{"id":"W2066770613","doi":"10.1016/s0001-8708(02)00063-4","title":"Euler equations on homogeneous spaces and Virasoro orbits","year":2003,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":229,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Isaac Newton Institute for Mathematical Sciences; National Science Foundation","keywords":"Mathematics; Geodesic; Integrable system; Invariant (physics); Geodesic flow; Homogeneous; Pure mathematics; Virasoro algebra; Dynamical systems theory; Group (periodic table); Space (punctuation); Euler's formula; Lie group; Euler equations; Mathematical analysis; Mathematical physics; Algebra over a field; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00008116994,0.00009555755,0.0001285339,0.00003402647,0.00005972042,0.00002771215,0.00005184616,0.00001778841,0.0001406006],"category_scores_gemma":[0.00004022062,0.00008162121,0.00002530507,0.00008550536,0.00003705272,0.00009069957,0.00001270685,0.00007765074,0.0000299311],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000007098629,"about_ca_system_score_gemma":0.00001295144,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003372089,"about_ca_topic_score_gemma":0.000008265626,"domain_scores_codex":[0.9994905,0.00001944077,0.0001472812,0.0001175619,0.00008039321,0.0001448303],"domain_scores_gemma":[0.9994731,0.0002757411,0.00005340337,0.0001475398,0.00001434527,0.00003585562],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000001248616,0.0002229068,0.00305447,0.00002755012,0.00001067516,0.000001986983,0.0006144188,0.0006985028,0.00005574774,0.9887326,0.00001940962,0.006560453],"study_design_scores_gemma":[0.0007288257,0.0000994133,0.0002978424,0.000165425,0.00002954002,0.000004530482,0.002767888,0.01024212,0.002497365,0.9318653,0.05084608,0.0004556892],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7234123,0.001333025,0.03858535,0.0001232183,0.0003028634,0.0003508254,0.00005000491,0.0000357343,0.2358067],"genre_scores_gemma":[0.9756179,0.00006569505,0.02333701,0.0000227723,0.0000633243,0.00001274373,0.000004706874,0.00001413258,0.000861705],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2522056,"threshold_uncertainty_score":0.3328416,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0116303770387201,"score_gpt":0.2818477186743629,"score_spread":0.2702173416356428,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}