{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UPSVXO3JDXCGVCCY4SSZVVO3ZJ","short_pith_number":"pith:UPSVXO3J","canonical_record":{"source":{"id":"2508.18866","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T09:41:29Z","cross_cats_sorted":[],"title_canon_sha256":"371e9a300bde0cbfce26ecefa7213b2468c3e14f1378ab5634502e8fda10b718","abstract_canon_sha256":"b613250263c402b45a278656d7fbe5e84b18eac8be3e2d0dd8ffadd272f7d9ad"},"schema_version":"1.0"},"canonical_sha256":"a3e55bbb691dc46a8858e4a59ad5dbca4ff6ca95683fd60de45020337559f470","source":{"kind":"arxiv","id":"2508.18866","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.18866","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"2508.18866v1","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18866","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"UPSVXO3JDXCG","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"pith_short_16","alias_value":"UPSVXO3JDXCGVCCY","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"pith_short_8","alias_value":"UPSVXO3J","created_at":"2026-07-05T11:59:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UPSVXO3JDXCGVCCY4SSZVVO3ZJ","target":"record","payload":{"canonical_record":{"source":{"id":"2508.18866","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T09:41:29Z","cross_cats_sorted":[],"title_canon_sha256":"371e9a300bde0cbfce26ecefa7213b2468c3e14f1378ab5634502e8fda10b718","abstract_canon_sha256":"b613250263c402b45a278656d7fbe5e84b18eac8be3e2d0dd8ffadd272f7d9ad"},"schema_version":"1.0"},"canonical_sha256":"a3e55bbb691dc46a8858e4a59ad5dbca4ff6ca95683fd60de45020337559f470","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:59:32.638545Z","signature_b64":"BfmsNy5Uj8GmsDnsHB9/FRw9jHt9hQbyAd6s2b+c4Ym+a7wJ4RI85Z14C1y8wIqG4GfcnXYerihP4FarXZ3+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3e55bbb691dc46a8858e4a59ad5dbca4ff6ca95683fd60de45020337559f470","last_reissued_at":"2026-07-05T11:59:32.638047Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:59:32.638047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.18866","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":"2026-07-05T11:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phy1iuBSB0FVLhmP3PdXVEehfcGlbtfv0+lxPzw6L2Elb7QBlybnRy2UF5LxeXsCSGbTPyiLP+ZbNHPm+hsqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:24:09.883124Z"},"content_sha256":"d9557591824e13ba76c54ccab1676baf7e2176388d67d36ee72b156ec3e6166d","schema_version":"1.0","event_id":"sha256:d9557591824e13ba76c54ccab1676baf7e2176388d67d36ee72b156ec3e6166d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UPSVXO3JDXCGVCCY4SSZVVO3ZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Properties of a Forward-Backward-Forward Differential Equation and Its Discrete Version for Solving Quasimonotone Variational Inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hongwei Liu, Yeyu Zhang","submitted_at":"2025-08-26T09:41:29Z","abstract_excerpt":"This paper investigates the asymptotic behavior of a forward-backward-forward (FBF) type differential equation and its discrete counterpart for solving quasimonotone variational inequalities (VIs). Building on recent continuous-time dynamical system frameworks for VIs, we extend these methods to accommodate quasimonotone operators. We establish weak and strong convergence under significantly relaxed conditions, without requiring strong pseudomonotonicity or sequential weak-to-weak continuity. Additionally, we prove ergodic convergence of the continuous trajectories, offering further insight in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18866","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/2508.18866/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":"2026-07-05T11:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KscakTonN8zMph3pd/FWeEZ7f4KSMEKIKtrKTVt7MgOiREqy+dB1Lsyh1vxS0znAT8OufaVCdEkEOOA8t87fAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:24:09.884008Z"},"content_sha256":"60c5936498cffa41cfd279b7e90dfa258f1ae713cc8c0ceeaeeea74f915b8e9a","schema_version":"1.0","event_id":"sha256:60c5936498cffa41cfd279b7e90dfa258f1ae713cc8c0ceeaeeea74f915b8e9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPSVXO3JDXCGVCCY4SSZVVO3ZJ/bundle.json","state_url