{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:YC2ZSU47NT3XAXSOKIMO523R7O","short_pith_number":"pith:YC2ZSU47","canonical_record":{"source":{"id":"0806.3920","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-06-24T16:35:55Z","cross_cats_sorted":[],"title_canon_sha256":"685ef387eba53c4d25dded5ea679df527d93ea82b62a26f5f4595221756860fc","abstract_canon_sha256":"ecd738c8900e6a90a7483f9d944bd07036ca7d6bc6f4539afa31c9db03d1715d"},"schema_version":"1.0"},"canonical_sha256":"c0b599539f6cf7705e4e5218eeeb71fbb30c7430e15a8e2b3134a6f8588cf94b","source":{"kind":"arxiv","id":"0806.3920","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.3920","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"0806.3920v8","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.3920","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"YC2ZSU47NT3X","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"YC2ZSU47NT3XAXSO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"YC2ZSU47","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:YC2ZSU47NT3XAXSOKIMO523R7O","target":"record","payload":{"canonical_record":{"source":{"id":"0806.3920","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-06-24T16:35:55Z","cross_cats_sorted":[],"title_canon_sha256":"685ef387eba53c4d25dded5ea679df527d93ea82b62a26f5f4595221756860fc","abstract_canon_sha256":"ecd738c8900e6a90a7483f9d944bd07036ca7d6bc6f4539afa31c9db03d1715d"},"schema_version":"1.0"},"canonical_sha256":"c0b599539f6cf7705e4e5218eeeb71fbb30c7430e15a8e2b3134a6f8588cf94b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:46.656875Z","signature_b64":"ZKUl0Av6MXxE8PgpEATKs/fZkJSdvJwC1uOdqdxUPWaH9ga9U/Dhm02vrV8KcmQbqYtKgXqza8TnKBcUZTnoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0b599539f6cf7705e4e5218eeeb71fbb30c7430e15a8e2b3134a6f8588cf94b","last_reissued_at":"2026-05-18T03:38:46.656147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:46.656147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0806.3920","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jz5F+k/6IVzo9JwS3dPnEH6yP14qT7xvuFctBKDd89LbxEwmou5BxAMW7ycuLaR5AdO18cqhxIeP24EG1IhVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:16:29.891614Z"},"content_sha256":"3a01ff76990b7405c323ea961b7b349539520046ef65934e0deb381189554876","schema_version":"1.0","event_id":"sha256:3a01ff76990b7405c323ea961b7b349539520046ef65934e0deb381189554876"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:YC2ZSU47NT3XAXSOKIMO523R7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nested iterative algorithms for convex constrained image recovery problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Caroline Chaux, Jean-Christophe Pesquet, Nelly Pustelnik","submitted_at":"2008-06-24T16:35:55Z","abstract_excerpt":"The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex constraint set of the sum of two convex functions f and g, where f may be non-smooth and g is differentiable with a Lipschitz-continuous gradient. To reach this goal, we derive two types of algorithms that combine forward-backward and Douglas-Rachford iterations. The weak convergence of the proposed algorithms is proved. In the case when the Lipschitz-conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3920","kind":"arxiv","version":8},"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":"2026-05-18T03:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cIo5A3cLkLwaReG5YAJUzXW3SqtYs/zZILoeQtzuW6m9UBIVsZZxmiJn61cbnFM663jjYksvI8dy5uluZ5WSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:16:29.892308Z"},"content_sha256":"e8e3dd93a83f8f7a0b41f9d876b86a6729aaa71a0df1a1e393d93c7f50689709","schema_version":"1.0","event_id":"sha256:e8e3dd93a83f8f7a0b41f9d876b86a6729aaa71a0df1a1e393d93c7f50689709"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YC2ZSU47NT3XAXSOKIMO523R7O/bundle.json","state_url":"https://pith.science/pith/YC2ZSU47NT3XAXSOKIMO523R7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YC2ZSU47NT3XAXSOKIMO523R7O/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":"2026-05-26T19:16:29Z","links":{"resolver":"https://pith.science/pith/YC2ZSU47NT3XAXSOKIMO523R7O","bundle":"https://pith.science/pith/YC2ZSU47NT3XAXSOKIMO523R7O/bundle.json","state":"https://pith.science/pith/YC2ZSU47NT3XAXSOKIMO523R7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YC2ZSU47NT3XAXSOKIMO523R7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:YC2ZSU47NT3XAXSOKIMO523R7O","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":"ecd738c8900e6a90a7483f9d944bd07036ca7d6bc6f4539afa31c9db03d1715d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-06-24T16:35:55Z","title_canon_sha256":"685ef387eba53c4d25dded5ea679df527d93ea82b62a26f5f4595221756860fc"},"schema_version":"1.0","source":{"id":"0806.3920","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.3920","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"0806.3920v8","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.3920","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"YC2ZSU47NT3X","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"YC2ZSU47NT3XAXSO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"YC2ZSU47","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:e8e3dd93a83f8f7a0b41f9d876b86a6729aaa71a0df1a1e393d93c7f50689709","target":"graph","created_at":"2026-05-18T03:38:46Z","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":"The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex constraint set of the sum of two convex functions f and g, where f may be non-smooth and g is differentiable with a Lipschitz-continuous gradient. To reach this goal, we derive two types of algorithms that combine forward-backward and Douglas-Rachford iterations. The weak convergence of the proposed algorithms is proved. In the case when the Lipschitz-conti","authors_text":"Caroline Chaux, Jean-Christophe Pesquet, Nelly Pustelnik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-06-24T16:35:55Z","title":"Nested iterative algorithms for convex constrained image recovery problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3920","kind":"arxiv","version":8},"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":"sha256:3a01ff76990b7405c323ea961b7b349539520046ef65934e0deb381189554876","target":"record","created_at":"2026-05-18T03:38:46Z","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":"ecd738c8900e6a90a7483f9d944bd07036ca7d6bc6f4539afa31c9db03d1715d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-06-24T16:35:55Z","title_canon_sha256":"685ef387eba53c4d25dded5ea679df527d93ea82b62a26f5f4595221756860fc"},"schema_version":"1.0","source":{"id":"0806.3920","kind":"arxiv","version":8}},"canonical_sha256":"c0b599539f6cf7705e4e5218eeeb71fbb30c7430e15a8e2b3134a6f8588cf94b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0b599539f6cf7705e4e5218eeeb71fbb30c7430e15a8e2b3134a6f8588cf94b","first_computed_at":"2026-05-18T03:38:46.656147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:46.656147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZKUl0Av6MXxE8PgpEATKs/fZkJSdvJwC1uOdqdxUPWaH9ga9U/Dhm02vrV8KcmQbqYtKgXqza8TnKBcUZTnoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:46.656875Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.3920","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a01ff76990b7405c323ea961b7b349539520046ef65934e0deb381189554876","sha256:e8e3dd93a83f8f7a0b41f9d876b86a6729aaa71a0df1a1e393d93c7f50689709"],"state_sha256":"c613fcd9ec551866f3750b1cc09f0a5b0012fa6597e5a85dea23396604268bcf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGP8oSpGRPm1oIc6I/zvtxtIgtCXMTz67fn9Mk2ZT4QQcS14oqvl7J9IBeFCBjitOJIKsaVCX5wMrSk89YLiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:16:29.896336Z","bundle_sha256":"4fe18468bdf424089267c11fd8dd162b0c0f3e83d8de5b6293ced1ee34e821a4"}}