{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:K5D3623CPPBJDZIXGICD2EWOQ3","short_pith_number":"pith:K5D3623C","canonical_record":{"source":{"id":"2605.17731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T01:27:51Z","cross_cats_sorted":[],"title_canon_sha256":"6597af9ceb0e0b3f992496c94e14223363db4fc734d8a02e9e622edaa38bea07","abstract_canon_sha256":"599d1b79273a2feb50fd229653420f22bf6201af71150e1350a4089703f80267"},"schema_version":"1.0"},"canonical_sha256":"5747bf6b627bc291e51732043d12ce86d447c70507c4e492ec753c8f26c16609","source":{"kind":"arxiv","id":"2605.17731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17731","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17731v1","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17731","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"K5D3623CPPBJ","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"K5D3623CPPBJDZIX","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"K5D3623C","created_at":"2026-05-20T00:04:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:K5D3623CPPBJDZIXGICD2EWOQ3","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T01:27:51Z","cross_cats_sorted":[],"title_canon_sha256":"6597af9ceb0e0b3f992496c94e14223363db4fc734d8a02e9e622edaa38bea07","abstract_canon_sha256":"599d1b79273a2feb50fd229653420f22bf6201af71150e1350a4089703f80267"},"schema_version":"1.0"},"canonical_sha256":"5747bf6b627bc291e51732043d12ce86d447c70507c4e492ec753c8f26c16609","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:55.224127Z","signature_b64":"wvKpk7V10+LgTPvX9z3AL1AliiT4pyE2R4kfnKsBIRxQBgQyUM01l270OlQ+8R8BQtBwN8ZCTPSRPFu/eFTgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5747bf6b627bc291e51732043d12ce86d447c70507c4e492ec753c8f26c16609","last_reissued_at":"2026-05-20T00:04:55.223354Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:55.223354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17731","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":"2026-05-20T00:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mIjcCVQdJHWPB3DdWJdGikehpHZ/E8R7C3Tj+aWMCMb0Jixcv/2GmPeCojs6AjIX7dPzORWTkg4u0QZVoyLlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:52:42.805480Z"},"content_sha256":"ddbc2dba4ab996ac5bc0d7334d27535f49302658a2f2a43202154ee99a9da36c","schema_version":"1.0","event_id":"sha256:ddbc2dba4ab996ac5bc0d7334d27535f49302658a2f2a43202154ee99a9da36c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:K5D3623CPPBJDZIXGICD2EWOQ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A reflected forward-backward splitting algorithmic framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Haowen Zheng, Qiao-Li Dong, Shuangbao Li, Yongyu Fu","submitted_at":"2026-05-18T01:27:51Z","abstract_excerpt":"In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and Lipschitz continuous operators. We provide a unified convergence analysis under mild conditions, eliminating the need to analyze the convergence of each algorithm individually. The heuristic strategies for matrix selections are proposed through a numerical experiment, based on which a new algorithm is derived. A further numerical experiment on the regularized saddl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17731","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17731/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":"2026-05-20T00:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BOKc37987Puz2qh5mkOv0GpNJCzwbjW3xKVpO9A/l4GCp2jSrRmqD5uXtLUxC1mLTL20qMLLmp9cQG2JCZMMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:52:42.806252Z"},"content_sha256":"6df9ad2e1aa0795ebe6907825ac1cac56a02343d3d1b1220ea48eb0daa798f5c","schema_version":"1.0","event_id":"sha256:6df9ad2e1aa0795ebe6907825ac1cac56a02343d3d1b1220ea48eb0daa798f5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5D3623CPPBJDZIXGICD2EWOQ3/bundle.json","state_url":"https://pith.science/pith/K5D3623CPPBJDZIXGICD2EWOQ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5D3623CPPBJDZIXGICD2EWOQ3/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":"2026-06-07T23:52:42Z","links":{"resolver":"https://pith.science/pith/K5D3623CPPBJDZIXGICD2EWOQ3","bundle":"https://pith.science/pith/K5D3623CPPBJDZIXGICD2EWOQ3/bundle.json","state":"https://pith.science/pith/K5D3623CPPBJDZIXGICD2EWOQ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5D3623CPPBJDZIXGICD2EWOQ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K5D3623CPPBJDZIXGICD2EWOQ3","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":"599d1b79273a2feb50fd229653420f22bf6201af71150e1350a4089703f80267","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T01:27:51Z","title_canon_sha256":"6597af9ceb0e0b3f992496c94e14223363db4fc734d8a02e9e622edaa38bea07"},"schema_version":"1.0","source":{"id":"2605.17731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17731","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17731v1","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17731","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"K5D3623CPPBJ","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"K5D3623CPPBJDZIX","created_at":"2026-05-20T00:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"K5D3623C","created_at":"2026-05-20T00:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:6df9ad2e1aa0795ebe6907825ac1cac56a02343d3d1b1220ea48eb0daa798f5c","target":"graph","created_at":"2026-05-20T00:04:55Z","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/2605.17731/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and Lipschitz continuous operators. We provide a unified convergence analysis under mild conditions, eliminating the need to analyze the convergence of each algorithm individually. The heuristic strategies for matrix selections are proposed through a numerical experiment, based on which a new algorithm is derived. A further numerical experiment on the regularized saddl","authors_text":"Haowen Zheng, Qiao-Li Dong, Shuangbao Li, Yongyu Fu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T01:27:51Z","title":"A reflected forward-backward splitting algorithmic framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17731","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:ddbc2dba4ab996ac5bc0d7334d27535f49302658a2f2a43202154ee99a9da36c","target":"record","created_at":"2026-05-20T00:04:55Z","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":"599d1b79273a2feb50fd229653420f22bf6201af71150e1350a4089703f80267","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T01:27:51Z","title_canon_sha256":"6597af9ceb0e0b3f992496c94e14223363db4fc734d8a02e9e622edaa38bea07"},"schema_version":"1.0","source":{"id":"2605.17731","kind":"arxiv","version":1}},"canonical_sha256":"5747bf6b627bc291e51732043d12ce86d447c70507c4e492ec753c8f26c16609","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5747bf6b627bc291e51732043d12ce86d447c70507c4e492ec753c8f26c16609","first_computed_at":"2026-05-20T00:04:55.223354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:55.223354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wvKpk7V10+LgTPvX9z3AL1AliiT4pyE2R4kfnKsBIRxQBgQyUM01l270OlQ+8R8BQtBwN8ZCTPSRPFu/eFTgBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:55.224127Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddbc2dba4ab996ac5bc0d7334d27535f49302658a2f2a43202154ee99a9da36c","sha256:6df9ad2e1aa0795ebe6907825ac1cac56a02343d3d1b1220ea48eb0daa798f5c"],"state_sha256":"4685abafa60c190b4b3b9e3910fbae4a565c414de073050b70d9d1e6e28aed0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C4TqLv7IyKIv7+QL3jCzO+mLTnfMaA2S/CvAFEXN1RSDaCXTBgcVMTjF0auJeniOO+YIEDUIRfvyC1bbz4olDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:52:42.810480Z","bundle_sha256":"ad6a63e92d82764efc1ec653b190cfaa24f22e76f1234f58cda0e630154c6ac3"}}