{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CXN5IOEF7CSWRDPYDLHNTSR5EB","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":"a02a0a0f96b423984eb1e477723205a0b0a6b093a1a995badcf3f84c3e699025","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-17T19:02:40Z","title_canon_sha256":"9bca9615ffe85643cfbcbd06389579ee83a0cbabfdb9f34e4a8b4115183ddc5b"},"schema_version":"1.0","source":{"id":"1108.3551","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3551","created_at":"2026-05-18T03:20:33Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3551v3","created_at":"2026-05-18T03:20:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3551","created_at":"2026-05-18T03:20:33Z"},{"alias_kind":"pith_short_12","alias_value":"CXN5IOEF7CSW","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CXN5IOEF7CSWRDPY","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CXN5IOEF","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:2b3a355f623d346bd381d75a510338a9d16b804be45c77e192eb42745d6864c3","target":"graph","created_at":"2026-05-18T03:20:33Z","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"},"paper":{"abstract_excerpt":"We give a natural notion of nondegeneracy for singular points of integrable non-Hamiltonian systems, and show that such nondegenerate singularities are locally geometrically linearizable and deformation rigid in the analytic case. We conjecture that the same result also holds in the smooth case, and prove this conjecture for systems of type $(n,0)$, i.e. $n$ commuting smooth vector fields on a $n$-manifold.","authors_text":"Nguyen Tien Zung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-17T19:02:40Z","title":"Nondegenerate singularities of integrable dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3551","kind":"arxiv","version":3},"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":"sha256:378a6d924d3055f2a01d8ad55a211e95282a290cbce1795bbea8397f0a35ea03","target":"record","created_at":"2026-05-18T03:20:33Z","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":"a02a0a0f96b423984eb1e477723205a0b0a6b093a1a995badcf3f84c3e699025","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-17T19:02:40Z","title_canon_sha256":"9bca9615ffe85643cfbcbd06389579ee83a0cbabfdb9f34e4a8b4115183ddc5b"},"schema_version":"1.0","source":{"id":"1108.3551","kind":"arxiv","version":3}},"canonical_sha256":"15dbd43885f8a5688df81aced9ca3d205b441fd063c877acf916435351c0ea0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15dbd43885f8a5688df81aced9ca3d205b441fd063c877acf916435351c0ea0b","first_computed_at":"2026-05-18T03:20:33.079067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:33.079067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+3lrdV2F7yCDqnoYFUXCJKu/NUozZFqiPyL76BcFwvsZatmeGYgh0vBMhFD4+Yu/MPUenebh2qTEyJnpC7dAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:33.079973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3551","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:378a6d924d3055f2a01d8ad55a211e95282a290cbce1795bbea8397f0a35ea03","sha256:2b3a355f623d346bd381d75a510338a9d16b804be45c77e192eb42745d6864c3"],"state_sha256":"20c79c8a23245fd3b0b1d339a8ba82322664f42b27d61fe6c3b449b71f494f66"}