{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:N7CHAIPXZIJ7UPDL4TBXDN4TCE","short_pith_number":"pith:N7CHAIPX","canonical_record":{"source":{"id":"1308.6337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-08-29T01:09:49Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"c1199931f78d6734d90882d04b8017fca827b8b3c8601c0f49e015235711ab93","abstract_canon_sha256":"7ecb196fc5cb3a5db9d2a653ea3e2bccc291f6aacdca693dd15e492e691b4a5d"},"schema_version":"1.0"},"canonical_sha256":"6fc47021f7ca13fa3c6be4c371b793110a93778950049e9aae826f889974921e","source":{"kind":"arxiv","id":"1308.6337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6337","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6337v1","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6337","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"N7CHAIPXZIJ7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N7CHAIPXZIJ7UPDL","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N7CHAIPX","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:N7CHAIPXZIJ7UPDL4TBXDN4TCE","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-08-29T01:09:49Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"c1199931f78d6734d90882d04b8017fca827b8b3c8601c0f49e015235711ab93","abstract_canon_sha256":"7ecb196fc5cb3a5db9d2a653ea3e2bccc291f6aacdca693dd15e492e691b4a5d"},"schema_version":"1.0"},"canonical_sha256":"6fc47021f7ca13fa3c6be4c371b793110a93778950049e9aae826f889974921e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:40.225946Z","signature_b64":"j2YGfSMh50VL3Scde2KC50BAwvuxJ21UHeO56Bmcupi36VSWwvAZxYctUcU2hm8enx0MSIr1fkjwaic1nno2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fc47021f7ca13fa3c6be4c371b793110a93778950049e9aae826f889974921e","last_reissued_at":"2026-05-18T03:14:40.225206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:40.225206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6337","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":"2026-05-18T03:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmseaW5uokdFjAIYwJ/tsMOsVPClMA/FB9kfM0kCoSM8mVNe6wuLKQXezsk7uA205WzJEOFx53XQClzpmzckBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:07:03.537945Z"},"content_sha256":"7f6e6d008551f8c171dc81a01a2b884c2bbbe6d8f6bb31691b31119f92b414c4","schema_version":"1.0","event_id":"sha256:7f6e6d008551f8c171dc81a01a2b884c2bbbe6d8f6bb31691b31119f92b414c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:N7CHAIPXZIJ7UPDL4TBXDN4TCE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A dual algorithm for a class of augmented convex models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.OC","authors_text":"Hui Zhang, Lizhi Cheng, Wotao Yin","submitted_at":"2013-08-29T01:09:49Z","abstract_excerpt":"Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient algorithm. The proposed algorithm includes the linearized Bregman algorithm and the singular value thresholding algorithm as special cases. Based on fundamental properties of proximal operators, we present a concise approach to establish the convergence of both primal and dual sequences, improving the results in the existing literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6337","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":"2026-05-18T03:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+N3yW5dC8HM4+7TiDXmsMlTVNmk9aw/8e9YDhPvrtUeRyPbYJ2h0SonH2MbWMMOAvy5r+btRKAwd55XeBahgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:07:03.538297Z"},"content_sha256":"af0423173f2337a17f218573c3c78970ecb4490a3411eeb66a70a24367a05b69","schema_version":"1.0","event_id":"sha256:af0423173f2337a17f218573c3c78970ecb4490a3411eeb66a70a24367a05b69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7CHAIPXZIJ7UPDL4TBXDN4TCE/bundle.json","state_url":"https://pith.science/pith/N7CHAIPXZIJ7UPDL4TBXDN4TCE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7CHAIPXZIJ7UPDL4TBXDN4TCE/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":"2026-05-30T04:07:03Z","links":{"resolver":"https://pith.science/pith/N7CHAIPXZIJ7UPDL4TBXDN4TCE","bundle":"https://pith.science/pith/N7CHAIPXZIJ7UPDL4TBXDN4TCE/bundle.json","state":"https://pith.science/pith/N7CHAIPXZIJ7UPDL4TBXDN4TCE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7CHAIPXZIJ7UPDL4TBXDN4TCE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N7CHAIPXZIJ7UPDL4TBXDN4TCE","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":"7ecb196fc5cb3a5db9d2a653ea3e2bccc291f6aacdca693dd15e492e691b4a5d","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-08-29T01:09:49Z","title_canon_sha256":"c1199931f78d6734d90882d04b8017fca827b8b3c8601c0f49e015235711ab93"},"schema_version":"1.0","source":{"id":"1308.6337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6337","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6337v1","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6337","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"N7CHAIPXZIJ7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N7CHAIPXZIJ7UPDL","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N7CHAIPX","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:af0423173f2337a17f218573c3c78970ecb4490a3411eeb66a70a24367a05b69","target":"graph","created_at":"2026-05-18T03:14:40Z","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":"Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient algorithm. The proposed algorithm includes the linearized Bregman algorithm and the singular value thresholding algorithm as special cases. Based on fundamental properties of proximal operators, we present a concise approach to establish the convergence of both primal and dual sequences, improving the results in the existing literature.","authors_text":"Hui Zhang, Lizhi Cheng, Wotao Yin","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-08-29T01:09:49Z","title":"A dual algorithm for a class of augmented convex models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6337","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":"sha256:7f6e6d008551f8c171dc81a01a2b884c2bbbe6d8f6bb31691b31119f92b414c4","target":"record","created_at":"2026-05-18T03:14:40Z","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":"7ecb196fc5cb3a5db9d2a653ea3e2bccc291f6aacdca693dd15e492e691b4a5d","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-08-29T01:09:49Z","title_canon_sha256":"c1199931f78d6734d90882d04b8017fca827b8b3c8601c0f49e015235711ab93"},"schema_version":"1.0","source":{"id":"1308.6337","kind":"arxiv","version":1}},"canonical_sha256":"6fc47021f7ca13fa3c6be4c371b793110a93778950049e9aae826f889974921e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fc47021f7ca13fa3c6be4c371b793110a93778950049e9aae826f889974921e","first_computed_at":"2026-05-18T03:14:40.225206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:40.225206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j2YGfSMh50VL3Scde2KC50BAwvuxJ21UHeO56Bmcupi36VSWwvAZxYctUcU2hm8enx0MSIr1fkjwaic1nno2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:40.225946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f6e6d008551f8c171dc81a01a2b884c2bbbe6d8f6bb31691b31119f92b414c4","sha256:af0423173f2337a17f218573c3c78970ecb4490a3411eeb66a70a24367a05b69"],"state_sha256":"b64ac5042b729d3eca7dff038f04154710ffde08c8107e0c236802fd492e6de6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BI8AFmMsRn9lYBd2PWdLZDQOFVCHCpXMSS4VGGRPL8A9uTesD5jpfw2kaTd6hqsDyswBUR5Aim2/ncyAAmpYDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:07:03.541623Z","bundle_sha256":"fdbb06a0bfe770b16fc0bdde8d5ff74f5f664f2e607211cd8b40eb095ce9c2c7"}}