{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:A4KBJJQXJON62FIKL5ESOAEJQQ","merge_version":"pith-open-graph-merge-v1","event_count":20,"valid_event_count":20,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ed5937847825dc8a1c2cf5e292c3070ae0f84b984af9ee8184da45aa9a0a104b","cross_cats_sorted":["math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-20T04:50:40Z","title_canon_sha256":"d7d4e59257c7fc78237c6df0e31c580af303b005bdf0491d0e3af4a3ca54fabf"},"schema_version":"1.0","source":{"id":"2605.20697","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20697","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20697v1","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20697","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"A4KBJJQXJON6","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_16","alias_value":"A4KBJJQXJON62FIK","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_8","alias_value":"A4KBJJQX","created_at":"2026-05-21T01:04:49Z"}],"graph_snapshots":[{"event_id":"sha256:6d2fcbdc63da392f19bfb6fc027d09c564b296def8a82da73d6a96e69b8258ec","target":"graph","created_at":"2026-05-21T01:04:49Z","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/2605.20697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study second-order Consensus-Based Optimization (CBO), a derivative-free global optimization algorithm in which both the consensus drift and the multiplicative exploratory noise act on the particle velocities. We establish the first quantitative uniform-in-time propagation of chaos results for the second-order CBO dynamics, together with an almost uniform-in-time stability estimate for the microscopic particle system. The main difficulty is that in the second-order model, both the consensus mechanism and the stochastic forcing act only on the velocity variable, while the position evolves vi","authors_text":"Dohyeon Kim, Franca Hoffmann, Seung-Yeal Ha","cross_cats":["math.AP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-20T04:50:40Z","title":"Uniform-in-time propagation of chaos for Second-Order Consensus-Based Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20697","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:aa37c06862f6704a82f9c613a6514bb1ee38991c034df59ac76e19b857a47e46","target":"record","created_at":"2026-05-21T01:04:49Z","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":"ed5937847825dc8a1c2cf5e292c3070ae0f84b984af9ee8184da45aa9a0a104b","cross_cats_sorted":["math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-20T04:50:40Z","title_canon_sha256":"d7d4e59257c7fc78237c6df0e31c580af303b005bdf0491d0e3af4a3ca54fabf"},"schema_version":"1.0","source":{"id":"2605.20697","kind":"arxiv","version":1}},"canonical_sha256":"071414a6174b9bed150a5f49270089843c48d60c6144ecf19afac52992204e06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"071414a6174b9bed150a5f49270089843c48d60c6144ecf19afac52992204e06","first_computed_at":"2026-05-21T01:04:49.674842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:49.674842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0oMDSaZUD4xXCDsWUhnowcIO1LqpDHcCHiGKV+83zkx5LKWIPtSkt9OKzxEIQdnvqqLuiJIjZfNYyh3DwhHbCA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:49.675553Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20697","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:132d39efd162dd743e0a0d26a4a01405950a30df1344983cddcba0b9c12c7024","sha256:168526da9fec474e3e87270b288c3c84bb06225d7ea92158d9771b7e76456b4b","sha256:1d88dae49e127f9ff42eec17fb3b6e67dcf9311fb706575d3de9e857d3fb852f","sha256:1f670294f774f7a963038042e74e756095fc5881358cced41e7978676e3bc9c4","sha256:2835bf379945c071a70bc4a0bb85eebd3f7d9fef14ba25826481db6cb414fe25","sha256:293cc0e9824e2f79991a719a2fbbb5bba8352410ac03cda50be23655565f0dc4","sha256:40d83534981dfe579310d4c573981efd30cd8f9360bb644f6d04b67fcd4af0ae","sha256:63ad053f47984b25514c1206347c349d5ce3c46000cc07c90a1c694c812ede59","sha256:7b29d660962a155311aa862dd5c09c474fd0637adc092f684d02c0225e243803","sha256:81a6649e3e46f1d0902c2c9f360f262b9dcf624a4c25cd1cba6ae4e7573beac9","sha256:924be4b20bbe8d0d112ba9e7b3c554d49700d4e56207f31f9ee0fec7d12fb78c","sha256:99a4572fc94863267a52a42e85787f7ea51b8447674c68b9edaec426fe59daff","sha256:9b9ac4898f95cc80352ef7cd4dcf6a03b55f794da8209d4c82279903f4a519b9","sha256:cd2064c3cbff7b4355fad3d3815b76392878806c3518258f9cb11713b6b9390b","sha256:d0a562c4167cb443b0c79703e62d98167e1d3fd2b85086ac65520e206ec0074c","sha256:f09fc6e3bd94dad37238cd597d5426f149ff15728e4d5580a6dd6cb46d9f9014","sha256:f7ced349c9528e9df59b97d60e7e996058d889906cd9b32b5cceb8c5e3c6a112","sha256:f9c1c84bdeccd4c9733eca8d8dce653999ef201c5f3e7abc459821727794a10b"]}],"invalid_events":[],"applied_event_ids":["sha256:aa37c06862f6704a82f9c613a6514bb1ee38991c034df59ac76e19b857a47e46","sha256:6d2fcbdc63da392f19bfb6fc027d09c564b296def8a82da73d6a96e69b8258ec"],"state_sha256":"59a9f4d52498d71518df043d65684a3ec64893784a91ff11f95fdfa5f81bd14c"}