{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WJRJBR644T4L73W3Q3ARUXOBAG","short_pith_number":"pith:WJRJBR64","schema_version":"1.0","canonical_sha256":"b26290c7dce4f8bfeedb86c11a5dc101a21ca5583cf3c0d0495059def0e15304","source":{"kind":"arxiv","id":"1008.4377","version":1},"attestation_state":"computed","paper":{"title":"Generalized Euler-Poincar\\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AP","authors_text":"Cornelia Vizman, Feride Tiglay","submitted_at":"2010-08-25T20:49:45Z","abstract_excerpt":"We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar\\'e equations on Lie groups and homogeneous spaces. Orbit invariants play an important role in this context and we use these invariants to prove global existence and uniqueness results for a class of PDE. This class includes Euler-Poincar\\'e equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, $\\mu$CH and $\\mu$DP equations, and the geodesic e"},"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":"1008.4377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-25T20:49:45Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"906f655e11f93b538b7f7a25fd218d6b83c7842ed456e8a49d2c3c21af00473c","abstract_canon_sha256":"44f9fc8eebd9f1ae3feddacacf0653b87d1078c1000e580749544a26ffb385c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:42.672135Z","signature_b64":"DDDdCZWarA3gj8mk/yaahVeG/+eT0Cju6y/RECLnsjlKad7i/HB4OMTd3Tvesk7R1AsA7nyY8r5oIEVfsGbmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b26290c7dce4f8bfeedb86c11a5dc101a21ca5583cf3c0d0495059def0e15304","last_reissued_at":"2026-05-18T02:05:42.671527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:42.671527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Euler-Poincar\\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AP","authors_text":"Cornelia Vizman, Feride Tiglay","submitted_at":"2010-08-25T20:49:45Z","abstract_excerpt":"We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar\\'e equations on Lie groups and homogeneous spaces. Orbit invariants play an important role in this context and we use these invariants to prove global existence and uniqueness results for a class of PDE. This class includes Euler-Poincar\\'e equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, $\\mu$CH and $\\mu$DP equations, and the geodesic e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4377","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":"1008.4377","created_at":"2026-05-18T02:05:42.671607+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.4377v1","created_at":"2026-05-18T02:05:42.671607+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4377","created_at":"2026-05-18T02:05:42.671607+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJRJBR644T4L","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJRJBR644T4L73W3","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJRJBR64","created_at":"2026-05-18T12:26:15.391820+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/WJRJBR644T4L73W3Q3ARUXOBAG","json":"https://pith.science/pith/WJRJBR644T4L73W3Q3ARUXOBAG.json","graph_json":"https://pith.science/api/pith-number/WJRJBR644T4L73W3Q3ARUXOBAG/graph.json","events_json":"https://pith.science/api/pith-number/WJRJBR644T4L73W3Q3ARUXOBAG/events.json","paper":"https://pith.science/paper/WJRJBR64"},"agent_actions":{"view_html":"https://pith.science/pith/WJRJBR644T4L73W3Q3ARUXOBAG","download_json":"https://pith.science/pith/WJRJBR644T4L73W3Q3ARUXOBAG.json","view_paper":"https://pith.science/paper/WJRJBR64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.4377&json=true","fetch_graph":"https://pith.science/api/pith-number/WJRJBR644T4L73W3Q3ARUXOBAG/graph.json","fetch_events":"https://pith.science/api/pith-number/WJRJBR644T4L73W3Q3ARUXOBAG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJRJBR644T4L73W3Q3ARUXOBAG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJRJBR644T4L73W3Q3ARUXOBAG/action/storage_attestation","attest_author":"https://pith.science/pith/WJRJBR644T4L73W3Q3ARUXOBAG/action/author_attestation","sign_citation":"https://pith.science/pith/WJRJBR644T4L73W3Q3ARUXOBAG/action/citation_signature","submit_replication":"https://pith.science/pith/WJRJBR644T4L73W3Q3ARUXOBAG/action/replication_record"}},"created_at":"2026-05-18T02:05:42.671607+00:00","updated_at":"2026-05-18T02:05:42.671607+00:00"}