{"id":"W4386702471","doi":"10.1134/s0081543823020098","title":"Lie Algebras and Integrable Systems: Elastic Curves and Rolling Geodesics","year":2023,"lang":"en","type":"article","venue":"Proceedings of the Steklov Institute of Mathematics","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Isospectral; Geodesic; Mathematics; Integrable system; Lie algebra; Pure mathematics; Tangent; Lie group; Affine connection; Quadratic equation; Affine transformation; