{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ULDSUB6VAGNOV5UIN6M66GDBP3","short_pith_number":"pith:ULDSUB6V","canonical_record":{"source":{"id":"1212.5942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-24T17:58:26Z","cross_cats_sorted":[],"title_canon_sha256":"d1db78b9e69a7da7bb3781e1260bb0d97152778763ea0c0bc60f6bc27b7b729d","abstract_canon_sha256":"a0bd98558f54ff52dd7cc1388d62bfff28e168398b82b161bd31b59f46ccbc9a"},"schema_version":"1.0"},"canonical_sha256":"a2c72a07d5019aeaf6886f99ef18617ed32d3fa9339703992016bb6b3c03ae80","source":{"kind":"arxiv","id":"1212.5942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5942","created_at":"2026-05-18T03:37:50Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5942v1","created_at":"2026-05-18T03:37:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5942","created_at":"2026-05-18T03:37:50Z"},{"alias_kind":"pith_short_12","alias_value":"ULDSUB6VAGNO","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"ULDSUB6VAGNOV5UI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"ULDSUB6V","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ULDSUB6VAGNOV5UIN6M66GDBP3","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-24T17:58:26Z","cross_cats_sorted":[],"title_canon_sha256":"d1db78b9e69a7da7bb3781e1260bb0d97152778763ea0c0bc60f6bc27b7b729d","abstract_canon_sha256":"a0bd98558f54ff52dd7cc1388d62bfff28e168398b82b161bd31b59f46ccbc9a"},"schema_version":"1.0"},"canonical_sha256":"a2c72a07d5019aeaf6886f99ef18617ed32d3fa9339703992016bb6b3c03ae80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:50.983992Z","signature_b64":"1V/7jm2C55WmG8jj0DWUNDW6tLrlwfgfpuvBityiCitUcrr2f2MidVROAfpUsJmoHNq7b5mJd1GlPpqqWphiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2c72a07d5019aeaf6886f99ef18617ed32d3fa9339703992016bb6b3c03ae80","last_reissued_at":"2026-05-18T03:37:50.983278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:50.983278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5942","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":"2026-05-18T03:37:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"njn6UaU86wQqO9E7Zt9bDQW9zABkGN9z0X+nnknUBj2Y5+ijUCmnYr4vE+u6yE0+Jy3EGcFBN5HH7L6qo2FgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:05:02.427946Z"},"content_sha256":"a1f52e1c7e35ccaebc95ce7142cd5c4b3c76017f5639d2e1dc2b5ad87fc73951","schema_version":"1.0","event_id":"sha256:a1f52e1c7e35ccaebc95ce7142cd5c4b3c76017f5639d2e1dc2b5ad87fc73951"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ULDSUB6VAGNOV5UIN6M66GDBP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Forward-Douglas-Rachford splitting and forward-partial inverse method for solving monotone inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Luis M. Brice\\~no-Arias","submitted_at":"2012-12-24T17:58:26Z","abstract_excerpt":"We provide two weakly convergent algorithms for finding a zero of the sum of a maximally monotone operator, a cocoercive operator, and the normal cone to a closed vector subspace of a real Hilbert space. The methods exploit the intrinsic structure of the problem by activating explicitly the cocoercive operator in the first step, and taking advantage of a vector space decomposition in the second step. The second step of the first method is a Douglas-Rachford iteration involving the maximally monotone operator and the normal cone. In the second method it is a proximal step involving the partial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5942","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":"2026-05-18T03:37:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HyHvKnPvaMTIfavy5aFg1deULP69RQBZZy47ujcqm/EZIPhgRek5y0bgLtGobqY5tLWUH8aJTyHLcdu1yHyUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T03:05:02.428572Z"},"content_sha256":"cfe542ce48e706da839048731b3db27ef822a9c7016d1ddbb0960623592583ca","schema_version":"1.0","event_id":"sha256:cfe542ce48e706da839048731b3db27ef822a9c7016d1ddbb0960623592583ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULDSUB6VAGNOV5UIN6M66GDBP3/bundle.json","state_url":"https://pith.science/