{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:DSMKJ7BD2HFGYHV2XTGAXSHFX3","short_pith_number":"pith:DSMKJ7BD","canonical_record":{"source":{"id":"2509.12182","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2025-09-15T17:45:27Z","cross_cats_sorted":["eess.SY"],"title_canon_sha256":"6635312e03c9510d1e633a0a9e7dcdbdfbb4fc6eb50369edf6ffe864cfb5d481","abstract_canon_sha256":"31203f9c762523959fa62e6c3de6fc51d29bf63ebbbaab95b9ddc32609569404"},"schema_version":"1.0"},"canonical_sha256":"1c98a4fc23d1ca6c1ebabccc0bc8e5bedb9d6bd1434bf2978db2d85ee9f5e865","source":{"kind":"arxiv","id":"2509.12182","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.12182","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"2509.12182v2","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.12182","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"DSMKJ7BD2HFG","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"pith_short_16","alias_value":"DSMKJ7BD2HFGYHV2","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"pith_short_8","alias_value":"DSMKJ7BD","created_at":"2026-07-02T08:42:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:DSMKJ7BD2HFGYHV2XTGAXSHFX3","target":"record","payload":{"canonical_record":{"source":{"id":"2509.12182","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2025-09-15T17:45:27Z","cross_cats_sorted":["eess.SY"],"title_canon_sha256":"6635312e03c9510d1e633a0a9e7dcdbdfbb4fc6eb50369edf6ffe864cfb5d481","abstract_canon_sha256":"31203f9c762523959fa62e6c3de6fc51d29bf63ebbbaab95b9ddc32609569404"},"schema_version":"1.0"},"canonical_sha256":"1c98a4fc23d1ca6c1ebabccc0bc8e5bedb9d6bd1434bf2978db2d85ee9f5e865","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T08:42:23.308054Z","signature_b64":"rTu/nqKUwlKOBv8A1FVsnK9NqMrDgXZB/t5TVfXODg+xmdowzor4aFVDKlmeKXP6fPQphJ8MC4dgUYZqLSZEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c98a4fc23d1ca6c1ebabccc0bc8e5bedb9d6bd1434bf2978db2d85ee9f5e865","last_reissued_at":"2026-07-02T08:42:23.307563Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T08:42:23.307563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.12182","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-02T08:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ad9balyWyLkiNHhaCKWILIPEYU77rIwHQRoj65oc6yddM6YBNvRX5nZF+klm+HXxxOfmxqZBcC9uxPeqXc2HCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-18T16:31:41.472094Z"},"content_sha256":"f3d234eba2ef064e73459c6c13fdfdefee694ff10930f59fedfea2e4ecf9b943","schema_version":"1.0","event_id":"sha256:f3d234eba2ef064e73459c6c13fdfdefee694ff10930f59fedfea2e4ecf9b943"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:DSMKJ7BD2HFGYHV2XTGAXSHFX3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Converse Control Lyapunov Theorem for Joint Safety and Stability","license":"","headline":"","cross_cats":["eess.SY"],"primary_cat":"math.OC","authors_text":"Jun Liu, Maxwell Fitzsimmons, Thanin Quartz","submitted_at":"2025-09-15T17:45:27Z","abstract_excerpt":"We show that the existence of a strictly compatible pair of control Lyapunov and control barrier functions is equivalent to the existence of a single smooth Lyapunov function that certifies both asymptotic stability and safety. This characterization complements existing literature on converse Lyapunov functions by establishing a partial differential equation (PDE) characterization with prescribed boundary conditions on the safe set, ensuring that the safe set is exactly certified by this Lyapunov function. The result also implies that if a safety and stability specification cannot be certified"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.12182","kind":"arxiv","version":2},"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/2509.12182/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":"2026-07-02T08:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U/eIKhM/lRyuafbT7A83mh2HBHvu39HXF6TyoPpPJjtjn13PirvJ2eGjDa6rVWr0lBFfQkDD2Gu7U5pjYr4sAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-18T16:31:41.472477Z"},"content_sha256":"c8c03eed5532c97f18e4fc3eb5ee1ad986d99f8e23bdcc4406cfb274426dbc6d","schema_version":"1.0","event_id":"sha256:c8c03eed5532c97f18e4fc3eb5ee1ad986d99f8e23bdcc4406cfb274426dbc6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DSMKJ7BD2HFGYHV2XTGAXSHFX3/bundle.json","state_url":"https://pith.science