{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6MPNGGOYCVATLUAZ6QAW6NIRX7","short_pith_number":"pith:6MPNGGOY","canonical_record":{"source":{"id":"1210.5844","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-10-22T09:12:48Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"24cf5fe0c8d84eeeb4fc417d250fc2a40890e293dfc459e408acfa3cdffb01fc","abstract_canon_sha256":"0ab033a7a010d918e5ffed39fbe30382b5294bc24a2a29ea85e6734df8d65d11"},"schema_version":"1.0"},"canonical_sha256":"f31ed319d8154135d019f4016f3511bfe71d2cc8fa773874f1c2b18ba2336d1c","source":{"kind":"arxiv","id":"1210.5844","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5844","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5844v3","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5844","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"6MPNGGOYCVAT","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6MPNGGOYCVATLUAZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6MPNGGOY","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6MPNGGOYCVATLUAZ6QAW6NIRX7","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5844","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-10-22T09:12:48Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"24cf5fe0c8d84eeeb4fc417d250fc2a40890e293dfc459e408acfa3cdffb01fc","abstract_canon_sha256":"0ab033a7a010d918e5ffed39fbe30382b5294bc24a2a29ea85e6734df8d65d11"},"schema_version":"1.0"},"canonical_sha256":"f31ed319d8154135d019f4016f3511bfe71d2cc8fa773874f1c2b18ba2336d1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:04.016880Z","signature_b64":"Yt94tlwp33Ujypif8uG9ppru5zwv8CPNGjGfEpQya4lfZH/+puzEQHZh/iEscIwdrbxGnXxGg+QL2hOHps1FCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f31ed319d8154135d019f4016f3511bfe71d2cc8fa773874f1c2b18ba2336d1c","last_reissued_at":"2026-05-18T02:56:04.016246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:04.016246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5844","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7zAnMu3A4X38GT3k/sjWs2WFkfe6+VzqkaqKdXJL/ogi+O4cx911J1vyP+zmZzPYfsdIXK9VnkmXiYX09XaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:59:01.643252Z"},"content_sha256":"0c8f881b2d0d88107b3cff46a7cde32af9a4b5f0ed6500ce5872b2934a7f4e83","schema_version":"1.0","event_id":"sha256:0c8f881b2d0d88107b3cff46a7cde32af9a4b5f0ed6500ce5872b2934a7f4e83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6MPNGGOYCVATLUAZ6QAW6NIRX7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Epigraphical splitting for solving constrained convex formulations of inverse problems with proximal tools","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.NA","authors_text":"B\\'eatrice Pesquet-Popescu, Giovanni Chierchia, Jean-Christophe Pesquet, Nelly Pustelnik","submitted_at":"2012-10-22T09:12:48Z","abstract_excerpt":"We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For such constraints, the associated projection operator generally does not have a simple form. We circumvent this difficulty by splitting the lower level set into as many epigraphs as functions involved in the sum. A closed half-space constraint is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5844","kind":"arxiv","version":3},"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":"2026-05-18T02:56:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ku5c8pLDHBkgt1mPJlD1jZGXSv9QzbtJrPX6EzYqpmb0HUE2h5zUhJ9r8hcyHDjZPV5FjF8DxhqLSjp8jgpVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:59:01.643614Z"},"content_sha256":"cd2ffb2397bbedddf41cabb978e63d7ef19fbd8ef340293cb3ca383735ef5f70","schema_version":"1.0","event_id":"sha256:cd2ffb2397bbedddf41cabb978e63d7ef19fbd8ef340293cb3ca383735ef5f70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MPNGGOYCVATLUAZ6QAW6NIRX7/bundle.json","state_url":"https://pith.science/pith/6MPNGGOYCVATLUAZ6QAW6NIRX7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MPNGGOYCVATLUAZ6QAW6NIRX7/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":"2026-06-27T14:59:01Z","links":{"resolver":"https://pith.science/pith/6MPNGGOYCVATLUAZ6QAW6NIRX7","bundle":"https://pith.science/pith/6MPNGGOYCVATLUAZ6QAW6NIRX7/bundle.json","state":"https://pith.science/pith/6MPNGGOYCVATLUAZ6QAW6NIRX7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MPNGGOYCVATLUAZ6QAW6NIRX7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6MPNGGOYCVATLUAZ6QAW6NIRX7","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":"0ab033a7a010d918e5ffed39fbe30382b5294bc24a2a29ea85e6734df8d65d11","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-10-22T09:12:48Z","title_canon_sha256":"24cf5fe0c8d84eeeb4fc417d250fc2a40890e293dfc459e408acfa3cdffb01fc"},"schema_version":"1.0","source":{"id":"1210.5844","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5844","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5844v3","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5844","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"6MPNGGOYCVAT","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6MPNGGOYCVATLUAZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6MPNGGOY","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:cd2ffb2397bbedddf41cabb978e63d7ef19fbd8ef340293cb3ca383735ef5f70","target":"graph","created_at":"2026-05-18T02:56:04Z","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 propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For such constraints, the associated projection operator generally does not have a simple form. We circumvent this difficulty by splitting the lower level set into as many epigraphs as functions involved in the sum. A closed half-space constraint is ","authors_text":"B\\'eatrice Pesquet-Popescu, Giovanni Chierchia, Jean-Christophe Pesquet, Nelly Pustelnik","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-10-22T09:12:48Z","title":"Epigraphical splitting for solving constrained convex formulations of inverse problems with proximal tools"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5844","kind":"arxiv","version":3},"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":"sha256:0c8f881b2d0d88107b3cff46a7cde32af9a4b5f0ed6500ce5872b2934a7f4e83","target":"record","created_at":"2026-05-18T02:56:04Z","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":"0ab033a7a010d918e5ffed39fbe30382b5294bc24a2a29ea85e6734df8d65d11","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2012-10-22T09:12:48Z","title_canon_sha256":"24cf5fe0c8d84eeeb4fc417d250fc2a40890e293dfc459e408acfa3cdffb01fc"},"schema_version":"1.0","source":{"id":"1210.5844","kind":"arxiv","version":3}},"canonical_sha256":"f31ed319d8154135d019f4016f3511bfe71d2cc8fa773874f1c2b18ba2336d1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f31ed319d8154135d019f4016f3511bfe71d2cc8fa773874f1c2b18ba2336d1c","first_computed_at":"2026-05-18T02:56:04.016246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:04.016246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yt94tlwp33Ujypif8uG9ppru5zwv8CPNGjGfEpQya4lfZH/+puzEQHZh/iEscIwdrbxGnXxGg+QL2hOHps1FCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:04.016880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5844","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c8f881b2d0d88107b3cff46a7cde32af9a4b5f0ed6500ce5872b2934a7f4e83","sha256:cd2ffb2397bbedddf41cabb978e63d7ef19fbd8ef340293cb3ca383735ef5f70"],"state_sha256":"17c9d915f1b3538376060011c3d0be482a3d6e7ea80386a00470cb71f1d81617"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jqPR4dTmiVERd+clOEuSN3dVLukr72kFiiZlFkO27tDyrnud0oeIvfQdaBx8QlKUoPK8QctPREMRLXN9EEefDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:59:01.645671Z","bundle_sha256":"b989153e023b8b87b3f1db754ad60b41f7cc1807cab8365648522e6d270dfbde"}}