{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7SI45NOVBEZTGMQEBNYXF57UTP","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":"9f576800a80735e0bcd048a820ef625227e5203518cdbb1cd8d73ca8d803ee51","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-27T23:51:05Z","title_canon_sha256":"9449e2619e8c97f7ca7aade02d2f47b030920417480ce3baf3befdb8fd5ddcda"},"schema_version":"1.0","source":{"id":"1211.6480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6480","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6480v1","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6480","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"7SI45NOVBEZT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7SI45NOVBEZTGMQE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7SI45NOV","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:aede2ef97b68f9697ffba23f13098524a692630b8d2e8937386bc2768a86f5c8","target":"graph","created_at":"2026-05-18T03:39:51Z","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":"For an integrable Hamiltonian $H_0=1/2\\sum_{i=1}^dy_i^2$ $(d\\geq 2)$, we show that any Lagrangian torus with a given unique rotation vector can be destructed by arbitrarily $C^{2d-\\delta}$-small perturbations. In contrast with it, it has been shown that KAM torus with constant type frequency persists under $C^{2d+\\delta}$-small perturbations.","authors_text":"Chong-Qing Cheng, Lin Wang","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-27T23:51:05Z","title":"Destruction of Lagrangian torus for positive definite Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6480","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:daedf0abda230388ea2b7636e5dbb8e79190a32d0f443dc0f6ba3619a152f003","target":"record","created_at":"2026-05-18T03:39:51Z","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":"9f576800a80735e0bcd048a820ef625227e5203518cdbb1cd8d73ca8d803ee51","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-27T23:51:05Z","title_canon_sha256":"9449e2619e8c97f7ca7aade02d2f47b030920417480ce3baf3befdb8fd5ddcda"},"schema_version":"1.0","source":{"id":"1211.6480","kind":"arxiv","version":1}},"canonical_sha256":"fc91ceb5d509333332040b7172f7f49bcd3c590d0fd7287aaca2aa9b8b3d1039","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc91ceb5d509333332040b7172f7f49bcd3c590d0fd7287aaca2aa9b8b3d1039","first_computed_at":"2026-05-18T03:39:51.426982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:51.426982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H7PiAZKpE5w0L2i0QJpTXE2sFGbsV5qbT0c5e0nj85L+bAFQ8svReJQ/I7IeJKcZyFz8/ePPoNop1+QLiCs4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:51.427774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daedf0abda230388ea2b7636e5dbb8e79190a32d0f443dc0f6ba3619a152f003","sha256:aede2ef97b68f9697ffba23f13098524a692630b8d2e8937386bc2768a86f5c8"],"state_sha256":"06f9ed0e633739bcb33f06edc557642aea25b4bbb32053e8a0c5e5dae2ac265a"}