{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:MB25DTWXSI6IO7FK33H3Y7BFK6","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":"3c0aa8a7e9960f587c0a376221137369b9a91b86c8f73f96da056bb59fe7ca7f","cross_cats_sorted":["cs.RO","cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-03-17T16:08:54Z","title_canon_sha256":"d31de8171df560212abb4915a9358a49f5e375c5a087e1618bc3528dc044269f"},"schema_version":"1.0","source":{"id":"2303.10081","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.10081","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"2303.10081v2","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.10081","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"MB25DTWXSI6I","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_16","alias_value":"MB25DTWXSI6IO7FK","created_at":"2026-07-05T06:33:32Z"},{"alias_kind":"pith_short_8","alias_value":"MB25DTWX","created_at":"2026-07-05T06:33:32Z"}],"graph_snapshots":[{"event_id":"sha256:7459dbf6dbbecd5926ba16f6aa4f0bd1a4840fe775060c7fd964813e6b74388b","target":"graph","created_at":"2026-07-05T06:33:32Z","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/2303.10081/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of verification and synthesis of robust control barrier functions (CBF) for control-affine polynomial systems with bounded additive uncertainty and convex polynomial constraints on the control. We first formulate robust CBF verification and synthesis as multilevel polynomial optimization problems (POP), where verification optimizes -- in three levels -- the uncertainty, control, and state, while synthesis additionally optimizes the parameter of a chosen parametric CBF candidate. We then show that, by invoking the KKT conditions of the inner optimizations over uncertainty a","authors_text":"Heng Yang, Marco Pavone, Shucheng Kang, Yuxiao Chen","cross_cats":["cs.RO","cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-03-17T16:08:54Z","title":"Verification and Synthesis of Robust Control Barrier Functions: Multilevel Polynomial Optimization and Semidefinite Relaxation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.10081","kind":"arxiv","version":2},"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:f712b4efb97ad2af8a96a34e3bc4914ae0ac9658d6e0d51484d7cc5f1a5c7aef","target":"record","created_at":"2026-07-05T06:33:32Z","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":"3c0aa8a7e9960f587c0a376221137369b9a91b86c8f73f96da056bb59fe7ca7f","cross_cats_sorted":["cs.RO","cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-03-17T16:08:54Z","title_canon_sha256":"d31de8171df560212abb4915a9358a49f5e375c5a087e1618bc3528dc044269f"},"schema_version":"1.0","source":{"id":"2303.10081","kind":"arxiv","version":2}},"canonical_sha256":"6075d1ced7923c877caadecfbc7c25579e60c47d687743c914f6b8e71912a75d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6075d1ced7923c877caadecfbc7c25579e60c47d687743c914f6b8e71912a75d","first_computed_at":"2026-07-05T06:33:32.946981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:33:32.946981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pmw/3pUEJR7kXQ1LW2MFd+41pD/iBudJVHJrNvxJywpn1e6jUA1JxzDD5IkoSjcNJVSE2GHjl0HNLMXewspACw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:33:32.947376Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.10081","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f712b4efb97ad2af8a96a34e3bc4914ae0ac9658d6e0d51484d7cc5f1a5c7aef","sha256:7459dbf6dbbecd5926ba16f6aa4f0bd1a4840fe775060c7fd964813e6b74388b"],"state_sha256":"bc48819b33316f58cd59aebc7aeca0c6508dbd104e60c6aaaac104bab8f836b2"}