/pith/DSMKJ7BD2HFGYHV2XTGAXSHFX3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DSMKJ7BD2HFGYHV2XTGAXSHFX3/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":"2026-07-18T16:31:41Z","links":{"resolver":"https://pith.science/pith/DSMKJ7BD2HFGYHV2XTGAXSHFX3","bundle":"https://pith.science/pith/DSMKJ7BD2HFGYHV2XTGAXSHFX3/bundle.json","state":"https://pith.science/pith/DSMKJ7BD2HFGYHV2XTGAXSHFX3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DSMKJ7BD2HFGYHV2XTGAXSHFX3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DSMKJ7BD2HFGYHV2XTGAXSHFX3","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":"31203f9c762523959fa62e6c3de6fc51d29bf63ebbbaab95b9ddc32609569404","cross_cats_sorted":["eess.SY"],"license":"","primary_cat":"math.OC","submitted_at":"2025-09-15T17:45:27Z","title_canon_sha256":"6635312e03c9510d1e633a0a9e7dcdbdfbb4fc6eb50369edf6ffe864cfb5d481"},"schema_version":"1.0","source":{"id":"2509.12182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.12182","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"2509.12182v2","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.12182","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"DSMKJ7BD2HFG","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"pith_short_16","alias_value":"DSMKJ7BD2HFGYHV2","created_at":"2026-07-02T08:42:23Z"},{"alias_kind":"pith_short_8","alias_value":"DSMKJ7BD","created_at":"2026-07-02T08:42:23Z"}],"graph_snapshots":[{"event_id":"sha256:c8c03eed5532c97f18e4fc3eb5ee1ad986d99f8e23bdcc4406cfb274426dbc6d","target":"graph","created_at":"2026-07-02T08:42:23Z","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/2509.12182/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the existence of a strictly compatible pair of control Lyapunov and control barrier functions is equivalent to the existence of a single smooth Lyapunov function that certifies both asymptotic stability and safety. This characterization complements existing literature on converse Lyapunov functions by establishing a partial differential equation (PDE) characterization with prescribed boundary conditions on the safe set, ensuring that the safe set is exactly certified by this Lyapunov function. The result also implies that if a safety and stability specification cannot be certified","authors_text":"Jun Liu, Maxwell Fitzsimmons, Thanin Quartz","cross_cats":["eess.SY"],"headline":"","license":"","primary_cat":"math.OC","submitted_at":"2025-09-15T17:45:27Z","title":"A Converse Control Lyapunov Theorem for Joint Safety and Stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.12182","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:f3d234eba2ef064e73459c6c13fdfdefee694ff10930f59fedfea2e4ecf9b943","target":"record","created_at":"2026-07-02T08:42:23Z","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":"31203f9c762523959fa62e6c3de6fc51d29bf63ebbbaab95b9ddc32609569404","cross_cats_sorted":["eess.SY"],"license":"","primary_cat":"math.OC","submitted_at":"2025-09-15T17:45:27Z","title_canon_sha256":"6635312e03c9510d1e633a0a9e7dcdbdfbb4fc6eb50369edf6ffe864cfb5d481"},"schema_version":"1.0","source":{"id":"2509.12182","kind":"arxiv","version":2}},"canonical_sha256":"1c98a4fc23d1ca6c1ebabccc0bc8e5bedb9d6bd1434bf2978db2d85ee9f5e865","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c98a4fc23d1ca6c1ebabccc0bc8e5bedb9d6bd1434bf2978db2d85ee9f5e865","first_computed_at":"2026-07-02T08:42:23.307563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T08:42:23.307563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rTu/nqKUwlKOBv8A1FVsnK9NqMrDgXZB/t5TVfXODg+xmdowzor4aFVDKlmeKXP6fPQphJ8MC4dgUYZqLSZEAg==","signature_status":"signed_v1","signed_at":"2026-07-02T08:42:23.308054Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.12182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3d234eba2ef064e73459c6c13fdfdefee694ff10930f59fedfea2e4ecf9b943","sha256:c8c03eed5532c97f18e4fc3eb5ee1ad986d99f8e23bdcc4406cfb274426dbc6d"],"state_sha256":"1d920fb0bf333c14ca22efd91cae2116c99c4117b842945005a7e9d4779aca3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eEY3z5MsbJhiI9UtpUKNHBqIyZRZZ2fNtdYJr5hRplj5QO4GrJWK7KHPf2/0/byu8YEz42ZRiAbQqHgJduTFDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-18T16:31:41.474935Z","bundle_sha256":"19a5cce4defcea7e5ffa02a2a1ddc528a550728facf840d16763f25a6d9bbeaf"}}