pith/ULDSUB6VAGNOV5UIN6M66GDBP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULDSUB6VAGNOV5UIN6M66GDBP3/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":"2026-05-23T03:05:02Z","links":{"resolver":"https://pith.science/pith/ULDSUB6VAGNOV5UIN6M66GDBP3","bundle":"https://pith.science/pith/ULDSUB6VAGNOV5UIN6M66GDBP3/bundle.json","state":"https://pith.science/pith/ULDSUB6VAGNOV5UIN6M66GDBP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULDSUB6VAGNOV5UIN6M66GDBP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ULDSUB6VAGNOV5UIN6M66GDBP3","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":"a0bd98558f54ff52dd7cc1388d62bfff28e168398b82b161bd31b59f46ccbc9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-24T17:58:26Z","title_canon_sha256":"d1db78b9e69a7da7bb3781e1260bb0d97152778763ea0c0bc60f6bc27b7b729d"},"schema_version":"1.0","source":{"id":"1212.5942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5942","created_at":"2026-05-18T03:37:50Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5942v1","created_at":"2026-05-18T03:37:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5942","created_at":"2026-05-18T03:37:50Z"},{"alias_kind":"pith_short_12","alias_value":"ULDSUB6VAGNO","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"ULDSUB6VAGNOV5UI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"ULDSUB6V","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:cfe542ce48e706da839048731b3db27ef822a9c7016d1ddbb0960623592583ca","target":"graph","created_at":"2026-05-18T03:37:50Z","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 provide two weakly convergent algorithms for finding a zero of the sum of a maximally monotone operator, a cocoercive operator, and the normal cone to a closed vector subspace of a real Hilbert space. The methods exploit the intrinsic structure of the problem by activating explicitly the cocoercive operator in the first step, and taking advantage of a vector space decomposition in the second step. The second step of the first method is a Douglas-Rachford iteration involving the maximally monotone operator and the normal cone. In the second method it is a proximal step involving the partial ","authors_text":"Luis M. Brice\\~no-Arias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-24T17:58:26Z","title":"Forward-Douglas-Rachford splitting and forward-partial inverse method for solving monotone inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5942","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:a1f52e1c7e35ccaebc95ce7142cd5c4b3c76017f5639d2e1dc2b5ad87fc73951","target":"record","created_at":"2026-05-18T03:37:50Z","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":"a0bd98558f54ff52dd7cc1388d62bfff28e168398b82b161bd31b59f46ccbc9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-24T17:58:26Z","title_canon_sha256":"d1db78b9e69a7da7bb3781e1260bb0d97152778763ea0c0bc60f6bc27b7b729d"},"schema_version":"1.0","source":{"id":"1212.5942","kind":"arxiv","version":1}},"canonical_sha256":"a2c72a07d5019aeaf6886f99ef18617ed32d3fa9339703992016bb6b3c03ae80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2c72a07d5019aeaf6886f99ef18617ed32d3fa9339703992016bb6b3c03ae80","first_computed_at":"2026-05-18T03:37:50.983278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:50.983278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1V/7jm2C55WmG8jj0DWUNDW6tLrlwfgfpuvBityiCitUcrr2f2MidVROAfpUsJmoHNq7b5mJd1GlPpqqWphiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:50.983992Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1f52e1c7e35ccaebc95ce7142cd5c4b3c76017f5639d2e1dc2b5ad87fc73951","sha256:cfe542ce48e706da839048731b3db27ef822a9c7016d1ddbb0960623592583ca"],"state_sha256":"8556e5c7ff101decdcdd2ef9cf581528bf7207029a96827777fcb304b1306084"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ax9CdovdYbhrklGilx4k/BM//0UgO6dJlWhpPwYzYrgI+YSdFa8cARmaSE141z1bSCvAbKTcyk/SPwx3AnQlCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T03:05:02.432431Z","bundle_sha256":"1a32056bb112a79fa81295743b4c857fd4fa7a208698b25ebd577ed31cea7837"}}