{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OX4FQDFKT2SEOUNSF6DSZSFON4","short_pith_number":"pith:OX4FQDFK","canonical_record":{"source":{"id":"1503.03142","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-11T01:24:27Z","cross_cats_sorted":[],"title_canon_sha256":"e0ea02ae4b2ed223a8751365dbf3fa4f4876b5cdf010452d93da3677dd8b9a5b","abstract_canon_sha256":"0cb39941735de0c409df1723da6b219eaf977d67f6e508bd7de715cb2ad5f21d"},"schema_version":"1.0"},"canonical_sha256":"75f8580caa9ea44751b22f872cc8ae6f1ae5f48932f4b3b27063a6094a09fb4d","source":{"kind":"arxiv","id":"1503.03142","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03142","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03142v4","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03142","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"OX4FQDFKT2SE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OX4FQDFKT2SEOUNS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OX4FQDFK","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OX4FQDFKT2SEOUNSF6DSZSFON4","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03142","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-11T01:24:27Z","cross_cats_sorted":[],"title_canon_sha256":"e0ea02ae4b2ed223a8751365dbf3fa4f4876b5cdf010452d93da3677dd8b9a5b","abstract_canon_sha256":"0cb39941735de0c409df1723da6b219eaf977d67f6e508bd7de715cb2ad5f21d"},"schema_version":"1.0"},"canonical_sha256":"75f8580caa9ea44751b22f872cc8ae6f1ae5f48932f4b3b27063a6094a09fb4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:32.246277Z","signature_b64":"c4r94m4ttIZWDKN0UW3dfXp773yw8/C/C51Bw1lADBIh7ofA7z2m3muoy0Kvp33Mtop3Xhujul03Zfc3CIRDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75f8580caa9ea44751b22f872cc8ae6f1ae5f48932f4b3b27063a6094a09fb4d","last_reissued_at":"2026-05-18T01:23:32.245728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:32.245728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03142","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1yLu29EOv3nsWpvU3sT66Z5P68ozhO+jHOXmS0gR2om2+iDPjT62DUILcZHUpn/HcOZwC5HKlSD1WyWjlUg1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:47:46.788389Z"},"content_sha256":"9a5762688506442013be898b96233bade414c5093cd328dd0a599e8797c54a19","schema_version":"1.0","event_id":"sha256:9a5762688506442013be898b96233bade414c5093cd328dd0a599e8797c54a19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OX4FQDFKT2SEOUNSF6DSZSFON4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variant of forward-backward splitting method for the systems of inclusion problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"R. D\\'iaz Mill\\'an","submitted_at":"2015-03-11T01:24:27Z","abstract_excerpt":"In this paper, we propose variants of forward-backward splitting method for solving the system of splitting inclusion problem. We propose a conceptual algorithm containing three variants, each having a different projection steps. The algorithm consists in two parts, the first and main contains an explicit Armijo-type search in the spirit of the extragradient-like methods for variational inequalities. In the iterative process the operator forward-backward is computed only one time for each inclusion problem, this represent a great computational saving if we compare with Tseng's algorithm, becau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03142","kind":"arxiv","version":4},"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":"2026-05-18T01:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AkWL2VmPeJq3nvsN7yjIxN3SZ62YfCLLRzh7ZpkaigSH3ddAnZqlYe9cAe6mZBYgIUeRlL+fhBRxWJcT+USiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:47:46.788741Z"},"content_sha256":"923891cfb2a4109b476e5db384fa8a9f3ac80f379485b7adc3a6711bda08ea8c","schema_version":"1.0","event_id":"sha256:923891cfb2a4109b476e5db384fa8a9f3ac80f379485b7adc3a6711bda08ea8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OX4FQDFKT2SEOUNSF6DSZSFON4/bundle.json","state_url":"https://pith.science/pith/OX4FQDFKT2SEOUNSF6DSZSFON4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OX4FQDFKT2SEOUNSF6DSZSFON4/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":"2026-06-26T11:47:46Z","links":{"resolver":"https://pith.science/pith/OX4FQDFKT2SEOUNSF6DSZSFON4","bundle":"https://pith.science/pith/OX4FQDFKT2SEOUNSF6DSZSFON4/bundle.json","state":"https://pith.science/pith/OX4FQDFKT2SEOUNSF6DSZSFON4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OX4FQDFKT2SEOUNSF6DSZSFON4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OX4FQDFKT2SEOUNSF6DSZSFON4","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":"0cb39941735de0c409df1723da6b219eaf977d67f6e508bd7de715cb2ad5f21d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-11T01:24:27Z","title_canon_sha256":"e0ea02ae4b2ed223a8751365dbf3fa4f4876b5cdf010452d93da3677dd8b9a5b"},"schema_version":"1.0","source":{"id":"1503.03142","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03142","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03142v4","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03142","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"OX4FQDFKT2SE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OX4FQDFKT2SEOUNS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OX4FQDFK","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:923891cfb2a4109b476e5db384fa8a9f3ac80f379485b7adc3a6711bda08ea8c","target":"graph","created_at":"2026-05-18T01:23:32Z","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":"In this paper, we propose variants of forward-backward splitting method for solving the system of splitting inclusion problem. We propose a conceptual algorithm containing three variants, each having a different projection steps. The algorithm consists in two parts, the first and main contains an explicit Armijo-type search in the spirit of the extragradient-like methods for variational inequalities. In the iterative process the operator forward-backward is computed only one time for each inclusion problem, this represent a great computational saving if we compare with Tseng's algorithm, becau","authors_text":"R. D\\'iaz Mill\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-11T01:24:27Z","title":"A variant of forward-backward splitting method for the systems of inclusion problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03142","kind":"arxiv","version":4},"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":"sha256:9a5762688506442013be898b96233bade414c5093cd328dd0a599e8797c54a19","target":"record","created_at":"2026-05-18T01:23:32Z","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":"0cb39941735de0c409df1723da6b219eaf977d67f6e508bd7de715cb2ad5f21d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-11T01:24:27Z","title_canon_sha256":"e0ea02ae4b2ed223a8751365dbf3fa4f4876b5cdf010452d93da3677dd8b9a5b"},"schema_version":"1.0","source":{"id":"1503.03142","kind":"arxiv","version":4}},"canonical_sha256":"75f8580caa9ea44751b22f872cc8ae6f1ae5f48932f4b3b27063a6094a09fb4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75f8580caa9ea44751b22f872cc8ae6f1ae5f48932f4b3b27063a6094a09fb4d","first_computed_at":"2026-05-18T01:23:32.245728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:32.245728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c4r94m4ttIZWDKN0UW3dfXp773yw8/C/C51Bw1lADBIh7ofA7z2m3muoy0Kvp33Mtop3Xhujul03Zfc3CIRDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:32.246277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03142","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a5762688506442013be898b96233bade414c5093cd328dd0a599e8797c54a19","sha256:923891cfb2a4109b476e5db384fa8a9f3ac80f379485b7adc3a6711bda08ea8c"],"state_sha256":"255b92446cb340b8d757a482ecac412ba5c27768714cdf771a3941c333b979da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CKf0Z4Y2mdyddyxCTIqZ0AkqOluDzIRLOA6HD0FWG+n/tfUbimnEKT/b1s5SZlXRFZzHzfnQWuCNhTTpJH64BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:47:46.790705Z","bundle_sha256":"6a2e3b8bdc04f559dfa0ff6a95c0aa9c7228be985d4193c1c08b358022d284d8"}}