{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:WNVY4P4ASEF7H4TGE2W5WUIFTC","short_pith_number":"pith:WNVY4P4A","canonical_record":{"source":{"id":"0812.0423","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-02T03:52:28Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"57f979c25603bebee50801b55f0a0194a2b5cf227ee90ce20722aa03287a9ee3","abstract_canon_sha256":"21c06807b6ba436b3965eae1ef53fccfd1f223b3c13a09fa2795336972dd34f7"},"schema_version":"1.0"},"canonical_sha256":"b36b8e3f80910bf3f26626addb5105989d2aa8afef80ef07d8d77fbb826cd8e2","source":{"kind":"arxiv","id":"0812.0423","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0423","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0423v2","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0423","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"WNVY4P4ASEF7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"WNVY4P4ASEF7H4TG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"WNVY4P4A","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:WNVY4P4ASEF7H4TGE2W5WUIFTC","target":"record","payload":{"canonical_record":{"source":{"id":"0812.0423","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-02T03:52:28Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"57f979c25603bebee50801b55f0a0194a2b5cf227ee90ce20722aa03287a9ee3","abstract_canon_sha256":"21c06807b6ba436b3965eae1ef53fccfd1f223b3c13a09fa2795336972dd34f7"},"schema_version":"1.0"},"canonical_sha256":"b36b8e3f80910bf3f26626addb5105989d2aa8afef80ef07d8d77fbb826cd8e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:04.615945Z","signature_b64":"GNwOLdqQrNz533h4XW/x68eqbRtUv6sFeQaSfj6YJOUkpeHmLFZJLYZ6i7nnfOWYFbzbtJ0ZN7wZ/8EqVqe4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b36b8e3f80910bf3f26626addb5105989d2aa8afef80ef07d8d77fbb826cd8e2","last_reissued_at":"2026-05-18T02:18:04.615140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:04.615140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.0423","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":"2026-05-18T02:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDYaLASchbwymcpjq1mm4Xm4eJpaD8rapHozX2Kv48kXAM5kwTkXKGOmdciTgDRkdLV2IWk7M0IrbANR4mYgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:52:19.637187Z"},"content_sha256":"39ab420e483bdfef35e0c9ac6aa111c32a8c4d300f865fbd79c9e1dde4dbfc7e","schema_version":"1.0","event_id":"sha256:39ab420e483bdfef35e0c9ac6aa111c32a8c4d300f865fbd79c9e1dde4dbfc7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:WNVY4P4ASEF7H4TGE2W5WUIFTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A proximal method for composite minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"A.S. Lewis, S.J. Wright","submitted_at":"2008-12-02T03:52:28Z","abstract_excerpt":"We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term. Properties of local solutions of this subproblem underlie both a global convergence result and an identification property of the active manifold containing the solution of the original problem. Preliminary computational resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0423","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":"2026-05-18T02:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFfOxUHsS+PIPl6/85/7HdGHAmCEjSMJXKo70fL2psXRreHWB+NjOsPsLhtEA24Mxoh54qJAvBjb71qqUKHaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:52:19.637927Z"},"content_sha256":"c2aafcf41667a08d7cb51b983688b14cb86125641c7084c98ab7c2b45881b14e","schema_version":"1.0","event_id":"sha256:c2aafcf41667a08d7cb51b983688b14cb86125641c7084c98ab7c2b45881b14e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WNVY4P4ASEF7H4TGE2W5WUIFTC/bundle.json","state_url":"https://pith.science/pith/WNVY4P4ASEF7H4TGE2W5WUIFTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WNVY4P4ASEF7H4TGE2W5WUIFTC/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":"2026-06-09T19:52:19Z","links":{"resolver":"https://pith.science/pith/WNVY4P4ASEF7H4TGE2W5WUIFTC","bundle":"https://pith.science/pith/WNVY4P4ASEF7H4TGE2W5WUIFTC/bundle.json","state":"https://pith.science/pith/WNVY4P4ASEF7H4TGE2W5WUIFTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WNVY4P4ASEF7H4TGE2W5WUIFTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:WNVY4P4ASEF7H4TGE2W5WUIFTC","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":"21c06807b6ba436b3965eae1ef53fccfd1f223b3c13a09fa2795336972dd34f7","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-02T03:52:28Z","title_canon_sha256":"57f979c25603bebee50801b55f0a0194a2b5cf227ee90ce20722aa03287a9ee3"},"schema_version":"1.0","source":{"id":"0812.0423","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0423","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0423v2","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0423","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"WNVY4P4ASEF7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"WNVY4P4ASEF7H4TG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"WNVY4P4A","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c2aafcf41667a08d7cb51b983688b14cb86125641c7084c98ab7c2b45881b14e","target":"graph","created_at":"2026-05-18T02:18:04Z","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 consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term. Properties of local solutions of this subproblem underlie both a global convergence result and an identification property of the active manifold containing the solution of the original problem. Preliminary computational resu","authors_text":"A.S. Lewis, S.J. Wright","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-02T03:52:28Z","title":"A proximal method for composite minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0423","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":"sha256:39ab420e483bdfef35e0c9ac6aa111c32a8c4d300f865fbd79c9e1dde4dbfc7e","target":"record","created_at":"2026-05-18T02:18:04Z","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":"21c06807b6ba436b3965eae1ef53fccfd1f223b3c13a09fa2795336972dd34f7","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-02T03:52:28Z","title_canon_sha256":"57f979c25603bebee50801b55f0a0194a2b5cf227ee90ce20722aa03287a9ee3"},"schema_version":"1.0","source":{"id":"0812.0423","kind":"arxiv","version":2}},"canonical_sha256":"b36b8e3f80910bf3f26626addb5105989d2aa8afef80ef07d8d77fbb826cd8e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b36b8e3f80910bf3f26626addb5105989d2aa8afef80ef07d8d77fbb826cd8e2","first_computed_at":"2026-05-18T02:18:04.615140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:04.615140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GNwOLdqQrNz533h4XW/x68eqbRtUv6sFeQaSfj6YJOUkpeHmLFZJLYZ6i7nnfOWYFbzbtJ0ZN7wZ/8EqVqe4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:04.615945Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0423","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39ab420e483bdfef35e0c9ac6aa111c32a8c4d300f865fbd79c9e1dde4dbfc7e","sha256:c2aafcf41667a08d7cb51b983688b14cb86125641c7084c98ab7c2b45881b14e"],"state_sha256":"65080825459035f69c2c07608268334b373c81b644e09c6e78e0b5d74fa75fc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rjs8WFYSu+89O4xuWLMQMsC3lz9FsQrRhQAjhgolVCEUSFZ0iVRzSjs/TTTF/PBle6xA3GjnZCLIHPduR7rdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:52:19.642008Z","bundle_sha256":"b5ed9ec121aeeb7c87d32accd6cc9b05075d0f3fec350a060274af1f897f0dfa"}}