{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XWQ4XOOPKV5UXMQMKMGDJCEUYI","short_pith_number":"pith:XWQ4XOOP","canonical_record":{"source":{"id":"1408.1887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-08T15:25:48Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"00ad908a624d51f6455182beea71665aaa5eec1688aa0400b814fd91902a8928","abstract_canon_sha256":"072736a42276294049fa13780e4b89e8597f7d48141b1e682fae959a17478150"},"schema_version":"1.0"},"canonical_sha256":"bda1cbb9cf557b4bb20c530c348894c23aec07b30d6f0e3206895379fd66392a","source":{"kind":"arxiv","id":"1408.1887","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1887","created_at":"2026-05-18T00:24:25Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1887v1","created_at":"2026-05-18T00:24:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1887","created_at":"2026-05-18T00:24:25Z"},{"alias_kind":"pith_short_12","alias_value":"XWQ4XOOPKV5U","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XWQ4XOOPKV5UXMQM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XWQ4XOOP","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XWQ4XOOPKV5UXMQMKMGDJCEUYI","target":"record","payload":{"canonical_record":{"source":{"id":"1408.1887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-08T15:25:48Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"00ad908a624d51f6455182beea71665aaa5eec1688aa0400b814fd91902a8928","abstract_canon_sha256":"072736a42276294049fa13780e4b89e8597f7d48141b1e682fae959a17478150"},"schema_version":"1.0"},"canonical_sha256":"bda1cbb9cf557b4bb20c530c348894c23aec07b30d6f0e3206895379fd66392a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:25.481609Z","signature_b64":"IqtWs9ueoDLR1XnRbrvWfwL6d3xFs6T1hF+Wqlf+HKfGQFPutJTWdwOZezIJ17NKL72u3HcWNiVdz09V7mqaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bda1cbb9cf557b4bb20c530c348894c23aec07b30d6f0e3206895379fd66392a","last_reissued_at":"2026-05-18T00:24:25.481089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:25.481089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.1887","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":"2026-05-18T00:24:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hfTLSwn2O1ctbw/n1NWfzaM9EgDNrDCNijsuOrru36YA1BDTxNzn7smcaondI6gvU0dBiEMpFoMJ9jKreiW8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:43:04.773626Z"},"content_sha256":"278261633857227976fc439b0047c4a24a6ce7d46aac64b52ad2b00128b1932a","schema_version":"1.0","event_id":"sha256:278261633857227976fc439b0047c4a24a6ce7d46aac64b52ad2b00128b1932a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XWQ4XOOPKV5UXMQMKMGDJCEUYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proximal Heterogeneous Block Input-Output Method and application to Blind Ptychographic Diffraction Imaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"D. Russell Luke, Matthew K. Tam, Robert Hesse, Shoham Sabach","submitted_at":"2014-08-08T15:25:48Z","abstract_excerpt":"We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind ptychographic imaging. Compared to other schemes in the literature, our approach differs in two ways: (i) it is posed within a clear mathematical framework with practically verifiable assumptions, and (ii) under the given assumptions, it is provably convergent to critical points. A numerical comparison of our proposed algorithm with the current state-of-the-art "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1887","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":"2026-05-18T00:24:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TdnWQowaU60zqbTHce9lF5ICg8BqwFvr3WZyr9nUm/CBS9DzTPnlFTR9GQX7G4Zs7PlFJb364zm1/iQn64VXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:43:04.774358Z"},"content_sha256":"31b3708d69641b3dc61728d9c66928a11ef14806104a1c21df5858d155b6076e","schema_version":"1.0","event_id":"sha256:31b3708d69641b3dc61728d9c66928a11ef14806104a1c21df5858d155b6076e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWQ4XOOPKV5UXMQMKMGDJCEUYI/bundle.json","state_url":"https://pith.science/pith/XWQ4XOOPKV5UXMQMKMGDJCEUYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWQ4XOOPKV5UXMQMKMGDJCEUYI/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":"2026-05-28T22:43:04Z","links":{"resolver":"https://pith.science/pith/XWQ4XOOPKV5UXMQMKMGDJCEUYI","bundle":"https://pith.science/pith/XWQ4XOOPKV5UXMQMKMGDJCEUYI/bundle.json","state":"https://pith.science/pith/XWQ4XOOPKV5UXMQMKMGDJCEUYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWQ4XOOPKV5UXMQMKMGDJCEUYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XWQ4XOOPKV5UXMQMKMGDJCEUYI","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":"072736a42276294049fa13780e4b89e8597f7d48141b1e682fae959a17478150","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-08T15:25:48Z","title_canon_sha256":"00ad908a624d51f6455182beea71665aaa5eec1688aa0400b814fd91902a8928"},"schema_version":"1.0","source":{"id":"1408.1887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1887","created_at":"2026-05-18T00:24:25Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1887v1","created_at":"2026-05-18T00:24:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1887","created_at":"2026-05-18T00:24:25Z"},{"alias_kind":"pith_short_12","alias_value":"XWQ4XOOPKV5U","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XWQ4XOOPKV5UXMQM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XWQ4XOOP","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:31b3708d69641b3dc61728d9c66928a11ef14806104a1c21df5858d155b6076e","target":"graph","created_at":"2026-05-18T00:24:25Z","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":"We propose a general alternating minimization algorithm for nonconvex optimization problems with separable structure and nonconvex coupling between blocks of variables. To fix our ideas, we apply the methodology to the problem of blind ptychographic imaging. Compared to other schemes in the literature, our approach differs in two ways: (i) it is posed within a clear mathematical framework with practically verifiable assumptions, and (ii) under the given assumptions, it is provably convergent to critical points. A numerical comparison of our proposed algorithm with the current state-of-the-art ","authors_text":"D. Russell Luke, Matthew K. Tam, Robert Hesse, Shoham Sabach","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-08T15:25:48Z","title":"Proximal Heterogeneous Block Input-Output Method and application to Blind Ptychographic Diffraction Imaging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1887","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":"sha256:278261633857227976fc439b0047c4a24a6ce7d46aac64b52ad2b00128b1932a","target":"record","created_at":"2026-05-18T00:24:25Z","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":"072736a42276294049fa13780e4b89e8597f7d48141b1e682fae959a17478150","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-08T15:25:48Z","title_canon_sha256":"00ad908a624d51f6455182beea71665aaa5eec1688aa0400b814fd91902a8928"},"schema_version":"1.0","source":{"id":"1408.1887","kind":"arxiv","version":1}},"canonical_sha256":"bda1cbb9cf557b4bb20c530c348894c23aec07b30d6f0e3206895379fd66392a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bda1cbb9cf557b4bb20c530c348894c23aec07b30d6f0e3206895379fd66392a","first_computed_at":"2026-05-18T00:24:25.481089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:25.481089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IqtWs9ueoDLR1XnRbrvWfwL6d3xFs6T1hF+Wqlf+HKfGQFPutJTWdwOZezIJ17NKL72u3HcWNiVdz09V7mqaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:25.481609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:278261633857227976fc439b0047c4a24a6ce7d46aac64b52ad2b00128b1932a","sha256:31b3708d69641b3dc61728d9c66928a11ef14806104a1c21df5858d155b6076e"],"state_sha256":"86814d7ac2b4ce2cda1913c95116bb5795708bcb2d3bb046c7b0d676583f1ad6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9qXi+Xk3tr5QCmILy77YiB0i0TIQtA+WBVzmluG5esGIZVocpUtaFVL6Ql+Gv0eiMANTxiipRmw3F4Tl8oKNCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:43:04.778166Z","bundle_sha256":"5349c924179da1cb5f60f1da17f4537a959451af78927b26da3067e15cf9265c"}}