{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TLEDSHJBRHYXTRRX7AAV4UUMGH","short_pith_number":"pith:TLEDSHJB","canonical_record":{"source":{"id":"2410.16281","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.RO","submitted_at":"2024-10-04T21:42:25Z","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.OC"],"title_canon_sha256":"fe9a217086095adb2d213ff59d0365dd460ed6ba65a1e74a3ae290284ebf472b","abstract_canon_sha256":"93da6028c2d543840f4969577e2bc62e6e3e7f22eea724c4a88b8c8e95a8deb8"},"schema_version":"1.0"},"canonical_sha256":"9ac8391d2189f179c637f8015e528c31d622a8a471a2a7d868191b63b30bd460","source":{"kind":"arxiv","id":"2410.16281","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.16281","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"2410.16281v1","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.16281","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"TLEDSHJBRHYX","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"pith_short_16","alias_value":"TLEDSHJBRHYXTRRX","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"pith_short_8","alias_value":"TLEDSHJB","created_at":"2026-07-05T09:23:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TLEDSHJBRHYXTRRX7AAV4UUMGH","target":"record","payload":{"canonical_record":{"source":{"id":"2410.16281","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.RO","submitted_at":"2024-10-04T21:42:25Z","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.OC"],"title_canon_sha256":"fe9a217086095adb2d213ff59d0365dd460ed6ba65a1e74a3ae290284ebf472b","abstract_canon_sha256":"93da6028c2d543840f4969577e2bc62e6e3e7f22eea724c4a88b8c8e95a8deb8"},"schema_version":"1.0"},"canonical_sha256":"9ac8391d2189f179c637f8015e528c31d622a8a471a2a7d868191b63b30bd460","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:23:33.898857Z","signature_b64":"8J0LooRwjIUegOEwv/U3mdrmbeIdyF916abaQ1QjHV2/nE0mlX0/gyiWic9CqNkRd7GvqOVfQK7eKiKe2/i3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ac8391d2189f179c637f8015e528c31d622a8a471a2a7d868191b63b30bd460","last_reissued_at":"2026-07-05T09:23:33.898367Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:23:33.898367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.16281","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":"2026-07-05T09:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4OD4WnZ7Nup6Jz47Brxi2qWtISw9x//SFnOwa+6yBTKOlz1QfBk3LmFE1AF0D7HffYBZUy/qppQMstTY1tmZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:49:32.896866Z"},"content_sha256":"fb6678572422e2aa0f26020b030de1be199d0e270fd94f96e4cd61b27bfac0a4","schema_version":"1.0","event_id":"sha256:fb6678572422e2aa0f26020b030de1be199d0e270fd94f96e4cd61b27bfac0a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TLEDSHJBRHYXTRRX7AAV4UUMGH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LG","cs.SY","eess.SY","math.OC"],"primary_cat":"cs.RO","authors_text":"Changliu Liu, Hanjiang Hu, Tianhao Wei, Yujie Yang","submitted_at":"2024-10-04T21:42:25Z","abstract_excerpt":"Control barrier functions (CBFs) are important in safety-critical systems and robot control applications. Neural networks have been used to parameterize and synthesize CBFs with bounded control input for complex systems. However, it is still challenging to verify pre-trained neural networks CBFs (neural CBFs) in an efficient symbolic manner. To this end, we propose a new efficient verification framework for ReLU-based neural CBFs through symbolic derivative bound propagation by combining the linearly bounded nonlinear dynamic system and the gradient bounds of neural CBFs. Specifically, with He"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.16281","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/2410.16281/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":"2026-07-05T09:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUNLjteexiVJIZ8J+VW8ghO8XAkjSx3VOsLzPGS9RaJLiTOaMxTrbC14StuKTwF6uB0P7UIHDfSpTLP0IZZFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T08:49:32.897441Z"},"content_sha256":"e02eb52a38915b0d3704e2120573eb7fec46a3cdf6021f0a0add2234a17a81f6","schema_version":"1.0","event_id":"sha256:e02eb52a38915b0d3704e2120573eb7fec46a3cdf6021f0a0add2234a17a81f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLEDSHJBRHYXTRRX7AAV4UUMGH/bundle.json","state_url":"https://pith.science/pith/TLEDSHJBRHYXTRRX7AAV4UUMGH