{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YVPXOAYIUKADARDBVR4L5GSYM7","short_pith_number":"pith:YVPXOAYI","canonical_record":{"source":{"id":"1311.7045","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T17:16:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"93478d74e8a7852d5516229b577e609c7bf2f7990fa090f216bdfff7f96b2860","abstract_canon_sha256":"b4483268653efbeb7b4b23fb1b078aab85787ced17d9eb4010814fcf9095ded1"},"schema_version":"1.0"},"canonical_sha256":"c55f770308a280304461ac78be9a5867f221508adb597fba33a8b98096e7337a","source":{"kind":"arxiv","id":"1311.7045","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7045","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7045v4","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7045","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"pith_short_12","alias_value":"YVPXOAYIUKAD","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YVPXOAYIUKADARDB","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YVPXOAYI","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YVPXOAYIUKADARDBVR4L5GSYM7","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7045","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T17:16:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"93478d74e8a7852d5516229b577e609c7bf2f7990fa090f216bdfff7f96b2860","abstract_canon_sha256":"b4483268653efbeb7b4b23fb1b078aab85787ced17d9eb4010814fcf9095ded1"},"schema_version":"1.0"},"canonical_sha256":"c55f770308a280304461ac78be9a5867f221508adb597fba33a8b98096e7337a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:23.077009Z","signature_b64":"HqZT0zRokWGol1mAfS5mW4YBRjoZvmbGtrsk7wze9wP9Bb1cL7gj1lPwcLoZI2hllg9qC4uA9LSNVpDEXTJnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c55f770308a280304461ac78be9a5867f221508adb597fba33a8b98096e7337a","last_reissued_at":"2026-05-18T02:47:23.076378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:23.076378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7045","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vfgNlu+tpw9boHLrJHw8U2+o46xPCCWKTGUWezYL9ydt9Y+JrccxJPdrjSCZHYyEtxXXEiUbuYjf7zkBS8K2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:31:31.991979Z"},"content_sha256":"f9c0994429185f89be2e7b470c3687cf15c1042b8afe53f06ca97251b97faf14","schema_version":"1.0","event_id":"sha256:f9c0994429185f89be2e7b470c3687cf15c1042b8afe53f06ca97251b97faf14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YVPXOAYIUKADARDBVR4L5GSYM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase retrieval from low-rate samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fanny Yang, Holger Boche, Volker Pohl","submitted_at":"2013-11-27T17:16:02Z","abstract_excerpt":"The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a union of subspaces, respectively. A stable analytic reconstruction procedure of low complexity is given. Additionally it is proven that signal recovery from these measurements can be solved exactly via a semidefinite program. A practical implementation with 4 deterministic diffraction patterns is provided and some numerical experiments with noisy measurements co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7045","kind":"arxiv","version":4},"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":"2026-05-18T02:47:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iaIwCDEEgkzKoZn7EvspW3rkf73/pwXMbILKkZ7iVXkvkwu98IEBpc1Q6oUCx1DHZddFQdf3jUtiOfl5BA6LCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:31:31.992429Z"},"content_sha256":"0186edebea472b406d7bdc5db5d4d6594c3daadb2e7eafc6867ef12e282f599d","schema_version":"1.0","event_id":"sha256:0186edebea472b406d7bdc5db5d4d6594c3daadb2e7eafc6867ef12e282f599d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YVPXOAYIUKADARDBVR4L5GSYM7/bundle.json","state_url":"https://pith.science/pith/YVPXOAYIUKADARDBVR4L5GSYM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YVPXOAYIUKADARDBVR4L5GSYM7/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":"2026-05-25T23:31:31Z","links":{"resolver":"https://pith.science/pith/YVPXOAYIUKADARDBVR4L5GSYM7","bundle":"https://pith.science/pith/YVPXOAYIUKADARDBVR4L5GSYM7/bundle.json","state":"https://pith.science/pith/YVPXOAYIUKADARDBVR4L5GSYM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YVPXOAYIUKADARDBVR4L5GSYM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YVPXOAYIUKADARDBVR4L5GSYM7","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":"b4483268653efbeb7b4b23fb1b078aab85787ced17d9eb4010814fcf9095ded1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T17:16:02Z","title_canon_sha256":"93478d74e8a7852d5516229b577e609c7bf2f7990fa090f216bdfff7f96b2860"},"schema_version":"1.0","source":{"id":"1311.7045","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7045","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7045v4","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7045","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"pith_short_12","alias_value":"YVPXOAYIUKAD","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YVPXOAYIUKADARDB","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YVPXOAYI","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:0186edebea472b406d7bdc5db5d4d6594c3daadb2e7eafc6867ef12e282f599d","target":"graph","created_at":"2026-05-18T02:47:23Z","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 paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a union of subspaces, respectively. A stable analytic reconstruction procedure of low complexity is given. Additionally it is proven that signal recovery from these measurements can be solved exactly via a semidefinite program. A practical implementation with 4 deterministic diffraction patterns is provided and some numerical experiments with noisy measurements co","authors_text":"Fanny Yang, Holger Boche, Volker Pohl","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T17:16:02Z","title":"Phase retrieval from low-rate samples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7045","kind":"arxiv","version":4},"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:f9c0994429185f89be2e7b470c3687cf15c1042b8afe53f06ca97251b97faf14","target":"record","created_at":"2026-05-18T02:47:23Z","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":"b4483268653efbeb7b4b23fb1b078aab85787ced17d9eb4010814fcf9095ded1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-11-27T17:16:02Z","title_canon_sha256":"93478d74e8a7852d5516229b577e609c7bf2f7990fa090f216bdfff7f96b2860"},"schema_version":"1.0","source":{"id":"1311.7045","kind":"arxiv","version":4}},"canonical_sha256":"c55f770308a280304461ac78be9a5867f221508adb597fba33a8b98096e7337a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c55f770308a280304461ac78be9a5867f221508adb597fba33a8b98096e7337a","first_computed_at":"2026-05-18T02:47:23.076378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:23.076378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HqZT0zRokWGol1mAfS5mW4YBRjoZvmbGtrsk7wze9wP9Bb1cL7gj1lPwcLoZI2hllg9qC4uA9LSNVpDEXTJnBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:23.077009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7045","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9c0994429185f89be2e7b470c3687cf15c1042b8afe53f06ca97251b97faf14","sha256:0186edebea472b406d7bdc5db5d4d6594c3daadb2e7eafc6867ef12e282f599d"],"state_sha256":"5bd8100cff3e82fa2f027d739e253684d348829f7ae103df49c8845d3010eb20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nx7TZuxFITsLlaHzcImqE77W5d/LKrSvELpaJlVN1axA5ivMKKXXDV1Qo+7I0WGcXmnPiYIWsvmbZOFmfwVTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:31:31.995457Z","bundle_sha256":"eab52dafd27e583c4e4ee4e92d5b4d1495858905cc34d07107719c7ec5043584"}}