{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SSDX7SE7CMJTDYJRKKM3MAGXUB","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":"2644a734ef10f88e17bcfaa3c391e5388c4f35df0c2f8a35983d8472acdc06de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-31T10:39:32Z","title_canon_sha256":"d34ed90c451968c671af0cb8dbba68c39dce4c9e8ff6209c880a90595986a634"},"schema_version":"1.0","source":{"id":"2506.00501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00501","created_at":"2026-07-05T11:13:35Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00501v1","created_at":"2026-07-05T11:13:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00501","created_at":"2026-07-05T11:13:35Z"},{"alias_kind":"pith_short_12","alias_value":"SSDX7SE7CMJT","created_at":"2026-07-05T11:13:35Z"},{"alias_kind":"pith_short_16","alias_value":"SSDX7SE7CMJTDYJR","created_at":"2026-07-05T11:13:35Z"},{"alias_kind":"pith_short_8","alias_value":"SSDX7SE7","created_at":"2026-07-05T11:13:35Z"}],"graph_snapshots":[{"event_id":"sha256:819f674e6cd2895fdba1220d37c7043c5ba3bcd19fbba9a1ad9598bc01a9c7cc","target":"graph","created_at":"2026-07-05T11:13:35Z","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/2506.00501/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and analyze a continuous primal-dual dynamical system in the context of the minimization problem $f(x)+g(Ax)$, where $f$ and $g$ are convex functions and $A$ is a linear operator. In this setting, the trajectories of the Arrow-Hurwicz continuous flow may not converge, accumulating at points that are not solutions. Our proposal is inspired by the primal-dual algorithm of Chambolle and Pock (2011), where convergence and splitting on the primal-dual variable are ensured by adequately preconditioning the proximal-point algorithm. We consider a family of preconditioners, which are allo","authors_text":"Cesare Molinari, Juan Peypouquet, Silvia Villa, Vassilis Apidopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-31T10:39:32Z","title":"Preconditioned primal-dual dynamics in convex optimization: non-ergodic convergence rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00501","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":"sha256:7abe5db6992e8de84944065fe18647d5f504cad4b52f031ec725c20a1a8ea06e","target":"record","created_at":"2026-07-05T11:13:35Z","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":"2644a734ef10f88e17bcfaa3c391e5388c4f35df0c2f8a35983d8472acdc06de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-31T10:39:32Z","title_canon_sha256":"d34ed90c451968c671af0cb8dbba68c39dce4c9e8ff6209c880a90595986a634"},"schema_version":"1.0","source":{"id":"2506.00501","kind":"arxiv","version":1}},"canonical_sha256":"94877fc89f131331e1315299b600d7a0696322e05dd7ca28407439e58ab0008d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94877fc89f131331e1315299b600d7a0696322e05dd7ca28407439e58ab0008d","first_computed_at":"2026-07-05T11:13:35.973029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:35.973029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pOR0mzPfXnR/+uArEYlv1Q+IiImA+b4b9EmCGULiNlBx3nsK7APBHwWVuAcmepOYSUB5JuJv00tjkyluTa3nBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:35.973456Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.00501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7abe5db6992e8de84944065fe18647d5f504cad4b52f031ec725c20a1a8ea06e","sha256:819f674e6cd2895fdba1220d37c7043c5ba3bcd19fbba9a1ad9598bc01a9c7cc"],"state_sha256":"cbac2ac645784c0d0799fa8967d854b0abdae84184b698997a1db7bbd3b4c750"}