{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SKGWSVF6M2CEHRRKEPQKEOIRQL","short_pith_number":"pith:SKGWSVF6","schema_version":"1.0","canonical_sha256":"928d6954be668443c62a23e0a2391182dddf03ae22e072dcb419840382601e5b","source":{"kind":"arxiv","id":"1706.07738","version":1},"attestation_state":"computed","paper":{"title":"Frame Phase-retrievability and Exact phase-retrievable frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Deguang Han, Ted Juste, Wenchang Sun, Youfa Li","submitted_at":"2017-06-23T15:05:46Z","abstract_excerpt":"An exact phase-retrievable frame $\\{f_{i}\\}_{i}^{N}$ for an $n$-dimensional Hilbert space is a phase-retrievable frame that fails to be phase-retrievable if any one element is removed from the frame. Such a frame could have different lengths. We shall prove that for the real Hilbert space case, exact phase-retrievable frame of length $N$ exists for every $2n-1\\leq N\\leq n(n+1)/2$. For arbitrary frames we introduce the concept of redundancy with respect to its phase-retrievability and the concept of frames with exact PR-redundancy. We investigate the phase-retrievability by studying its maximal"},"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":"1706.07738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-23T15:05:46Z","cross_cats_sorted":[],"title_canon_sha256":"14a392c82c789493ba877205711c3caca8e25fd5c707d84612be372bfe563e1d","abstract_canon_sha256":"dc6887138aebe51700281966aae7a0bc9a5093664d2cced483814cddeaa31a20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:48.309672Z","signature_b64":"a5NbOlFZtO/rZZWpULbX9oN+TFnKOfBFWCsHHqsah6hhl55eyeFbJFZpMvkzwf9V/XJ9TMmB3zqZFM9rp08iCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"928d6954be668443c62a23e0a2391182dddf03ae22e072dcb419840382601e5b","last_reissued_at":"2026-05-18T00:41:48.309151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:48.309151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frame Phase-retrievability and Exact phase-retrievable frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Deguang Han, Ted Juste, Wenchang Sun, Youfa Li","submitted_at":"2017-06-23T15:05:46Z","abstract_excerpt":"An exact phase-retrievable frame $\\{f_{i}\\}_{i}^{N}$ for an $n$-dimensional Hilbert space is a phase-retrievable frame that fails to be phase-retrievable if any one element is removed from the frame. Such a frame could have different lengths. We shall prove that for the real Hilbert space case, exact phase-retrievable frame of length $N$ exists for every $2n-1\\leq N\\leq n(n+1)/2$. For arbitrary frames we introduce the concept of redundancy with respect to its phase-retrievability and the concept of frames with exact PR-redundancy. We investigate the phase-retrievability by studying its maximal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07738","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.07738","created_at":"2026-05-18T00:41:48.309229+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.07738v1","created_at":"2026-05-18T00:41:48.309229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07738","created_at":"2026-05-18T00:41:48.309229+00:00"},{"alias_kind":"pith_short_12","alias_value":"SKGWSVF6M2CE","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SKGWSVF6M2CEHRRK","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SKGWSVF6","created_at":"2026-05-18T12:31:43.269735+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/SKGWSVF6M2CEHRRKEPQKEOIRQL","json":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL.json","graph_json":"https://pith.science/api/pith-number/SKGWSVF6M2CEHRRKEPQKEOIRQL/graph.json","events_json":"https://pith.science/api/pith-number/SKGWSVF6M2CEHRRKEPQKEOIRQL/events.json","paper":"https://pith.science/paper/SKGWSVF6"},"agent_actions":{"view_html":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL","download_json":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL.json","view_paper":"https://pith.science/paper/SKGWSVF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.07738&json=true","fetch_graph":"https://pith.science/api/pith-number/SKGWSVF6M2CEHRRKEPQKEOIRQL/graph.json","fetch_events":"https://pith.science/api/pith-number/SKGWSVF6M2CEHRRKEPQKEOIRQL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/action/storage_attestation","attest_author":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/action/author_attestation","sign_citation":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/action/citation_signature","submit_replication":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/action/replication_record"}},"created_at":"2026-05-18T00:41:48.309229+00:00","updated_at":"2026-05-18T00:41:48.309229+00:00"}