{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:F6YI2JFB7YNIB3U3MVPTUFJPUC","short_pith_number":"pith:F6YI2JFB","canonical_record":{"source":{"id":"1405.5618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-22T03:02:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c00664c437e2097a48a6673f293290351b0898ed931baa177ef757dd3b445092","abstract_canon_sha256":"cfbaa533c5b24fece25cd57179f1c119d138ce3f62c24d8637bdd664ba01661c"},"schema_version":"1.0"},"canonical_sha256":"2fb08d24a1fe1a80ee9b655f3a152fa0a93a7d1cf6ffa8c40867c83c669dc8dc","source":{"kind":"arxiv","id":"1405.5618","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5618","created_at":"2026-05-18T01:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5618v2","created_at":"2026-05-18T01:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5618","created_at":"2026-05-18T01:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"F6YI2JFB7YNI","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F6YI2JFB7YNIB3U3","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F6YI2JFB","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:F6YI2JFB7YNIB3U3MVPTUFJPUC","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-22T03:02:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c00664c437e2097a48a6673f293290351b0898ed931baa177ef757dd3b445092","abstract_canon_sha256":"cfbaa533c5b24fece25cd57179f1c119d138ce3f62c24d8637bdd664ba01661c"},"schema_version":"1.0"},"canonical_sha256":"2fb08d24a1fe1a80ee9b655f3a152fa0a93a7d1cf6ffa8c40867c83c669dc8dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:09.442069Z","signature_b64":"n4rQoDm8kspZj4wL/7q3C31aa6fD9vIRZGJBlnVs6wByhx9fLUpZMeD911GZ4q5HC/rpLTJm7oaPlH3OhMaHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fb08d24a1fe1a80ee9b655f3a152fa0a93a7d1cf6ffa8c40867c83c669dc8dc","last_reissued_at":"2026-05-18T01:43:09.441362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:09.441362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5618","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79vxRyamUq03QAvLHPztzZGckEN1TCA/3lTbhYyh7oCByWY2BOfAOTIdiI+Cn0aBnB+AOr5Dq+WMgNq1nEv/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T22:51:36.334110Z"},"content_sha256":"5a9735ae979f62fa61bbe7a8ed0171ab701c5fb3b92ea4207fde9424d9244278","schema_version":"1.0","event_id":"sha256:5a9735ae979f62fa61bbe7a8ed0171ab701c5fb3b92ea4207fde9424d9244278"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:F6YI2JFB7YNIB3U3MVPTUFJPUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compressive Phase Retrieval via Generalized Approximate Message Passing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Philip Schniter, Sundeep Rangan","submitted_at":"2014-05-22T03:02:17Z","abstract_excerpt":"In phase retrieval, the goal is to recover a signal $\\mathbf{x}\\in\\mathbb{C}^N$ from the magnitudes of linear measurements $\\mathbf{Ax}\\in\\mathbb{C}^M$. While recent theory has established that $M\\approx 4N$ intensity measurements are necessary and sufficient to recover generic $\\mathbf{x}$, there is great interest in reducing the number of measurements through the exploitation of sparse $\\mathbf{x}$, which is known as compressive phase retrieval. In this work, we detail a novel, probabilistic approach to compressive phase retrieval based on the generalized approximate message passing (GAMP) a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5618","kind":"arxiv","version":2},"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":"2026-05-18T01:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zY5huCYunaiXXQNLIeKl3+lpRbIER4bjfoNy1QTx0P0kzParN3Ah3HL6nlNBeQFjE1vDBPiXfa1/IAb3M3owAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T22:51:36.334475Z"},"content_sha256":"d233cbbad040102112bedcb6e8526d50d71a4c656f2a23f0812a06ad207f1cd9","schema_version":"1.0","event_id":"sha256:d233cbbad040102112bedcb6e8526d50d71a4c656f2a23f0812a06ad207f1cd9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6YI2JFB7YNIB3U3MVPTUFJPUC/bundle.json","state_url":"https://pith.science/pith/F6YI2JFB7YNIB3U3MVPTUFJPUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