","created_at":"2026-05-18T12:29:37.295048+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/Q4EK4MKSNCYZVZKSICGKTKPDQI","json":"https://pith.science/pith/Q4EK4MKSNCYZVZKSICGKTKPDQI.json","graph_json":"https://pith.science/api/pith-number/Q4EK4MKSNCYZVZKSICGKTKPDQI/graph.json","events_json":"https://pith.science/api/pith-number/Q4EK4MKSNCYZVZKSICGKTKPDQI/events.json","paper":"https://pith.science/paper/Q4EK4MKS"},"agent_actions":{"view_html":"https://pith.science/pith/Q4EK4MKSNCYZVZKSICGKTKPDQI","download_json":"https://pith.science/pith/Q4EK4MKSNCYZVZKSICGKTKPDQI.json","view_paper":"https://pith.science/paper/Q4EK4MKS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04241&json=true","fetch_graph":"https://pith.science/api/pith-number/Q4EK4MKSNCYZVZKSICGKTKPDQI/graph.json","fetch_events":"https://pith.science/api/pith-number/Q4EK4MKSNCYZVZKSICGKTKPDQI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q4EK4MKSNCYZVZKSICGKTKPDQI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q4EK4MKSNCYZVZKSICGKTKPDQI/action/storage_attestation","attest_author":"https://pith.science/pith/Q4EK4MKSNCYZVZKSICGKTKPDQI/action/author_attestation","sign_citation":"https://pith.science/pith/Q4EK4MKSNCYZVZKSICGKTKPDQI/action/citation_signature","submit_replication":"https://pith.science/pith/Q4EK4MKSNCYZVZKSICGKTKPDQI/action/replication_record"}},"created_at":"2026-05-18T02:27:00.157516+00:00","updated_at":"2026-05-18T02:27:00.157516+00:00"}