{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:GNFXHX46RWROOPUBBNLTB6UXBU","short_pith_number":"pith:GNFXHX46","schema_version":"1.0","canonical_sha256":"334b73df9e8da2e73e810b5730fa970d3b00653447003f7e657883ba0967e9bb","source":{"kind":"arxiv","id":"math/9312213","version":1},"attestation_state":"computed","paper":{"title":"Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Dmitri V. Alekseevsky, Giuseppe Marmo, Janusz Grabowski, Peter W. Michor","submitted_at":"1993-12-01T00:00:00Z","abstract_excerpt":"On a cotangent bundle $T\\sp*G$ of a Lie group $G$ one can describe the standard Liouville form $\\theta$ and the symplectic form $d \\theta$ in terms of the right Maurer Cartan form and the left moment mapping (of the right action of $G$ on itself), and also in terms of the left Maurer-Cartan form and the right moment mapping, and also the Poisson structure can be written in related quantities. This leads to a wide class of exact symplectic stuctures on $T\\sp*G$ and to Poisson structures by replacing the canonical momenta of the right or left actions of $G$ on itself by arbitrary ones, followed "},"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/9312213","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"1993-12-01T00:00:00Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4bacfe1c855d91ee6f61e48a4032c19ee07e40f2088053e39968a29e0e62d76b","abstract_canon_sha256":"ff730f2280184ac2b9f8fd4080dcfb1776928617c46f09853b2303f74087420f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.742390Z","signature_b64":"mhEagbepXw/0o4ja+rE45YLNf9kzXeddK/SKGryl6P4G0IrXLpdHKlFOZKVIJvLrSzxqKgs4M3FUpTbOZ2GPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"334b73df9e8da2e73e810b5730fa970d3b00653447003f7e657883ba0967e9bb","last_reissued_at":"2026-05-18T01:05:51.741689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.741689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Dmitri V. Alekseevsky, Giuseppe Marmo, Janusz Grabowski, Peter W. Michor","submitted_at":"1993-12-01T00:00:00Z","abstract_excerpt":"On a cotangent bundle $T\\sp*G$ of a Lie group $G$ one can describe the standard Liouville form $\\theta$ and the symplectic form $d \\theta$ in terms of the right Maurer Cartan form and the left moment mapping (of the right action of $G$ on itself), and also in terms of the left Maurer-Cartan form and the right moment mapping, and also the Poisson structure can be written in related quantities. This leads to a wide class of exact symplectic stuctures on $T\\sp*G$ and to Poisson structures by replacing the canonical momenta of the right or left actions of $G$ on itself by arbitrary ones, followed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9312213","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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/9312213","created_at":"2026-05-18T01:05:51.741805+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9312213v1","created_at":"2026-05-18T01:05:51.741805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9312213","created_at":"2026-05-18T01:05:51.741805+00:00"},{"alias_kind":"pith_short_12","alias_value":"GNFXHX46RWRO","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"GNFXHX46RWROOPUB","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"GNFXHX46","created_at":"2026-05-18T12:25:47.102015+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU","json":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU.json","graph_json":"https://pith.science/api/pith-number/GNFXHX46RWROOPUBBNLTB6UXBU/graph.json","events_json":"https://pith.science/api/pith-number/GNFXHX46RWROOPUBBNLTB6UXBU/events.json","paper":"https://pith.science/paper/GNFXHX46"},"agent_actions":{"view_html":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU","download_json":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU.json","view_paper":"https://pith.science/paper/GNFXHX46","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9312213&json=true","fetch_graph":"https://pith.science/api/pith-number/GNFXHX46RWROOPUBBNLTB6UXBU/graph.json","fetch_events":"https://pith.science/api/pith-number/GNFXHX46RWROOPUBBNLTB6UXBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU/action/storage_attestation","attest_author":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU/action/author_attestation","sign_citation":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU/action/citation_signature","submit_replication":"https://pith.science/pith/GNFXHX46RWROOPUBBNLTB6UXBU/action/replication_record"}},"created_at":"2026-05-18T01:05:51.741805+00:00","updated_at":"2026-05-18T01:05:51.741805+00:00"}