{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SKGWSVF6M2CEHRRKEPQKEOIRQL","short_pith_number":"pith:SKGWSVF6","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"},"canonical_sha256":"928d6954be668443c62a23e0a2391182dddf03ae22e072dcb419840382601e5b","source":{"kind":"arxiv","id":"1706.07738","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07738","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07738v1","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07738","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"SKGWSVF6M2CE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SKGWSVF6M2CEHRRK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SKGWSVF6","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SKGWSVF6M2CEHRRKEPQKEOIRQL","target":"record","payload":{"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"},"canonical_sha256":"928d6954be668443c62a23e0a2391182dddf03ae22e072dcb419840382601e5b","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"},"source_kind":"arxiv","source_id":"1706.07738","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":"2026-05-18T00:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IvodTTn4DTUNw2ULluYX49SJ78lGHgS1U4tp4vCmCtI8pU28UZvfQ23AH20ISpH+n+YbFpDLz+uwT6p6eFMXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:34:30.192649Z"},"content_sha256":"7f66bf3839327af75fe0c753a551007b110ec283c671a327fb35af5bbcc9ec84","schema_version":"1.0","event_id":"sha256:7f66bf3839327af75fe0c753a551007b110ec283c671a327fb35af5bbcc9ec84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SKGWSVF6M2CEHRRKEPQKEOIRQL","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRzyyGXugBhJnJa19W8LdDXPeduEKgOzB0TAaz7te/c9Ac7PM+xe1//EAHWh10VLwyIOA6wv6bdc3JtnS6rcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:34:30.192994Z"},"content_sha256":"3e0fda8d14c3f1d45d428895b2929ebd0009501773833b18dbff9758069937d2","schema_version":"1.0","event_id":"sha256:3e0fda8d14c3f1d45d428895b2929ebd0009501773833b18dbff9758069937d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/bundle.json","state_url":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/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":"2026-06-03T15:34:30Z","links":{"resolver":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL","bundle":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/bundle.json","state":"https://pith.science/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKGWSVF6M2CEHRRKEPQKEOIRQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SKGWSVF6M2CEHRRKEPQKEOIRQL","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":"dc6887138aebe51700281966aae7a0bc9a5093664d2cced483814cddeaa31a20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-23T15:05:46Z","title_canon_sha256":"14a392c82c789493ba877205711c3caca8e25fd5c707d84612be372bfe563e1d"},"schema_version":"1.0","source":{"id":"1706.07738","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07738","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07738v1","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07738","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"SKGWSVF6M2CE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SKGWSVF6M2CEHRRK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SKGWSVF6","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:3e0fda8d14c3f1d45d428895b2929ebd0009501773833b18dbff9758069937d2","target":"graph","created_at":"2026-05-18T00:41:48Z","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":"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","authors_text":"Deguang Han, Ted Juste, Wenchang Sun, Youfa Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-23T15:05:46Z","title":"Frame Phase-retrievability and Exact phase-retrievable frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07738","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":"sha256:7f66bf3839327af75fe0c753a551007b110ec283c671a327fb35af5bbcc9ec84","target":"record","created_at":"2026-05-18T00:41:48Z","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":"dc6887138aebe51700281966aae7a0bc9a5093664d2cced483814cddeaa31a20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-23T15:05:46Z","title_canon_sha256":"14a392c82c789493ba877205711c3caca8e25fd5c707d84612be372bfe563e1d"},"schema_version":"1.0","source":{"id":"1706.07738","kind":"arxiv","version":1}},"canonical_sha256":"928d6954be668443c62a23e0a2391182dddf03ae22e072dcb419840382601e5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"928d6954be668443c62a23e0a2391182dddf03ae22e072dcb419840382601e5b","first_computed_at":"2026-05-18T00:41:48.309151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:48.309151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a5NbOlFZtO/rZZWpULbX9oN+TFnKOfBFWCsHHqsah6hhl55eyeFbJFZpMvkzwf9V/XJ9TMmB3zqZFM9rp08iCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:48.309672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07738","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f66bf3839327af75fe0c753a551007b110ec283c671a327fb35af5bbcc9ec84","sha256:3e0fda8d14c3f1d45d428895b2929ebd0009501773833b18dbff9758069937d2"],"state_sha256":"9bfcfa6208db9700415bcdea08568055e697fc8e53591d681258bf394016d500"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AWUGxUUUHgzpNeABDrmxM6ZMN/se5JhlCYeyRfEAJDdZYK28lLKytPMrw6Fpots2ZujFEMaQwL3CLtER1ay3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:34:30.194974Z","bundle_sha256":"bcf4fb95d0ce81c779470d86ce2785f5592b1d098f63d3f402ee6cd891f4adb7"}}