{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NC4IDJBXB5AKPQC5WULLGRL3SK","short_pith_number":"pith:NC4IDJBX","canonical_record":{"source":{"id":"1911.13179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-11-29T16:24:54Z","cross_cats_sorted":["eess.SP","math.IT"],"title_canon_sha256":"cf936a7cc4538eebffc721331cf583049029b7a10d111140a8c4cce2159151ef","abstract_canon_sha256":"3aa25ed35e57d88a704a11c0498e34a9bd0f21dd0e6960fabab47d4ea99e58d8"},"schema_version":"1.0"},"canonical_sha256":"68b881a4370f40a7c05db516b3457b92ab4d82f057492c8a432d30f07847b5f5","source":{"kind":"arxiv","id":"1911.13179","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.13179","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1911.13179v2","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.13179","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"NC4IDJBXB5AK","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"pith_short_16","alias_value":"NC4IDJBXB5AKPQC5","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"pith_short_8","alias_value":"NC4IDJBX","created_at":"2026-07-05T01:07:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NC4IDJBXB5AKPQC5WULLGRL3SK","target":"record","payload":{"canonical_record":{"source":{"id":"1911.13179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-11-29T16:24:54Z","cross_cats_sorted":["eess.SP","math.IT"],"title_canon_sha256":"cf936a7cc4538eebffc721331cf583049029b7a10d111140a8c4cce2159151ef","abstract_canon_sha256":"3aa25ed35e57d88a704a11c0498e34a9bd0f21dd0e6960fabab47d4ea99e58d8"},"schema_version":"1.0"},"canonical_sha256":"68b881a4370f40a7c05db516b3457b92ab4d82f057492c8a432d30f07847b5f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:51.441571Z","signature_b64":"1Ewwu1fu/9wmZ5qho6kZNjWR37I1keT6ztcf3z1F4d7vKzMKJiROmJghqOLMW/A+Uv3sSd5QmmfhrVz5Q6+wAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68b881a4370f40a7c05db516b3457b92ab4d82f057492c8a432d30f07847b5f5","last_reissued_at":"2026-07-05T01:07:51.441111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:51.441111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.13179","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":"2026-07-05T01:07:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKzf6CbBfIFLBwFr6lsV6qt+lxeBogbMrwSMR6pIbv0xM6k526bMSBaZcMo/RqUTPAuUN1drWPs18fJTHtCiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:24:27.225747Z"},"content_sha256":"69d2a2a9ae4d6c81be1faddd1e786b9891904aba1ae5f514ec342d329475c170","schema_version":"1.0","event_id":"sha256:69d2a2a9ae4d6c81be1faddd1e786b9891904aba1ae5f514ec342d329475c170"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NC4IDJBXB5AKPQC5WULLGRL3SK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on Douglas-Rachford, gradients, and phase retrieval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["eess.SP","math.IT"],"primary_cat":"cs.IT","authors_text":"Eitan Levin, Tamir Bendory","submitted_at":"2019-11-29T16:24:54Z","abstract_excerpt":"The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retrieval problem is solved using a family of algorithms that can be interpreted as variants of Douglas-Rachford splitting. In this work, we establish a connection between Douglas-Rachford and gradient algorithms. Specifically, we show that in some cases a generalization of Douglas-Rachford, called relaxed-reflect-reflect (RRR), can be viewed as gradient descent on a certain objective function. The solutions coincide with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.13179","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.13179/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:07:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gnzBUQ584YDq98wc66JpAXWHjaHlvn5LnmkmAh4L1tq+jEpadgp8w5H5GmzhZZpJ0svUpVz2pkp3/xYUKuIRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:24:27.226252Z"},"content_sha256":"d552fa1268051bf35716d85938158cab48b4c5449112d2ab8a15606954efd950","schema_version":"1.0","event_id":"sha256:d552fa1268051bf35716d85938158cab48b4c5449112d2ab8a15606954efd950"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NC4IDJBXB5AKPQC5WULLGRL3SK/bundle.json","state_url":"https://pith.science/pith/NC4IDJBXB5AKPQC5WULLGRL3SK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NC4IDJBXB5AKPQC5WULLGRL3SK/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":"2026-08-16T11:24:27Z","links":{"resolver":"https://pith.science/pith/NC4IDJBXB5AKPQC5WULLGRL3SK","bundle":"https://pith.science/pith/NC4IDJBXB5AKPQC5WULLGRL3SK/bundle.json","state":"https://pith.science/pith/NC4IDJBXB5AKPQC5WULLGRL3SK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NC4IDJBXB5AKPQC5WULLGRL3SK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NC4IDJBXB5AKPQC5WULLGRL3SK","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":"3aa25ed35e57d88a704a11c0498e34a9bd0f21dd0e6960fabab47d4ea99e58d8","cross_cats_sorted":["eess.SP","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-11-29T16:24:54Z","title_canon_sha256":"cf936a7cc4538eebffc721331cf583049029b7a10d111140a8c4cce2159151ef"},"schema_version":"1.0","source":{"id":"1911.13179","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.13179","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"arxiv_version","alias_value":"1911.13179v2","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.13179","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"pith_short_12","alias_value":"NC4IDJBXB5AK","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"pith_short_16","alias_value":"NC4IDJBXB5AKPQC5","created_at":"2026-07-05T01:07:51Z"},{"alias_kind":"pith_short_8","alias_value":"NC4IDJBX","created_at":"2026-07-05T01:07:51Z"}],"graph_snapshots":[{"event_id":"sha256:d552fa1268051bf35716d85938158cab48b4c5449112d2ab8a15606954efd950","target":"graph","created_at":"2026-07-05T01:07:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.13179/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retrieval problem is solved using a family of algorithms that can be interpreted as variants of Douglas-Rachford splitting. In this work, we establish a connection between Douglas-Rachford and gradient algorithms. Specifically, we show that in some cases a generalization of Douglas-Rachford, called relaxed-reflect-reflect (RRR), can be viewed as gradient descent on a certain objective function. The solutions coincide with t","authors_text":"Eitan Levin, Tamir Bendory","cross_cats":["eess.SP","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-11-29T16:24:54Z","title":"A note on Douglas-Rachford, gradients, and phase retrieval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.13179","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":"sha256:69d2a2a9ae4d6c81be1faddd1e786b9891904aba1ae5f514ec342d329475c170","target":"record","created_at":"2026-07-05T01:07:51Z","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":"3aa25ed35e57d88a704a11c0498e34a9bd0f21dd0e6960fabab47d4ea99e58d8","cross_cats_sorted":["eess.SP","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-11-29T16:24:54Z","title_canon_sha256":"cf936a7cc4538eebffc721331cf583049029b7a10d111140a8c4cce2159151ef"},"schema_version":"1.0","source":{"id":"1911.13179","kind":"arxiv","version":2}},"canonical_sha256":"68b881a4370f40a7c05db516b3457b92ab4d82f057492c8a432d30f07847b5f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68b881a4370f40a7c05db516b3457b92ab4d82f057492c8a432d30f07847b5f5","first_computed_at":"2026-07-05T01:07:51.441111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:07:51.441111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Ewwu1fu/9wmZ5qho6kZNjWR37I1keT6ztcf3z1F4d7vKzMKJiROmJghqOLMW/A+Uv3sSd5QmmfhrVz5Q6+wAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:07:51.441571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.13179","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69d2a2a9ae4d6c81be1faddd1e786b9891904aba1ae5f514ec342d329475c170","sha256:d552fa1268051bf35716d85938158cab48b4c5449112d2ab8a15606954efd950"],"state_sha256":"6a6ffa6df0df0382c12dd31483734e6fa9350c88e5cd4324df0d2adc9f80bc5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2vUPMe9bmKoRjuwl8UpAk/UMh6QIdEHYIy7QW9dvLhxjaeYUh7sjMO5zOAoEoEHhJjXI3v0QKfN9+4DdvX0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T11:24:27.230321Z","bundle_sha256":"7fe984f4466b5237ecbf810e3ac2652a7f2fa33ecfa8f11203ff983413cf1caa"}}