{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:524FMQ42RSQ7TNML2ZK7576M5E","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":"768d0281e4f57d7fa4e7584cbe686527ae941866317e9b27b559270c4e54789e","cross_cats_sorted":["cs.NA","math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-03-28T13:42:07Z","title_canon_sha256":"73ab992a3208922949542a2a5f6e84b4df33ccfc86d36129bcc703db750f2156"},"schema_version":"1.0","source":{"id":"2103.15130","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.15130","created_at":"2026-07-05T09:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"2103.15130v6","created_at":"2026-07-05T09:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.15130","created_at":"2026-07-05T09:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"524FMQ42RSQ7","created_at":"2026-07-05T09:04:06Z"},{"alias_kind":"pith_short_16","alias_value":"524FMQ42RSQ7TNML","created_at":"2026-07-05T09:04:06Z"},{"alias_kind":"pith_short_8","alias_value":"524FMQ42","created_at":"2026-07-05T09:04:06Z"}],"graph_snapshots":[{"event_id":"sha256:12543ddf22f35e05fe0f04af96693733da97ac4d22b27bfceb589ace558a3f23","target":"graph","created_at":"2026-07-05T09:04:06Z","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/2103.15130/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study consensus-based optimization (CBO), which is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on an experimentally supported intuition that, on average, CBO performs a gradient descent of the squared Euclidean distance to the global minimizer, we devise a novel technique for proving the convergence to the global minimizer in mean-field law for a rich class of objective functions. The result unveils internal mechanisms of CBO that are responsible for the","authors_text":"Konstantin Riedl, Massimo Fornasier, Timo Klock","cross_cats":["cs.NA","math.AP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-03-28T13:42:07Z","title":"Consensus-Based Optimization Methods Converge Globally"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.15130","kind":"arxiv","version":6},"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":"sha256:83255df579e3057066c3eb0e6f1835c2604e5f8821ee51a49eaaf8a4ef263ae8","target":"record","created_at":"2026-07-05T09:04:06Z","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":"768d0281e4f57d7fa4e7584cbe686527ae941866317e9b27b559270c4e54789e","cross_cats_sorted":["cs.NA","math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-03-28T13:42:07Z","title_canon_sha256":"73ab992a3208922949542a2a5f6e84b4df33ccfc86d36129bcc703db750f2156"},"schema_version":"1.0","source":{"id":"2103.15130","kind":"arxiv","version":6}},"canonical_sha256":"eeb856439a8ca1f9b58bd655feffcce936ced0be7787da7e91dc62fd18fe21e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeb856439a8ca1f9b58bd655feffcce936ced0be7787da7e91dc62fd18fe21e5","first_computed_at":"2026-07-05T09:04:06.289744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:04:06.289744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I0uccwFmtJ3CYCboNHgz6nuhbxPkTl3B5elzOxz3yKmAe8/A603wRagX/sHThV47Mq2isUHy2UtyQ/7ganoAAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:04:06.290156Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.15130","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83255df579e3057066c3eb0e6f1835c2604e5f8821ee51a49eaaf8a4ef263ae8","sha256:12543ddf22f35e05fe0f04af96693733da97ac4d22b27bfceb589ace558a3f23"],"state_sha256":"3b617d688ad6d0aabb3efb4e71c30eeefbc7bfc98fd6d66ce4595b76e7da6c81"}