{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:Z5UMM77FWMNS32HE6HRBI7VECC","short_pith_number":"pith:Z5UMM77F","canonical_record":{"source":{"id":"2310.17265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-10-26T09:31:56Z","cross_cats_sorted":[],"title_canon_sha256":"d358a90adb5e0453d53ec4cebca4c58c7b065f81afa9c947fb50a8465339d1ef","abstract_canon_sha256":"3af2d61537ccd88998f28e0949d1ca43ee6ccc3044b12ac47e0ff1a0ce549035"},"schema_version":"1.0"},"canonical_sha256":"cf68c67fe5b31b2de8e4f1e2147ea410bc98317fd203154f52dd9592d285ab46","source":{"kind":"arxiv","id":"2310.17265","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.17265","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"2310.17265v2","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.17265","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"Z5UMM77FWMNS","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_16","alias_value":"Z5UMM77FWMNS32HE","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_8","alias_value":"Z5UMM77F","created_at":"2026-07-05T09:11:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:Z5UMM77FWMNS32HE6HRBI7VECC","target":"record","payload":{"canonical_record":{"source":{"id":"2310.17265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-10-26T09:31:56Z","cross_cats_sorted":[],"title_canon_sha256":"d358a90adb5e0453d53ec4cebca4c58c7b065f81afa9c947fb50a8465339d1ef","abstract_canon_sha256":"3af2d61537ccd88998f28e0949d1ca43ee6ccc3044b12ac47e0ff1a0ce549035"},"schema_version":"1.0"},"canonical_sha256":"cf68c67fe5b31b2de8e4f1e2147ea410bc98317fd203154f52dd9592d285ab46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:11:45.726914Z","signature_b64":"8h3eqBftL56dSWpFRbqLwWH9m7WLLQ619tpu9JH1b8wgQFCgTpOFBQi8E5HySId7L4KQlQ+SIrfbnW/yCUaHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf68c67fe5b31b2de8e4f1e2147ea410bc98317fd203154f52dd9592d285ab46","last_reissued_at":"2026-07-05T09:11:45.726489Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:11:45.726489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.17265","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CKM9CdCdIhl6/Z2CfqwHjX86fT2NxeYBbOD2vfPhaDaG4sm6yHeG2wgLdN47c3TEBlVWJA+WCj52u+77iLBhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:50:57.089638Z"},"content_sha256":"2c917831a8a152db9ebf7db3d02685e987c0adf5a1a37843131afb9c96f63100","schema_version":"1.0","event_id":"sha256:2c917831a8a152db9ebf7db3d02685e987c0adf5a1a37843131afb9c96f63100"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:Z5UMM77FWMNS32HE6HRBI7VECC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Forward Primal-Dual Half-Forward Algorithm for Splitting Four Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fernando Rold\\'an","submitted_at":"2023-10-26T09:31:56Z","abstract_excerpt":"In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitzian operator, a cocoercive operator, and a linear composite term. In the case when the Lipschitzian operator is absent, our method reduces to the Condat-V\\~u algorithm. On the other hand, when the linear composite term is absent, the algorithm reduces to the Forward-Backward-Half-Forward algorithm (FBHF). Additionally, in each case, the set of step-sizes that guarantee the weak convergence of those methods are recovered. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17265","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.17265/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NWtV1+1exG9Jf0wi3ttSoQMud3YQtr6A4cBrrsAfc1ODWtdqP4d4QKIvRtj3wXrxeKCOzdDIvINyUcv6dwv9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:50:57.090220Z"},"content_sha256":"2aa18d6701dd93f4fc5a18162614049a7344f056ca162e8e30170d260c685bb3","schema_version":"1.0","event_id":"sha256:2aa18d6701dd93f4fc5a18162614049a7344f056ca162e8e30170d260c685bb3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5UMM77FWMNS32HE6HRBI7VECC/bundle.json","state_url":"https://pith.science/pith/Z5UMM77FWMNS32HE6HRBI7VECC