{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PVTNE4VBUX5BVU3BH7ILHCEY5E","short_pith_number":"pith:PVTNE4VB","canonical_record":{"source":{"id":"1611.03935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-12T01:54:23Z","cross_cats_sorted":["math.IT","math.OC"],"title_canon_sha256":"b4ac83d4197f1d82e6773d61883982231e3ea2fedef55c0ad95517d779c72c37","abstract_canon_sha256":"d10f60b52053924a5a49441e68b7e3b8ec0fb51ac644e9b022753b820390ea48"},"schema_version":"1.0"},"canonical_sha256":"7d66d272a1a5fa1ad3613fd0b38898e92509779fa7012d72c77a483e17c62014","source":{"kind":"arxiv","id":"1611.03935","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03935","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03935v1","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03935","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"PVTNE4VBUX5B","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PVTNE4VBUX5BVU3B","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PVTNE4VB","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PVTNE4VBUX5BVU3BH7ILHCEY5E","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-12T01:54:23Z","cross_cats_sorted":["math.IT","math.OC"],"title_canon_sha256":"b4ac83d4197f1d82e6773d61883982231e3ea2fedef55c0ad95517d779c72c37","abstract_canon_sha256":"d10f60b52053924a5a49441e68b7e3b8ec0fb51ac644e9b022753b820390ea48"},"schema_version":"1.0"},"canonical_sha256":"7d66d272a1a5fa1ad3613fd0b38898e92509779fa7012d72c77a483e17c62014","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:18.022863Z","signature_b64":"OCCMwZ0imaXlrQgQ0jqNCJF2FntcuoRfr3yUgPGx4WgoxvrigzSsQN8emFX4maasdzJGCPQKhZxuvFUE4N4yCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d66d272a1a5fa1ad3613fd0b38898e92509779fa7012d72c77a483e17c62014","last_reissued_at":"2026-05-18T00:59:18.022156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:18.022156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03935","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKMwLf+vLWhbPjZ4Q6i5lyZ6HKls61V9okS+aGwBmCdsYzBZuLyfR0HZmsCBjzKZ/Ty4ejTIC+Z3q47X6zQFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:38:27.824591Z"},"content_sha256":"43f20d8d50ab2d843c4afcf8efb0e29949112a623119509eb029c5f1af363b2e","schema_version":"1.0","event_id":"sha256:43f20d8d50ab2d843c4afcf8efb0e29949112a623119509eb029c5f1af363b2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PVTNE4VBUX5BVU3BH7ILHCEY5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Elementary Proof of Convex Phase Retrieval in the Natural Parameter Space via the Linear Program PhaseMax","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"Paul Hand, Vladislav Voroninski","submitted_at":"2016-11-12T01:54:23Z","abstract_excerpt":"The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to lifting, many approaches to phase retrieval have been developed, including non-convex optimization algorithms which operate in the natural parameter space, such as Wirtinger Flow. Very recently, a convex formulation called PhaseMax has been discovered, and it has been proven to achieve phase retrieval via linear programming in the natural parameter space under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03935","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RrL8ZkFj47W6Ucc8h8ltSNTQx9bip9hIRsLPGRYf4ADRjY0lH4uG+j/cHYlVWfWhbYBveu6DPbv9CSKcHTwrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:38:27.825342Z"},"content_sha256":"33372d5e9dd22ee68f5a9bcba8d1bbf4160da86e5585b5bdac87084b95774475","schema_version":"1.0","event_id":"sha256:33372d5e9dd22ee68f5a9bcba8d1bbf4160da86e5585b5bdac87084b95774475"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVTNE4VBUX5BVU3BH7ILHCEY5E/bundle.json","state_url":"https://pith.science/pith/PVTNE4VBUX5BVU3BH7ILHCEY5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVTNE4VBUX5BVU3BH7ILHCEY5E/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":"2026-05-31T12:38:27Z","links":{"resolver":"https://pith.science/pith/PVTNE4VBUX5BVU3BH7ILHCEY5E","bundle":"https://pith.science/pith/PVTNE4VBUX5BVU3BH7ILHCEY5E/bundle.json","state":"https://pith.science/pith/PVTNE4VBUX5BVU3BH7ILHCEY5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVTNE4VBUX5BVU3BH7ILHCEY5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PVTNE4VBUX5BVU3BH7ILHCEY5E","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":"d10f60b52053924a5a49441e68b7e3b8ec0fb51ac644e9b022753b820390ea48","cross_cats_sorted":["math.IT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-12T01:54:23Z","title_canon_sha256":"b4ac83d4197f1d82e6773d61883982231e3ea2fedef55c0ad95517d779c72c37"},"schema_version":"1.0","source":{"id":"1611.03935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03935","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03935v1","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03935","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"PVTNE4VBUX5B","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PVTNE4VBUX5BVU3B","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PVTNE4VB","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:33372d5e9dd22ee68f5a9bcba8d1bbf4160da86e5585b5bdac87084b95774475","target":"graph","created_at":"2026-05-18T00:59:18Z","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":"The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to lifting, many approaches to phase retrieval have been developed, including non-convex optimization algorithms which operate in the natural parameter space, such as Wirtinger Flow. Very recently, a convex formulation called PhaseMax has been discovered, and it has been proven to achieve phase retrieval via linear programming in the natural parameter space under ","authors_text":"Paul Hand, Vladislav Voroninski","cross_cats":["math.IT","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-12T01:54:23Z","title":"An Elementary Proof of Convex Phase Retrieval in the Natural Parameter Space via the Linear Program PhaseMax"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03935","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":"sha256:43f20d8d50ab2d843c4afcf8efb0e29949112a623119509eb029c5f1af363b2e","target":"record","created_at":"2026-05-18T00:59:18Z","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":"d10f60b52053924a5a49441e68b7e3b8ec0fb51ac644e9b022753b820390ea48","cross_cats_sorted":["math.IT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-12T01:54:23Z","title_canon_sha256":"b4ac83d4197f1d82e6773d61883982231e3ea2fedef55c0ad95517d779c72c37"},"schema_version":"1.0","source":{"id":"1611.03935","kind":"arxiv","version":1}},"canonical_sha256":"7d66d272a1a5fa1ad3613fd0b38898e92509779fa7012d72c77a483e17c62014","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d66d272a1a5fa1ad3613fd0b38898e92509779fa7012d72c77a483e17c62014","first_computed_at":"2026-05-18T00:59:18.022156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:18.022156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OCCMwZ0imaXlrQgQ0jqNCJF2FntcuoRfr3yUgPGx4WgoxvrigzSsQN8emFX4maasdzJGCPQKhZxuvFUE4N4yCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:18.022863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43f20d8d50ab2d843c4afcf8efb0e29949112a623119509eb029c5f1af363b2e","sha256:33372d5e9dd22ee68f5a9bcba8d1bbf4160da86e5585b5bdac87084b95774475"],"state_sha256":"ce493d9d7013581e51f681d0aa43ef35bb5475538b941e37d011acc13ef85194"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"si8XfioHffPPuOsEtLQCfdwo7B7mcaJGJ3I+qWk57rRFtwq72vcelJO+gbw5KiKVv6o1AWExt9fsaqc1toRHAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:38:27.829033Z","bundle_sha256":"5cb41ec82c5ef86ed82d3d2328bcb8410a02db23d9d2639de66f8cff54b60d2d"}}