6YI2JFB7YNIB3U3MVPTUFJPUC/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":"2026-06-19T22:51:36Z","links":{"resolver":"https://pith.science/pith/F6YI2JFB7YNIB3U3MVPTUFJPUC","bundle":"https://pith.science/pith/F6YI2JFB7YNIB3U3MVPTUFJPUC/bundle.json","state":"https://pith.science/pith/F6YI2JFB7YNIB3U3MVPTUFJPUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6YI2JFB7YNIB3U3MVPTUFJPUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F6YI2JFB7YNIB3U3MVPTUFJPUC","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":"cfbaa533c5b24fece25cd57179f1c119d138ce3f62c24d8637bdd664ba01661c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-22T03:02:17Z","title_canon_sha256":"c00664c437e2097a48a6673f293290351b0898ed931baa177ef757dd3b445092"},"schema_version":"1.0","source":{"id":"1405.5618","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5618","created_at":"2026-05-18T01:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5618v2","created_at":"2026-05-18T01:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5618","created_at":"2026-05-18T01:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"F6YI2JFB7YNI","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F6YI2JFB7YNIB3U3","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F6YI2JFB","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:d233cbbad040102112bedcb6e8526d50d71a4c656f2a23f0812a06ad207f1cd9","target":"graph","created_at":"2026-05-18T01:43:09Z","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":"In phase retrieval, the goal is to recover a signal $\\mathbf{x}\\in\\mathbb{C}^N$ from the magnitudes of linear measurements $\\mathbf{Ax}\\in\\mathbb{C}^M$. While recent theory has established that $M\\approx 4N$ intensity measurements are necessary and sufficient to recover generic $\\mathbf{x}$, there is great interest in reducing the number of measurements through the exploitation of sparse $\\mathbf{x}$, which is known as compressive phase retrieval. In this work, we detail a novel, probabilistic approach to compressive phase retrieval based on the generalized approximate message passing (GAMP) a","authors_text":"Philip Schniter, Sundeep Rangan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-22T03:02:17Z","title":"Compressive Phase Retrieval via Generalized Approximate Message Passing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5618","kind":"arxiv","version":2},"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":"sha256:5a9735ae979f62fa61bbe7a8ed0171ab701c5fb3b92ea4207fde9424d9244278","target":"record","created_at":"2026-05-18T01:43:09Z","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":"cfbaa533c5b24fece25cd57179f1c119d138ce3f62c24d8637bdd664ba01661c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-22T03:02:17Z","title_canon_sha256":"c00664c437e2097a48a6673f293290351b0898ed931baa177ef757dd3b445092"},"schema_version":"1.0","source":{"id":"1405.5618","kind":"arxiv","version":2}},"canonical_sha256":"2fb08d24a1fe1a80ee9b655f3a152fa0a93a7d1cf6ffa8c40867c83c669dc8dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fb08d24a1fe1a80ee9b655f3a152fa0a93a7d1cf6ffa8c40867c83c669dc8dc","first_computed_at":"2026-05-18T01:43:09.441362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:09.441362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n4rQoDm8kspZj4wL/7q3C31aa6fD9vIRZGJBlnVs6wByhx9fLUpZMeD911GZ4q5HC/rpLTJm7oaPlH3OhMaHDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:09.442069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5618","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a9735ae979f62fa61bbe7a8ed0171ab701c5fb3b92ea4207fde9424d9244278","sha256:d233cbbad040102112bedcb6e8526d50d71a4c656f2a23f0812a06ad207f1cd9"],"state_sha256":"ea114bd2714ef84ad27f63c8c55ea2b8caf965a18781c6097654d1835a5367f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQ/w/RNhVhTRDNAEpjI/LOaoCuuXXYPXuaINN8I2HsC13k3pkptk4/dGWOD7ZxXq81iNpRLnSXSlPgX4PJDPDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T22:51:36.336409Z","bundle_sha256":"f79834e5cd5ff6ed88794e1821d0a4c1fdf161ad9c4a5094bb2945d3247effc7"}}