{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NZVYG7SFT5GWJVGIPRXGRSSGUU","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":"64a21833d93861ab9065e60454f58df0aeddefd7ddb8e880f54399faf8d9fe25","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.plasm-ph","submitted_at":"2016-05-14T18:43:48Z","title_canon_sha256":"dffb6155227ee86693b49c975ba212768dde4d1d3fbc8f6b669be8e4d5364c72"},"schema_version":"1.0","source":{"id":"1605.04450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04450","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04450v1","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04450","created_at":"2026-05-18T01:14:47Z"},{"alias_kind":"pith_short_12","alias_value":"NZVYG7SFT5GW","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NZVYG7SFT5GWJVGI","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NZVYG7SF","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:aec5608ffce071f2d902c1070d81ffb010e2168da983b1c87e5016b75fd43c2a","target":"graph","created_at":"2026-05-18T01:14:47Z","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":"Positive definiteness of a Hamiltonian expanded about an equilibrium point provides only a necessary condition for stability, a criterion known as Dirichlet's theorem. The reason that this criterion is not necessary for stability is because of the possible existence of negative energy modes, which are linearly stable modes of oscillation that have negative energy. When such modes are present, the Hamiltonian is, in general, indefinite. Although such systems with negative energy modes are linearly stable (spectral stable), they are unstable to infinitesimal perturbations under the nonlinear dyn","authors_text":"Caroline G. L. Martins, C. Curry, P. J. Morison","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.plasm-ph","submitted_at":"2016-05-14T18:43:48Z","title":"A four dimensional map for escape from resonance: negative energy modes and nonlinear instability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04450","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":"sha256:4cb3714814be90a59001b23b6aa60be4c871d31b3fdbc497a3a174b1cfcf88c4","target":"record","created_at":"2026-05-18T01:14:47Z","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":"64a21833d93861ab9065e60454f58df0aeddefd7ddb8e880f54399faf8d9fe25","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.plasm-ph","submitted_at":"2016-05-14T18:43:48Z","title_canon_sha256":"dffb6155227ee86693b49c975ba212768dde4d1d3fbc8f6b669be8e4d5364c72"},"schema_version":"1.0","source":{"id":"1605.04450","kind":"arxiv","version":1}},"canonical_sha256":"6e6b837e459f4d64d4c87c6e68ca46a50756e378d3fe836b36ad538fb4559839","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e6b837e459f4d64d4c87c6e68ca46a50756e378d3fe836b36ad538fb4559839","first_computed_at":"2026-05-18T01:14:47.167881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:47.167881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VYT/LoZjCl0y4r5CRvy/rZtcAtaDrFrDIbc40aNMyVu4v0boSoUZ5B5HOKoQaEoibZBejnXfveJYCdETJS1PBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:47.168647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cb3714814be90a59001b23b6aa60be4c871d31b3fdbc497a3a174b1cfcf88c4","sha256:aec5608ffce071f2d902c1070d81ffb010e2168da983b1c87e5016b75fd43c2a"],"state_sha256":"4fe24533297022aa1ac644aa3e828bf3fa07eb871051205849b3c9a700edeeff"}