{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:GOE6MIWCSN35SAQUV3IPZQ2UZZ","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":"ef8f85db07ee7bf1c0aef9027066fa9b40ae3f4e5a9f48cd3c0ea5daa36c3c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-12-17T21:44:26Z","title_canon_sha256":"8cebaa595d453e3056bdcab8712b8ae8290669bf35b6c831c6e1d376f487501e"},"schema_version":"1.0","source":{"id":"0812.3415","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3415","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3415v5","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3415","created_at":"2026-05-18T04:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"GOE6MIWCSN35","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"GOE6MIWCSN35SAQU","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"GOE6MIWC","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:726a95a2a6f41ad097862c75c807c7a6ee1df6364721b4df07d35baebc4d1fe2","target":"graph","created_at":"2026-05-18T04:04:17Z","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 stability for all generic equilibria of the Lie-Poisson dynamics of the $\\mathfrak{so}(4)$ rigid body dynamics is completely determined. It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of $\\mathfrak{so}(n)$ are equilibrium points for the rigid body dynamics. In the case of $\\mathfrak{so}(4)$ there are three coordinate type Cartan subalgebras whose intersection with a regular adjoint orbit give three Weyl group orbits of equilibria. These coordinate type Cartan subalgebras are the analogues of the three axes of equilibria for the classi","authors_text":"Ioan Casu, Murat Turhan, Petre Birtea, Tudor S. Ratiu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-12-17T21:44:26Z","title":"Stability of equilibria for the $\\mathfrak{so}(4)$ free rigid body"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3415","kind":"arxiv","version":5},"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":"sha256:024e4b9a9d0f01b2bb1c7a5fdac6a988f628a79dde19736ee8f00ed03e8c22ff","target":"record","created_at":"2026-05-18T04:04:17Z","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":"ef8f85db07ee7bf1c0aef9027066fa9b40ae3f4e5a9f48cd3c0ea5daa36c3c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-12-17T21:44:26Z","title_canon_sha256":"8cebaa595d453e3056bdcab8712b8ae8290669bf35b6c831c6e1d376f487501e"},"schema_version":"1.0","source":{"id":"0812.3415","kind":"arxiv","version":5}},"canonical_sha256":"3389e622c29377d90214aed0fcc354ce46de1ed6b5f7487a44e8f47dbee4cee8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3389e622c29377d90214aed0fcc354ce46de1ed6b5f7487a44e8f47dbee4cee8","first_computed_at":"2026-05-18T04:04:17.409472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:17.409472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSsGdwuSTzQjl7obsfaSSYKzmjxGe+fwFzf76/eK5+te6a5qkL18quFFlCXCxtHQW1NbEa100Y3pP1Vg15DFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:17.410246Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3415","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:024e4b9a9d0f01b2bb1c7a5fdac6a988f628a79dde19736ee8f00ed03e8c22ff","sha256:726a95a2a6f41ad097862c75c807c7a6ee1df6364721b4df07d35baebc4d1fe2"],"state_sha256":"7ad52d3c5db09e8d5d066373db033cf792e588299d7ce21fe8f4b24b4f880f83"}