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLEDSHJBRHYXTRRX7AAV4UUMGH/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":"2026-08-12T08:49:32Z","links":{"resolver":"https://pith.science/pith/TLEDSHJBRHYXTRRX7AAV4UUMGH","bundle":"https://pith.science/pith/TLEDSHJBRHYXTRRX7AAV4UUMGH/bundle.json","state":"https://pith.science/pith/TLEDSHJBRHYXTRRX7AAV4UUMGH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLEDSHJBRHYXTRRX7AAV4UUMGH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TLEDSHJBRHYXTRRX7AAV4UUMGH","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":"93da6028c2d543840f4969577e2bc62e6e3e7f22eea724c4a88b8c8e95a8deb8","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.OC"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.RO","submitted_at":"2024-10-04T21:42:25Z","title_canon_sha256":"fe9a217086095adb2d213ff59d0365dd460ed6ba65a1e74a3ae290284ebf472b"},"schema_version":"1.0","source":{"id":"2410.16281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.16281","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"2410.16281v1","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.16281","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"TLEDSHJBRHYX","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"pith_short_16","alias_value":"TLEDSHJBRHYXTRRX","created_at":"2026-07-05T09:23:33Z"},{"alias_kind":"pith_short_8","alias_value":"TLEDSHJB","created_at":"2026-07-05T09:23:33Z"}],"graph_snapshots":[{"event_id":"sha256:e02eb52a38915b0d3704e2120573eb7fec46a3cdf6021f0a0add2234a17a81f6","target":"graph","created_at":"2026-07-05T09:23:33Z","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/2410.16281/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Control barrier functions (CBFs) are important in safety-critical systems and robot control applications. Neural networks have been used to parameterize and synthesize CBFs with bounded control input for complex systems. However, it is still challenging to verify pre-trained neural networks CBFs (neural CBFs) in an efficient symbolic manner. To this end, we propose a new efficient verification framework for ReLU-based neural CBFs through symbolic derivative bound propagation by combining the linearly bounded nonlinear dynamic system and the gradient bounds of neural CBFs. Specifically, with He","authors_text":"Changliu Liu, Hanjiang Hu, Tianhao Wei, Yujie Yang","cross_cats":["cs.LG","cs.SY","eess.SY","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.RO","submitted_at":"2024-10-04T21:42:25Z","title":"Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.16281","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:fb6678572422e2aa0f26020b030de1be199d0e270fd94f96e4cd61b27bfac0a4","target":"record","created_at":"2026-07-05T09:23:33Z","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":"93da6028c2d543840f4969577e2bc62e6e3e7f22eea724c4a88b8c8e95a8deb8","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.OC"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.RO","submitted_at":"2024-10-04T21:42:25Z","title_canon_sha256":"fe9a217086095adb2d213ff59d0365dd460ed6ba65a1e74a3ae290284ebf472b"},"schema_version":"1.0","source":{"id":"2410.16281","kind":"arxiv","version":1}},"canonical_sha256":"9ac8391d2189f179c637f8015e528c31d622a8a471a2a7d868191b63b30bd460","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ac8391d2189f179c637f8015e528c31d622a8a471a2a7d868191b63b30bd460","first_computed_at":"2026-07-05T09:23:33.898367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:23:33.898367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8J0LooRwjIUegOEwv/U3mdrmbeIdyF916abaQ1QjHV2/nE0mlX0/gyiWic9CqNkRd7GvqOVfQK7eKiKe2/i3Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T09:23:33.898857Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.16281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb6678572422e2aa0f26020b030de1be199d0e270fd94f96e4cd61b27bfac0a4","sha256:e02eb52a38915b0d3704e2120573eb7fec46a3cdf6021f0a0add2234a17a81f6"],"state_sha256":"bbec5265a5bdd7e270d8c4556acdae74b7f165723759a625b4eb585287880335"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LAvxgT1myZR7XVx4Zvd6t09m+vpJ6byQGiDXMmZoHX2b9NCxNx5klOUB3Vs3NnozFwtvH1dNE2vwhlBC1xsFBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T08:49:32.901872Z","bundle_sha256":"8d0a4ef8fc0e18de6b497d78622d5c51d773695ecf60f1f76e6301d377d337b2"}}