{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:53VTTP4Q4TAW5BZ3JYXN55XQKD","short_pith_number":"pith:53VTTP4Q","schema_version":"1.0","canonical_sha256":"eeeb39bf90e4c16e873b4e2edef6f050cc62e43b8174e2ecbf75c1b32dba19b9","source":{"kind":"arxiv","id":"2112.07997","version":1},"attestation_state":"computed","paper":{"title":"The global landscape of phase retrieval II: quotient intensity models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.NA","math.IT"],"primary_cat":"math.NA","authors_text":"Dong Li, Jian-Feng Cai, Meng Huang, Yang Wang","submitted_at":"2021-12-15T09:44:08Z","abstract_excerpt":"A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only measurements. In this work we introduce three novel quotient intensity-based models (QIMs) based a deep modification of the traditional intensity-based models. A remarkable feature of the new loss functions is that the corresponding geometric landscape is benign under the optimal sampling complexity. When the measurements $ a_i\\in \\Rn$ are Gaussian random vectors and the number of measurements $m\\ge Cn$, the QIMs admit no spurious local minimizers with high probability, i.e., the target so"},"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":"2112.07997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-12-15T09:44:08Z","cross_cats_sorted":["cs.IT","cs.NA","math.IT"],"title_canon_sha256":"65ba0097bc23cd2f858fbf9f227c02f5918715bca89cf88b7997c87aca4c2117","abstract_canon_sha256":"e84abb3d4ffda7921f62511da0e34dea201098f4889f14e5ec9e237ddea6bb3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:41:09.367400Z","signature_b64":"lJLfCuSk1VyW/KTLDSP0783BaAUcUP1DqjMK1f8FhpWBuknzZCiZxgLd9eB/XCobGY38rUze39keB7R1kXXKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeeb39bf90e4c16e873b4e2edef6f050cc62e43b8174e2ecbf75c1b32dba19b9","last_reissued_at":"2026-07-05T03:41:09.366730Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:41:09.366730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The global landscape of phase retrieval II: quotient intensity models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.NA","math.IT"],"primary_cat":"math.NA","authors_text":"Dong Li, Jian-Feng Cai, Meng Huang, Yang Wang","submitted_at":"2021-12-15T09:44:08Z","abstract_excerpt":"A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only measurements. In this work we introduce three novel quotient intensity-based models (QIMs) based a deep modification of the traditional intensity-based models. A remarkable feature of the new loss functions is that the corresponding geometric landscape is benign under the optimal sampling complexity. When the measurements $ a_i\\in \\Rn$ are Gaussian random vectors and the number of measurements $m\\ge Cn$, the QIMs admit no spurious local minimizers with high probability, i.e., the target so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.07997","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.07997/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2112.07997","created_at":"2026-07-05T03:41:09.366792+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.07997v1","created_at":"2026-07-05T03:41:09.366792+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.07997","created_at":"2026-07-05T03:41:09.366792+00:00"},{"alias_kind":"pith_short_12","alias_value":"53VTTP4Q4TAW","created_at":"2026-07-05T03:41:09.366792+00:00"},{"alias_kind":"pith_short_16","alias_value":"53VTTP4Q4TAW5BZ3","created_at":"2026-07-05T03:41:09.366792+00:00"},{"alias_kind":"pith_short_8","alias_value":"53VTTP4Q","created_at":"2026-07-05T03:41:09.366792+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/53VTTP4Q4TAW5BZ3JYXN55XQKD","json":"https://pith.science/pith/53VTTP4Q4TAW5BZ3JYXN55XQKD.json","graph_json":"https://pith.science/api/pith-number/53VTTP4Q4TAW5BZ3JYXN55XQKD/graph.json","events_json":"https://pith.science/api/pith-number/53VTTP4Q4TAW5BZ3JYXN55XQKD/events.json","paper":"https://pith.science/paper/53VTTP4Q"},"agent_actions":{"view_html":"https://pith.science/pith/53VTTP4Q4TAW5BZ3JYXN55XQKD","download_json":"https://pith.science/pith/53VTTP4Q4TAW5BZ3JYXN55XQKD.json","view_paper":"https://pith.science/paper/53VTTP4Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.07997&json=true","fetch_graph":"https://pith.science/api/pith-number/53VTTP4Q4TAW5BZ3JYXN55XQKD/graph.json","fetch_events":"https://pith.science/api/pith-number/53VTTP4Q4TAW5BZ3JYXN55XQKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53VTTP4Q4TAW5BZ3JYXN55XQKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53VTTP4Q4TAW5BZ3JYXN55XQKD/action/storage_attestation","attest_author":"https://pith.science/pith/53VTTP4Q4TAW5BZ3JYXN55XQKD/action/author_attestation","sign_citation":"https://pith.science/pith/53VTTP4Q4TAW5BZ3JYXN55XQKD/action/citation_signature","submit_replication":"https://pith.science/pith/53VTTP4Q4TAW5BZ3JYXN55XQKD/action/replication_record"}},"created_at":"2026-07-05T03:41:09.366792+00:00","updated_at":"2026-07-05T03:41:09.366792+00:00"}