{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NHVHZ4TG4PXQ6WQ7PA3DEB4HCM","short_pith_number":"pith:NHVHZ4TG","canonical_record":{"source":{"id":"1704.00867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-04T04:17:16Z","cross_cats_sorted":[],"title_canon_sha256":"4f8255e0805ca019ca995e9d59ef0be9ba56d1469870d6bc9d4ae915af7c4649","abstract_canon_sha256":"1a4d6fb031233e90f7ec96e9bd373dfd3cc2185ff1c7eb4fb1e90d5976d09d88"},"schema_version":"1.0"},"canonical_sha256":"69ea7cf266e3ef0f5a1f783632078713396f7af7d9a0fa4a691938d6ee426a26","source":{"kind":"arxiv","id":"1704.00867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00867","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00867v1","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00867","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"pith_short_12","alias_value":"NHVHZ4TG4PXQ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NHVHZ4TG4PXQ6WQ7","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NHVHZ4TG","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NHVHZ4TG4PXQ6WQ7PA3DEB4HCM","target":"record","payload":{"canonical_record":{"source":{"id":"1704.00867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-04T04:17:16Z","cross_cats_sorted":[],"title_canon_sha256":"4f8255e0805ca019ca995e9d59ef0be9ba56d1469870d6bc9d4ae915af7c4649","abstract_canon_sha256":"1a4d6fb031233e90f7ec96e9bd373dfd3cc2185ff1c7eb4fb1e90d5976d09d88"},"schema_version":"1.0"},"canonical_sha256":"69ea7cf266e3ef0f5a1f783632078713396f7af7d9a0fa4a691938d6ee426a26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:19.012659Z","signature_b64":"qBBqH/mr99l29lRaWLnL/lGWhoLk1oMIySDq1mQoglqtNbZAURqzZVLLKbgX7lT1FYDVnEgXObMZj7KoiOfNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69ea7cf266e3ef0f5a1f783632078713396f7af7d9a0fa4a691938d6ee426a26","last_reissued_at":"2026-05-18T00:47:19.011976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:19.011976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.00867","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":"2026-05-18T00:47:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3NZlfRwQ0bCqQz0NqOUfXtzfX1+zpsw+d835Vb7Zl2RdPjyec/IEvjD/ho35BG63+RLyGYLp3UAGGXEoz1+1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:39:59.233077Z"},"content_sha256":"e303ff8cbe5b4ddb82009ce0d59fc0748afce486d5641527b0630e367f98f3fc","schema_version":"1.0","event_id":"sha256:e303ff8cbe5b4ddb82009ce0d59fc0748afce486d5641527b0630e367f98f3fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NHVHZ4TG4PXQ6WQ7PA3DEB4HCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Openness and Feedback Stabilization of Nonlinear Control Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris S. Mordukhovich, Farhad Jafari, Robert J. Kipka, Rohit Gupta","submitted_at":"2017-04-04T04:17:16Z","abstract_excerpt":"It is well known from the seminal Brockett's theorem that the openness property of the mapping on the right-hand side of a given nonlinear ODE control system is a necessary condition for the existence of locally asymptotically stabilizing continuous stationary feedback laws. However, this condition fails to be sufficient for such a feedback stabilization. In this paper we develop an approach of variational analysis to continuous feedback stabilization of nonlinear control systems with replacing openness by the linear openness property, which has been well understood and characterized in variat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00867","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":""},"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":"2026-05-18T00:47:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCoikTH1+AoZTZX0xJJkQA/0DqlYi/0yws5UYRmBcrxX/ctQz1kKGLQeSdNnGJ7mlZyy1Ki2dNE1oSRgaUdOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:39:59.233742Z"},"content_sha256":"1876c3f399b914fff57aa769f7dbdaedb1952e098ff5e389e5ba832cba7ff6da","schema_version":"1.0","event_id":"sha256:1876c3f399b914fff57aa769f7dbdaedb1952e098ff5e389e5ba832cba7ff6da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NHVHZ4TG4PXQ6WQ7PA3DEB4HCM/bundle.json","state_url":"https://pith.science/pith/NHVHZ4TG4PXQ6WQ7PA3DEB4HCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NHVHZ4TG4PXQ6WQ7PA3DEB4HCM/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":"2026-05-26T21:39:59Z","links":{"resolver":"https://pith.science/pith/NHVHZ4TG4PXQ6WQ7PA3DEB4HCM","bundle":"https://pith.science/pith/NHVHZ4TG4PXQ6WQ7PA3DEB4HCM/bundle.json","state":"https://pith.science/pith/NHVHZ4TG4PXQ6WQ7PA3DEB4HCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NHVHZ4TG4PXQ6WQ7PA3DEB4HCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NHVHZ4TG4PXQ6WQ7PA3DEB4HCM","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":"1a4d6fb031233e90f7ec96e9bd373dfd3cc2185ff1c7eb4fb1e90d5976d09d88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-04T04:17:16Z","title_canon_sha256":"4f8255e0805ca019ca995e9d59ef0be9ba56d1469870d6bc9d4ae915af7c4649"},"schema_version":"1.0","source":{"id":"1704.00867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00867","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00867v1","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00867","created_at":"2026-05-18T00:47:19Z"},{"alias_kind":"pith_short_12","alias_value":"NHVHZ4TG4PXQ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NHVHZ4TG4PXQ6WQ7","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NHVHZ4TG","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:1876c3f399b914fff57aa769f7dbdaedb1952e098ff5e389e5ba832cba7ff6da","target":"graph","created_at":"2026-05-18T00:47:19Z","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"},"paper":{"abstract_excerpt":"It is well known from the seminal Brockett's theorem that the openness property of the mapping on the right-hand side of a given nonlinear ODE control system is a necessary condition for the existence of locally asymptotically stabilizing continuous stationary feedback laws. However, this condition fails to be sufficient for such a feedback stabilization. In this paper we develop an approach of variational analysis to continuous feedback stabilization of nonlinear control systems with replacing openness by the linear openness property, which has been well understood and characterized in variat","authors_text":"Boris S. Mordukhovich, Farhad Jafari, Robert J. Kipka, Rohit Gupta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-04T04:17:16Z","title":"Linear Openness and Feedback Stabilization of Nonlinear Control Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00867","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:e303ff8cbe5b4ddb82009ce0d59fc0748afce486d5641527b0630e367f98f3fc","target":"record","created_at":"2026-05-18T00:47:19Z","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":"1a4d6fb031233e90f7ec96e9bd373dfd3cc2185ff1c7eb4fb1e90d5976d09d88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-04T04:17:16Z","title_canon_sha256":"4f8255e0805ca019ca995e9d59ef0be9ba56d1469870d6bc9d4ae915af7c4649"},"schema_version":"1.0","source":{"id":"1704.00867","kind":"arxiv","version":1}},"canonical_sha256":"69ea7cf266e3ef0f5a1f783632078713396f7af7d9a0fa4a691938d6ee426a26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69ea7cf266e3ef0f5a1f783632078713396f7af7d9a0fa4a691938d6ee426a26","first_computed_at":"2026-05-18T00:47:19.011976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:19.011976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qBBqH/mr99l29lRaWLnL/lGWhoLk1oMIySDq1mQoglqtNbZAURqzZVLLKbgX7lT1FYDVnEgXObMZj7KoiOfNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:19.012659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e303ff8cbe5b4ddb82009ce0d59fc0748afce486d5641527b0630e367f98f3fc","sha256:1876c3f399b914fff57aa769f7dbdaedb1952e098ff5e389e5ba832cba7ff6da"],"state_sha256":"c9bd0fe09607ca011147eb5e870f89858732066081edda12fd9f8e794691dc18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q7X7T7WDjHwgJILTJaVUG5q/oDJ+Tu4Bh0dCIIB4wkwzR/0JOtLFR23XFtsoGwEe5eGcPSxExtoeJIzRIpJzAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:39:59.236934Z","bundle_sha256":"2459ee4b9b25009f781b3c90e1877cd7582eb5d609ee184d3520da723d4029da"}}