{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:VB6IHZ6MR4DW2TRHJFYQM42KBU","short_pith_number":"pith:VB6IHZ6M","schema_version":"1.0","canonical_sha256":"a87c83e7cc8f076d4e27497106734a0d21fdde958b761539d89d5083762ffbd5","source":{"kind":"arxiv","id":"math-ph/0109031","version":2},"attestation_state":"computed","paper":{"title":"Non-commutative Integrability, Moment Map and Geodesic Flows","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexey V. Bolsinov, Bozidar Jovanovic","submitted_at":"2001-09-27T14:38:32Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math-ph/0109031","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-09-27T14:38:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"bb18979ad82336e53bb26f6f26de3f42dc57939e0a6ff74481700e83dea09c82","abstract_canon_sha256":"db33e132ba7e696e8c44e79efbf5158223ff6cc5bdae2631a14d67ce66368fde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:33:40.282773Z","signature_b64":"VJXXtZAOKXfcuoqAIDpo5K6VQ5WfVV+a8pCH9M0x+LVf3XnjFqo37UZ0Qb6OJONi7igEqCqNb8ChZc9sCIABAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a87c83e7cc8f076d4e27497106734a0d21fdde958b761539d89d5083762ffbd5","last_reissued_at":"2026-07-04T14:33:40.282286Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:33:40.282286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-commutative Integrability, Moment Map and Geodesic Flows","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexey V. Bolsinov, Bozidar Jovanovic","submitted_at":"2001-09-27T14:38:32Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0109031","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0109031/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0109031","created_at":"2026-07-04T14:33:40.282364+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0109031v2","created_at":"2026-07-04T14:33:40.282364+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0109031","created_at":"2026-07-04T14:33:40.282364+00:00"},{"alias_kind":"pith_short_12","alias_value":"VB6IHZ6MR4DW","created_at":"2026-07-04T14:33:40.282364+00:00"},{"alias_kind":"pith_short_16","alias_value":"VB6IHZ6MR4DW2TRH","created_at":"2026-07-04T14:33:40.282364+00:00"},{"alias_kind":"pith_short_8","alias_value":"VB6IHZ6M","created_at":"2026-07-04T14:33:40.282364+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2507.12051","citing_title":"Integrable systems from Poisson reductions of generalized Hamiltonian torus actions","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2507.12051","citing_title":"Integrable systems from Poisson reductions of generalized Hamiltonian torus actions","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU","json":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU.json","graph_json":"https://pith.science/api/pith-number/VB6IHZ6MR4DW2TRHJFYQM42KBU/graph.json","events_json":"https://pith.science/api/pith-number/VB6IHZ6MR4DW2TRHJFYQM42KBU/events.json","paper":"https://pith.science/paper/VB6IHZ6M"},"agent_actions":{"view_html":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU","download_json":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU.json","view_paper":"https://pith.science/paper/VB6IHZ6M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0109031&json=true","fetch_graph":"https://pith.science/api/pith-number/VB6IHZ6MR4DW2TRHJFYQM42KBU/graph.json","fetch_events":"https://pith.science/api/pith-number/VB6IHZ6MR4DW2TRHJFYQM42KBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU/action/storage_attestation","attest_author":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU/action/author_attestation","sign_citation":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU/action/citation_signature","submit_replication":"https://pith.science/pith/VB6IHZ6MR4DW2TRHJFYQM42KBU/action/replication_record"}},"created_at":"2026-07-04T14:33:40.282364+00:00","updated_at":"2026-07-04T14:33:40.282364+00:00"}