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5UMM77FWMNS32HE6HRBI7VECC/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":"2026-08-13T14:50:57Z","links":{"resolver":"https://pith.science/pith/Z5UMM77FWMNS32HE6HRBI7VECC","bundle":"https://pith.science/pith/Z5UMM77FWMNS32HE6HRBI7VECC/bundle.json","state":"https://pith.science/pith/Z5UMM77FWMNS32HE6HRBI7VECC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5UMM77FWMNS32HE6HRBI7VECC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:Z5UMM77FWMNS32HE6HRBI7VECC","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":"3af2d61537ccd88998f28e0949d1ca43ee6ccc3044b12ac47e0ff1a0ce549035","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-10-26T09:31:56Z","title_canon_sha256":"d358a90adb5e0453d53ec4cebca4c58c7b065f81afa9c947fb50a8465339d1ef"},"schema_version":"1.0","source":{"id":"2310.17265","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.17265","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"2310.17265v2","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.17265","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"Z5UMM77FWMNS","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_16","alias_value":"Z5UMM77FWMNS32HE","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_8","alias_value":"Z5UMM77F","created_at":"2026-07-05T09:11:45Z"}],"graph_snapshots":[{"event_id":"sha256:2aa18d6701dd93f4fc5a18162614049a7344f056ca162e8e30170d260c685bb3","target":"graph","created_at":"2026-07-05T09:11:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.17265/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitzian operator, a cocoercive operator, and a linear composite term. In the case when the Lipschitzian operator is absent, our method reduces to the Condat-V\\~u algorithm. On the other hand, when the linear composite term is absent, the algorithm reduces to the Forward-Backward-Half-Forward algorithm (FBHF). Additionally, in each case, the set of step-sizes that guarantee the weak convergence of those methods are recovered. T","authors_text":"Fernando Rold\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-10-26T09:31:56Z","title":"Forward Primal-Dual Half-Forward Algorithm for Splitting Four Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17265","kind":"arxiv","version":2},"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":"sha256:2c917831a8a152db9ebf7db3d02685e987c0adf5a1a37843131afb9c96f63100","target":"record","created_at":"2026-07-05T09:11:45Z","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":"3af2d61537ccd88998f28e0949d1ca43ee6ccc3044b12ac47e0ff1a0ce549035","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-10-26T09:31:56Z","title_canon_sha256":"d358a90adb5e0453d53ec4cebca4c58c7b065f81afa9c947fb50a8465339d1ef"},"schema_version":"1.0","source":{"id":"2310.17265","kind":"arxiv","version":2}},"canonical_sha256":"cf68c67fe5b31b2de8e4f1e2147ea410bc98317fd203154f52dd9592d285ab46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf68c67fe5b31b2de8e4f1e2147ea410bc98317fd203154f52dd9592d285ab46","first_computed_at":"2026-07-05T09:11:45.726489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:11:45.726489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8h3eqBftL56dSWpFRbqLwWH9m7WLLQ619tpu9JH1b8wgQFCgTpOFBQi8E5HySId7L4KQlQ+SIrfbnW/yCUaHCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:11:45.726914Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.17265","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c917831a8a152db9ebf7db3d02685e987c0adf5a1a37843131afb9c96f63100","sha256:2aa18d6701dd93f4fc5a18162614049a7344f056ca162e8e30170d260c685bb3"],"state_sha256":"9fbd2e7540313a6f9cd9e1a03d27b743f16e38ed33b2ba777b3949b4c4e413e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GtCqVDCqaQWBKEfmO71cMCbDrwTt5ZEmxoHJjfGxApUu9cd8iV3vGgi0MXNulbtteqxfhEXaGxym9QalwPOqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T14:50:57.094178Z","bundle_sha256":"28170dee2b2cafe5241e0d90289b7136ed08115ddaad9c383803eb33111678e0"}}