{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RLAP6I53JD2OG33US65W2M233J","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":"4308b52f7d8270ea9d7027248fcb85f8120565190228661db8452fef548062c1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-09-21T14:12:53Z","title_canon_sha256":"416aa0556948e820291370c9d4cbe848d108e90fe2954bf57b5b89b384308de6"},"schema_version":"1.0","source":{"id":"1809.08136","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08136","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08136v3","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08136","created_at":"2026-05-18T00:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"RLAP6I53JD2O","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RLAP6I53JD2OG33U","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RLAP6I53","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:e859e743ee8baaebc89a85991e0e86152f86cfb4bf1ab02b1b86a63e2cfbc1e9","target":"graph","created_at":"2026-05-18T00:04:29Z","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":"Motivated by the research on sampling problems for a union of subspaces (UoS), we investigate in this paper the phase-retrieval problem for the signals that are residing in a union of (finitely generated) cones (UoC for short) in $\\mathbb{R}^{n}$. We propose a two-step PR-scheme: $\\hbox{PR}=\\hbox{detection}+\\hbox{recovery}$. We first establish a sufficient and necessary condition for the detectability of a UoC, and then design a detection algorithm that allows us to determine the cone where the target signal is residing. The phase-retrieval will be then performed within the detected cone, whic","authors_text":"Deguang Han, Youfa Li","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-09-21T14:12:53Z","title":"Two-step PR-scheme for recovering signals in detectable union of cones by magnitude measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08136","kind":"arxiv","version":3},"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":"sha256:8a5a346bd977b595b07f9e9e60e1c9fe6248fa9ecafdea359a9da0dc4dd63dc4","target":"record","created_at":"2026-05-18T00:04:29Z","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":"4308b52f7d8270ea9d7027248fcb85f8120565190228661db8452fef548062c1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-09-21T14:12:53Z","title_canon_sha256":"416aa0556948e820291370c9d4cbe848d108e90fe2954bf57b5b89b384308de6"},"schema_version":"1.0","source":{"id":"1809.08136","kind":"arxiv","version":3}},"canonical_sha256":"8ac0ff23bb48f4e36f7497bb6d335bda5071d8e61d0e1d47d572f360e2214e16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ac0ff23bb48f4e36f7497bb6d335bda5071d8e61d0e1d47d572f360e2214e16","first_computed_at":"2026-05-18T00:04:29.153094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:29.153094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvKOeDs0L68zmq/tQPyOW0CtRPQ2s0O/876R8urVCv5HPi1IcTVkBN9/Dsn8KAt0jl/jwdZIfNSPkBZ9MUqVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:29.153587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08136","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a5a346bd977b595b07f9e9e60e1c9fe6248fa9ecafdea359a9da0dc4dd63dc4","sha256:e859e743ee8baaebc89a85991e0e86152f86cfb4bf1ab02b1b86a63e2cfbc1e9"],"state_sha256":"3089a0404cb888205e274c9f85338f686591ea490e942c05e930b92e6ec45fe1"}