{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:APAYTDIWRQZGILIGLXBSLZHO2A","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":"7a4d27b85f5227b6fb3acfe721c3bfe70b7797bbad5fe6b5d59143c9eb29aaf6","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-12-17T15:40:38Z","title_canon_sha256":"aa7561e85e03fa64a5ca61141b6d49ae2f5357dc990be304d7fb39406d61d570"},"schema_version":"1.0","source":{"id":"0812.3320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3320","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3320v1","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3320","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"APAYTDIWRQZG","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"APAYTDIWRQZGILIG","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"APAYTDIW","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:cc90a96f56a051bb0f2602b8f541b1aee45d37c66b558b67e0e7625f0d7aed28","target":"graph","created_at":"2026-05-18T02:15:04Z","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":"The numerical integration of the Nose-Hoover dynamics gives a deterministic method that is used to sample the canonical Gibbs measure. The Nose-Hoover dynamics extends the physical Hamiltonian dynamics by the addition of a \"thermostat\" variable, that is coupled nonlinearly with the physical variables. The accuracy of the method depends on the dynamics being ergodic. Numerical experiments have been published earlier that are consistent with non-ergodicity of the dynamics for some model problems. The authors recently proved the non-ergodicity of the Nose-Hoover dynamics for the one-dimensional h","authors_text":"Frederic Legoll, Mitchell Luskin, Richard Moeckel","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-12-17T15:40:38Z","title":"Non-ergodicity of Nose-Hoover dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3320","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":"sha256:67fd61adb6587b98836b09ad49b8a547179e82b7b258fbf1462db0da6ecdf441","target":"record","created_at":"2026-05-18T02:15:04Z","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":"7a4d27b85f5227b6fb3acfe721c3bfe70b7797bbad5fe6b5d59143c9eb29aaf6","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-12-17T15:40:38Z","title_canon_sha256":"aa7561e85e03fa64a5ca61141b6d49ae2f5357dc990be304d7fb39406d61d570"},"schema_version":"1.0","source":{"id":"0812.3320","kind":"arxiv","version":1}},"canonical_sha256":"03c1898d168c32642d065dc325e4eed0030261ff5771a8405f57496f978d978e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03c1898d168c32642d065dc325e4eed0030261ff5771a8405f57496f978d978e","first_computed_at":"2026-05-18T02:15:04.536166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:04.536166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ir+TEPjzNlHY792hmot+5svJrXpFJRRsm4PREc5ShM/rTO6bxHhatMdnU0LXYWpeCicXObGA8VJyvhik5vJsAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:04.536730Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67fd61adb6587b98836b09ad49b8a547179e82b7b258fbf1462db0da6ecdf441","sha256:cc90a96f56a051bb0f2602b8f541b1aee45d37c66b558b67e0e7625f0d7aed28"],"state_sha256":"f8b3cff3e34a5151985e7d66a77ba2c4c5fd1fe3cadca72742c4aecd4f535fe1"}