{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LEIIC5DSSGBKLSHUYJX3FZFH6X","short_pith_number":"pith:LEIIC5DS","canonical_record":{"source":{"id":"1705.02356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-05T18:21:40Z","cross_cats_sorted":["cs.IT","math.IT","math.OC","stat.TH"],"title_canon_sha256":"358e4e53ee4a2a54a024bca82f00411d2b5abf71711527adb086cb4956f8bc5d","abstract_canon_sha256":"9ba79e276587706ee8dfbca778432b7100c801eefead866e165e6e4c437fb0fd"},"schema_version":"1.0"},"canonical_sha256":"59108174729182a5c8f4c26fb2e4a7f5e63a695e5e8b00ca6c6f22389e500021","source":{"kind":"arxiv","id":"1705.02356","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02356","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02356v2","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02356","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"LEIIC5DSSGBK","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LEIIC5DSSGBKLSHU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LEIIC5DS","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LEIIC5DSSGBKLSHUYJX3FZFH6X","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-05T18:21:40Z","cross_cats_sorted":["cs.IT","math.IT","math.OC","stat.TH"],"title_canon_sha256":"358e4e53ee4a2a54a024bca82f00411d2b5abf71711527adb086cb4956f8bc5d","abstract_canon_sha256":"9ba79e276587706ee8dfbca778432b7100c801eefead866e165e6e4c437fb0fd"},"schema_version":"1.0"},"canonical_sha256":"59108174729182a5c8f4c26fb2e4a7f5e63a695e5e8b00ca6c6f22389e500021","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:54.764526Z","signature_b64":"cis7uEEcamDd9z+T3q0Zr4/wg6ioT49AZ5DdvI+3PkJ8n7t02AEULkbJcxy2m45DbthVFNVhVUrvO9onDpK6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59108174729182a5c8f4c26fb2e4a7f5e63a695e5e8b00ca6c6f22389e500021","last_reissued_at":"2026-05-18T00:17:54.763829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:54.763829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02356","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":"2026-05-18T00:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2a5TnA39rtBeQCZ4mJT1dilqKzx+L07IgQIJZsHaq5Bd4hLfpEx7AAea27qobFnmJWY6QxY8t1VAE8/UaJpNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:04.879601Z"},"content_sha256":"fed4a319b85ff06668f175e387715b1771fc8d89e6e062c33f9df18135a0d043","schema_version":"1.0","event_id":"sha256:fed4a319b85ff06668f175e387715b1771fc8d89e6e062c33f9df18135a0d043"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LEIIC5DSSGBKLSHUYJX3FZFH6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Feng Ruan, John C. Duchi","submitted_at":"2017-05-05T18:21:40Z","abstract_excerpt":"We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems. We show that the prox-linear algorithm we develop can solve phase retrieval problems---even with adversarially faulty measurements---with high probability as soon as the number of measurements $m$ is a constant factor larger than the dimension $n$ of the signal to be recovered. The algorithm requires essentially no tuning---it consists of solving a sequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02356","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":"2026-05-18T00:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AHnRuLNBd686xA/riGp+aE54NEBIhik7Io1eOlKwMH9AcnzmYMGqPcmxN604C5N29IUmlCGpGk5r+kMD5oAbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:04.880302Z"},"content_sha256":"bc1cc125ae6f8bd52d382a9010ba01d2af630e7bb57d5a28d0294119382f1817","schema_version":"1.0","event_id":"sha256:bc1cc125ae6f8bd52d382a9010ba01d2af630e7bb57d5a28d0294119382f1817"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEIIC5DSSGBKLSHUYJX3FZFH6X/bundle.json","state_url":"https://pith.science/pith/LEIIC5DSSGBKLSHUYJX3FZFH6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEIIC5DSSGBKLSHUYJX3FZFH6X/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":"2026-05-29T17:53:04Z","links":{"resolver":"https://pith.science/pith/LEIIC5DSSGBKLSHUYJX3FZFH6X","bundle":"https://pith.science/pith/LEIIC5DSSGBKLSHUYJX3FZFH6X/bundle.json","state":"https://pith.science/pith/LEIIC5DSSGBKLSHUYJX3FZFH6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEIIC5DSSGBKLSHUYJX3FZFH6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LEIIC5DSSGBKLSHUYJX3FZFH6X","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":"9ba79e276587706ee8dfbca778432b7100c801eefead866e165e6e4c437fb0fd","cross_cats_sorted":["cs.IT","math.IT","math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-05T18:21:40Z","title_canon_sha256":"358e4e53ee4a2a54a024bca82f00411d2b5abf71711527adb086cb4956f8bc5d"},"schema_version":"1.0","source":{"id":"1705.02356","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02356","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02356v2","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02356","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"LEIIC5DSSGBK","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LEIIC5DSSGBKLSHU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LEIIC5DS","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:bc1cc125ae6f8bd52d382a9010ba01d2af630e7bb57d5a28d0294119382f1817","target":"graph","created_at":"2026-05-18T00:17:54Z","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 develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems. We show that the prox-linear algorithm we develop can solve phase retrieval problems---even with adversarially faulty measurements---with high probability as soon as the number of measurements $m$ is a constant factor larger than the dimension $n$ of the signal to be recovered. The algorithm requires essentially no tuning---it consists of solving a sequence","authors_text":"Feng Ruan, John C. Duchi","cross_cats":["cs.IT","math.IT","math.OC","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-05T18:21:40Z","title":"Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02356","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:fed4a319b85ff06668f175e387715b1771fc8d89e6e062c33f9df18135a0d043","target":"record","created_at":"2026-05-18T00:17:54Z","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":"9ba79e276587706ee8dfbca778432b7100c801eefead866e165e6e4c437fb0fd","cross_cats_sorted":["cs.IT","math.IT","math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-05T18:21:40Z","title_canon_sha256":"358e4e53ee4a2a54a024bca82f00411d2b5abf71711527adb086cb4956f8bc5d"},"schema_version":"1.0","source":{"id":"1705.02356","kind":"arxiv","version":2}},"canonical_sha256":"59108174729182a5c8f4c26fb2e4a7f5e63a695e5e8b00ca6c6f22389e500021","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59108174729182a5c8f4c26fb2e4a7f5e63a695e5e8b00ca6c6f22389e500021","first_computed_at":"2026-05-18T00:17:54.763829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:54.763829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cis7uEEcamDd9z+T3q0Zr4/wg6ioT49AZ5DdvI+3PkJ8n7t02AEULkbJcxy2m45DbthVFNVhVUrvO9onDpK6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:54.764526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02356","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fed4a319b85ff06668f175e387715b1771fc8d89e6e062c33f9df18135a0d043","sha256:bc1cc125ae6f8bd52d382a9010ba01d2af630e7bb57d5a28d0294119382f1817"],"state_sha256":"f7f1e57ba7e554503dba05c6142059681400a021941a21e10fa2693866ddf28f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M7blAGUHmlsfN9qcRTBQa/rQOFNKsU/mh0p2Td02JLP3IxsMRyWbJZVcnLBBEJeAxvOmWb3RzoHV4IQyuMpDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:53:04.884207Z","bundle_sha256":"032d5b864fd878f075717895cbec4f04f045284bf285b968f3bd7724bdf3398d"}}