":"https://pith.science/pith/UPSVXO3JDXCGVCCY4SSZVVO3ZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPSVXO3JDXCGVCCY4SSZVVO3ZJ/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":"2026-08-08T11:24:09Z","links":{"resolver":"https://pith.science/pith/UPSVXO3JDXCGVCCY4SSZVVO3ZJ","bundle":"https://pith.science/pith/UPSVXO3JDXCGVCCY4SSZVVO3ZJ/bundle.json","state":"https://pith.science/pith/UPSVXO3JDXCGVCCY4SSZVVO3ZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPSVXO3JDXCGVCCY4SSZVVO3ZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UPSVXO3JDXCGVCCY4SSZVVO3ZJ","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":"b613250263c402b45a278656d7fbe5e84b18eac8be3e2d0dd8ffadd272f7d9ad","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T09:41:29Z","title_canon_sha256":"371e9a300bde0cbfce26ecefa7213b2468c3e14f1378ab5634502e8fda10b718"},"schema_version":"1.0","source":{"id":"2508.18866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.18866","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"2508.18866v1","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.18866","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"UPSVXO3JDXCG","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"pith_short_16","alias_value":"UPSVXO3JDXCGVCCY","created_at":"2026-07-05T11:59:32Z"},{"alias_kind":"pith_short_8","alias_value":"UPSVXO3J","created_at":"2026-07-05T11:59:32Z"}],"graph_snapshots":[{"event_id":"sha256:60c5936498cffa41cfd279b7e90dfa258f1ae713cc8c0ceeaeeea74f915b8e9a","target":"graph","created_at":"2026-07-05T11:59:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.18866/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the asymptotic behavior of a forward-backward-forward (FBF) type differential equation and its discrete counterpart for solving quasimonotone variational inequalities (VIs). Building on recent continuous-time dynamical system frameworks for VIs, we extend these methods to accommodate quasimonotone operators. We establish weak and strong convergence under significantly relaxed conditions, without requiring strong pseudomonotonicity or sequential weak-to-weak continuity. Additionally, we prove ergodic convergence of the continuous trajectories, offering further insight in","authors_text":"Hongwei Liu, Yeyu Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T09:41:29Z","title":"Asymptotic Properties of a Forward-Backward-Forward Differential Equation and Its Discrete Version for Solving Quasimonotone Variational Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18866","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:d9557591824e13ba76c54ccab1676baf7e2176388d67d36ee72b156ec3e6166d","target":"record","created_at":"2026-07-05T11:59:32Z","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":"b613250263c402b45a278656d7fbe5e84b18eac8be3e2d0dd8ffadd272f7d9ad","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-08-26T09:41:29Z","title_canon_sha256":"371e9a300bde0cbfce26ecefa7213b2468c3e14f1378ab5634502e8fda10b718"},"schema_version":"1.0","source":{"id":"2508.18866","kind":"arxiv","version":1}},"canonical_sha256":"a3e55bbb691dc46a8858e4a59ad5dbca4ff6ca95683fd60de45020337559f470","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3e55bbb691dc46a8858e4a59ad5dbca4ff6ca95683fd60de45020337559f470","first_computed_at":"2026-07-05T11:59:32.638047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:59:32.638047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BfmsNy5Uj8GmsDnsHB9/FRw9jHt9hQbyAd6s2b+c4Ym+a7wJ4RI85Z14C1y8wIqG4GfcnXYerihP4FarXZ3+Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T11:59:32.638545Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.18866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9557591824e13ba76c54ccab1676baf7e2176388d67d36ee72b156ec3e6166d","sha256:60c5936498cffa41cfd279b7e90dfa258f1ae713cc8c0ceeaeeea74f915b8e9a"],"state_sha256":"990b934209e7a18902949ee95793b166f887a8339dbfcb19a5481aaf8bfebb42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4574RFLn6BhLWngzyVFsBEEttxYyEtxOm+GIBdeZOaX4WMQucGaYexwLsdGOo6nj61nyLaTYZOvUSjlzZ0J/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:24:09.892378Z","bundle_sha256":"4fe8aa6fb383abf6485f029d58dc0a0e1096c9799f1f681a508d5df665a8e669"}}