{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:E733PX4SW3ICCFTQ4QI5RSFBLH","short_pith_number":"pith:E733PX4S","canonical_record":{"source":{"id":"1310.1152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-10-04T02:55:34Z","cross_cats_sorted":[],"title_canon_sha256":"e9e5accf8a72c32926e2c3d662112d997509af83e68bef576d66f74b390751c2","abstract_canon_sha256":"86c06df4cedcf9ccfc077a1622b6f2c57327376486623647731c0f09868ba520"},"schema_version":"1.0"},"canonical_sha256":"27f7b7df92b6d0211670e411d8c8a159c156d4a15bfe658cb9fc6e7b28fcc09c","source":{"kind":"arxiv","id":"1310.1152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1152","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1152v1","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1152","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"E733PX4SW3IC","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E733PX4SW3ICCFTQ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E733PX4S","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:E733PX4SW3ICCFTQ4QI5RSFBLH","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-10-04T02:55:34Z","cross_cats_sorted":[],"title_canon_sha256":"e9e5accf8a72c32926e2c3d662112d997509af83e68bef576d66f74b390751c2","abstract_canon_sha256":"86c06df4cedcf9ccfc077a1622b6f2c57327376486623647731c0f09868ba520"},"schema_version":"1.0"},"canonical_sha256":"27f7b7df92b6d0211670e411d8c8a159c156d4a15bfe658cb9fc6e7b28fcc09c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:23.401147Z","signature_b64":"R0PhRY1N9lbM8D7n5mZUx484HGbSMkHEBp+SEe+ejRr/8JxY37AxSXYeknB9hlHkeXCU6WP5awthz3aZ5/f7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27f7b7df92b6d0211670e411d8c8a159c156d4a15bfe658cb9fc6e7b28fcc09c","last_reissued_at":"2026-05-18T03:11:23.399974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:23.399974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1152","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":"2026-05-18T03:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L+uR77BzJG3hHAqqxk5QqDkIwS1ySU+ttRz4CL/mKkbGIDqp9ss1Kk4pn9eZxHQTlzv02FYMeLUle10gQeP7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:22:49.055626Z"},"content_sha256":"13555c0d02a447171c5f901b4cc112cb9575bc8f177e665201d63fb1dc65fa3e","schema_version":"1.0","event_id":"sha256:13555c0d02a447171c5f901b4cc112cb9575bc8f177e665201d63fb1dc65fa3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:E733PX4SW3ICCFTQ4QI5RSFBLH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Primal-Dual Method of Partial Inverses for Composite Inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abdullah Alotaibi, Maryam A. Alghamdi, Naseer Shahzad, Patrick L. Combettes","submitted_at":"2013-10-04T02:55:34Z","abstract_excerpt":"Spingarn's method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the partial inverse formalism. The versatility of the resulting primal-dual splitting algorithm is illustrated through applications to structured monotone inclusions and optimization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1152","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":"2026-05-18T03:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Js8LaHzDMYLc0AD9xSfc3qlEsceQgrThaWlfUnnNw4XI3Oc1bAKkas8vLfmXYJCUcbkiaZXe+O8W3zthTYDoBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:22:49.055971Z"},"content_sha256":"e8078714131a872dc0c0390ffdd8a07d181a03815565d5f4fb8707a44e7ee24e","schema_version":"1.0","event_id":"sha256:e8078714131a872dc0c0390ffdd8a07d181a03815565d5f4fb8707a44e7ee24e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E733PX4SW3ICCFTQ4QI5RSFBLH/bundle.json","state_url":"https://pith.science/pith/E733PX4SW3ICCFTQ4QI5RSFBLH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E733PX4SW3ICCFTQ4QI5RSFBLH/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":"2026-06-26T04:22:49Z","links":{"resolver":"https://pith.science/pith/E733PX4SW3ICCFTQ4QI5RSFBLH","bundle":"https://pith.science/pith/E733PX4SW3ICCFTQ4QI5RSFBLH/bundle.json","state":"https://pith.science/pith/E733PX4SW3ICCFTQ4QI5RSFBLH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E733PX4SW3ICCFTQ4QI5RSFBLH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E733PX4SW3ICCFTQ4QI5RSFBLH","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":"86c06df4cedcf9ccfc077a1622b6f2c57327376486623647731c0f09868ba520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-10-04T02:55:34Z","title_canon_sha256":"e9e5accf8a72c32926e2c3d662112d997509af83e68bef576d66f74b390751c2"},"schema_version":"1.0","source":{"id":"1310.1152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1152","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1152v1","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1152","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"E733PX4SW3IC","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E733PX4SW3ICCFTQ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E733PX4S","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:e8078714131a872dc0c0390ffdd8a07d181a03815565d5f4fb8707a44e7ee24e","target":"graph","created_at":"2026-05-18T03:11:23Z","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":"Spingarn's method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the partial inverse formalism. The versatility of the resulting primal-dual splitting algorithm is illustrated through applications to structured monotone inclusions and optimization.","authors_text":"Abdullah Alotaibi, Maryam A. Alghamdi, Naseer Shahzad, Patrick L. Combettes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-10-04T02:55:34Z","title":"A Primal-Dual Method of Partial Inverses for Composite Inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1152","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":"sha256:13555c0d02a447171c5f901b4cc112cb9575bc8f177e665201d63fb1dc65fa3e","target":"record","created_at":"2026-05-18T03:11:23Z","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":"86c06df4cedcf9ccfc077a1622b6f2c57327376486623647731c0f09868ba520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-10-04T02:55:34Z","title_canon_sha256":"e9e5accf8a72c32926e2c3d662112d997509af83e68bef576d66f74b390751c2"},"schema_version":"1.0","source":{"id":"1310.1152","kind":"arxiv","version":1}},"canonical_sha256":"27f7b7df92b6d0211670e411d8c8a159c156d4a15bfe658cb9fc6e7b28fcc09c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27f7b7df92b6d0211670e411d8c8a159c156d4a15bfe658cb9fc6e7b28fcc09c","first_computed_at":"2026-05-18T03:11:23.399974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:23.399974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R0PhRY1N9lbM8D7n5mZUx484HGbSMkHEBp+SEe+ejRr/8JxY37AxSXYeknB9hlHkeXCU6WP5awthz3aZ5/f7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:23.401147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13555c0d02a447171c5f901b4cc112cb9575bc8f177e665201d63fb1dc65fa3e","sha256:e8078714131a872dc0c0390ffdd8a07d181a03815565d5f4fb8707a44e7ee24e"],"state_sha256":"a01d8d888cc384d115a5a93b19c72b6c1e6aecf760ff7d37949486b59d26226e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PQYjK0oE9s8+Umd8fhb5/Rx+Tas5KFP35UAdugEDypmgQwUXQce4R7+OWirY9YC76Wn+MQZ78yPCSyPbO61SCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T04:22:49.058366Z","bundle_sha256":"0bbb54f8dd78a8b644ca5cd66f44b9241233cbd8f01dc38bd102d7f2f10b1c50"}}