{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DV3UNLQWKULYPONDJ5TWJPYYEL","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":"babc7c0459868fb57a9149faf752b0493abf9a848ee98c53b2bce931819de2f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-28T02:50:27Z","title_canon_sha256":"1188dd94f149f5a1af507a45ad0b822dee42acacc5173743045c125ee43a32d1"},"schema_version":"1.0","source":{"id":"1902.10871","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10871","created_at":"2026-07-05T00:26:56Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10871v2","created_at":"2026-07-05T00:26:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10871","created_at":"2026-07-05T00:26:56Z"},{"alias_kind":"pith_short_12","alias_value":"DV3UNLQWKULY","created_at":"2026-07-05T00:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"DV3UNLQWKULYPOND","created_at":"2026-07-05T00:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"DV3UNLQW","created_at":"2026-07-05T00:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:c7871938083437c98b372f46aceb3a02cdfe14ad91ef27cd98f1b7eebc9faff0","target":"graph","created_at":"2026-07-05T00:26:56Z","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/1902.10871/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Local asymptotic stabilizability is a topic of great theoretical interest and practical importance. Broadly, if a system $\\dot{x} = f(x,u)$ is locally asymptotically stabilizable, we are guaranteed a feedback controller $u(x)$ that forces convergence to an equilibrium for trajectories initialized sufficiently close to it. A necessary condition was given by Brockett: such controllers exist only when $f$ is open at the equilibrium. Recently, Gupta, Jafari, Kipka and Mordukhovich considered a modification to this condition, replacing Brockett's topological openness by the linear openness property","authors_text":"Boris S. Mordukhovich, Bryce A. Christopherson, Farhad Jafari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-28T02:50:27Z","title":"A Variational Approach to Local Asymptotic and Exponential Stabilization of Nonlinear Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10871","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:b4966af45e8dfd03cdcff45d2497faa53888ad96fb08f19698659858c7bcd6b4","target":"record","created_at":"2026-07-05T00:26:56Z","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":"babc7c0459868fb57a9149faf752b0493abf9a848ee98c53b2bce931819de2f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-28T02:50:27Z","title_canon_sha256":"1188dd94f149f5a1af507a45ad0b822dee42acacc5173743045c125ee43a32d1"},"schema_version":"1.0","source":{"id":"1902.10871","kind":"arxiv","version":2}},"canonical_sha256":"1d7746ae16551787b9a34f6764bf1822f1f94c16e533fc741936c99fadf06477","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d7746ae16551787b9a34f6764bf1822f1f94c16e533fc741936c99fadf06477","first_computed_at":"2026-07-05T00:26:56.673007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:26:56.673007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8dt562jSAi/VJ8y02Ns9vxroGTfuyQC8Ks+836YBWw6VZ9iA8LdaPPzG0jrtqYT2rv0MgAdNj3Q7tVEk3MFbBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:26:56.673413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10871","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4966af45e8dfd03cdcff45d2497faa53888ad96fb08f19698659858c7bcd6b4","sha256:c7871938083437c98b372f46aceb3a02cdfe14ad91ef27cd98f1b7eebc9faff0"],"state_sha256":"a365f6bab84103c3f87e124085d600a6f5cd8bf4ac94464c63778bedc7148a10"}