{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C2K3JXMFFSDGI77CNLKVFA5PUO","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":"0915a6f3a8d34aa6fb62fdaa791d69fe032658a5fbb75b07cf4e2a3400a1bc30","cross_cats_sorted":["math.IT","math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-12T05:32:22Z","title_canon_sha256":"6744cfea5e29e04d68bc83adbf9c0440d6444d30ad9970c41308812ae38e2531"},"schema_version":"1.0","source":{"id":"1612.03547","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03547","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03547v1","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03547","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"pith_short_12","alias_value":"C2K3JXMFFSDG","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C2K3JXMFFSDGI77C","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C2K3JXMF","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:a1a25426e2f43d7a5cd152d6fed001d3984f2a9c29adeb968941f5b8550ace72","target":"graph","created_at":"2026-05-18T00:55:18Z","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":"We consider the problem of phase retrieval from corrupted magnitude observations. In particular we show that a fixed $x_0 \\in \\mathbb{R}^n$ can be recovered exactly from corrupted magnitude measurements $|\\langle a_i, x_0 \\rangle | + \\eta_i, \\quad i =1,2\\ldots m$ with high probability for $m = O(n)$, where $a_i \\in \\mathbb{R}^n$ are i.i.d standard Gaussian and $\\eta \\in \\mathbb{R}^m$ has fixed sparse support and is otherwise arbitrary, by using a version of the PhaseMax algorithm augmented with slack variables subject to a penalty. This linear programming formulation, which we call RobustPhase","authors_text":"Paul Hand, Vladislav Voroninski","cross_cats":["math.IT","math.OC","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-12T05:32:22Z","title":"Corruption Robust Phase Retrieval via Linear Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03547","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":"sha256:218b88951face1a8d11059af7f290fa2037ad839177f5bab9b9ec98766f3b54e","target":"record","created_at":"2026-05-18T00:55:18Z","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":"0915a6f3a8d34aa6fb62fdaa791d69fe032658a5fbb75b07cf4e2a3400a1bc30","cross_cats_sorted":["math.IT","math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-12T05:32:22Z","title_canon_sha256":"6744cfea5e29e04d68bc83adbf9c0440d6444d30ad9970c41308812ae38e2531"},"schema_version":"1.0","source":{"id":"1612.03547","kind":"arxiv","version":1}},"canonical_sha256":"1695b4dd852c86647fe26ad55283afa38c93f614eebe60950a6857a632869773","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1695b4dd852c86647fe26ad55283afa38c93f614eebe60950a6857a632869773","first_computed_at":"2026-05-18T00:55:18.995710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:18.995710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M4Cy4rIW+QaY0H3W2maDjkpopY8n4NKbzoRyRqhXboVr9y+jI/DHuHaDgC28zLIBm7vflFav0T0woRFM47b9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:18.996169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03547","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:218b88951face1a8d11059af7f290fa2037ad839177f5bab9b9ec98766f3b54e","sha256:a1a25426e2f43d7a5cd152d6fed001d3984f2a9c29adeb968941f5b8550ace72"],"state_sha256":"5ec652cb4b79b3609d64b894b71ed07b9f30c6cdcf90cddc3f2ccf664c075dd1"}