{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:VB6IHZ6MR4DW2TRHJFYQM42KBU","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":"db33e132ba7e696e8c44e79efbf5158223ff6cc5bdae2631a14d67ce66368fde","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-09-27T14:38:32Z","title_canon_sha256":"bb18979ad82336e53bb26f6f26de3f42dc57939e0a6ff74481700e83dea09c82"},"schema_version":"1.0","source":{"id":"math-ph/0109031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0109031","created_at":"2026-07-04T14:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0109031v2","created_at":"2026-07-04T14:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0109031","created_at":"2026-07-04T14:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"VB6IHZ6MR4DW","created_at":"2026-07-04T14:33:40Z"},{"alias_kind":"pith_short_16","alias_value":"VB6IHZ6MR4DW2TRH","created_at":"2026-07-04T14:33:40Z"},{"alias_kind":"pith_short_8","alias_value":"VB6IHZ6M","created_at":"2026-07-04T14:33:40Z"}],"graph_snapshots":[{"event_id":"sha256:919071cd266ac3f2dec7412dcfd879c6bdc77c30140ecf92a82fc9f0786454f5","target":"graph","created_at":"2026-07-04T14:33:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math-ph/0109031/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this paper is to discuss the relationship between commutative and non-commutative integrability of Hamiltonian systems and to construct new examples of integrable geodesic flows on Riemannian manifolds. In particular, we prove that the geodesic flow of the bi-invariant metric on any bi-quotient of a compact Lie group is integrable in non-commutative sense by means of polynomial integrals, and therefore, in classical commutative sense by means of $C^\\infty$--smooth integrals.","authors_text":"Alexey V. Bolsinov, Bozidar Jovanovic","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2001-09-27T14:38:32Z","title":"Non-commutative Integrability, Moment Map and Geodesic Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0109031","kind":"arxiv","version":2},"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:abcf178cfc19c3d1f8f164ee221353f3046a575888cc7661818bec2dd3d00e34","target":"record","created_at":"2026-07-04T14:33:40Z","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":"db33e132ba7e696e8c44e79efbf5158223ff6cc5bdae2631a14d67ce66368fde","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-09-27T14:38:32Z","title_canon_sha256":"bb18979ad82336e53bb26f6f26de3f42dc57939e0a6ff74481700e83dea09c82"},"schema_version":"1.0","source":{"id":"math-ph/0109031","kind":"arxiv","version":2}},"canonical_sha256":"a87c83e7cc8f076d4e27497106734a0d21fdde958b761539d89d5083762ffbd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a87c83e7cc8f076d4e27497106734a0d21fdde958b761539d89d5083762ffbd5","first_computed_at":"2026-07-04T14:33:40.282286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:33:40.282286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VJXXtZAOKXfcuoqAIDpo5K6VQ5WfVV+a8pCH9M0x+LVf3XnjFqo37UZ0Qb6OJONi7igEqCqNb8ChZc9sCIABAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:33:40.282773Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0109031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abcf178cfc19c3d1f8f164ee221353f3046a575888cc7661818bec2dd3d00e34","sha256:919071cd266ac3f2dec7412dcfd879c6bdc77c30140ecf92a82fc9f0786454f5"],"state_sha256":"337902ed043d6c9ff980c968334845fe70588fb3b0d6b1d0faecb10265119184"}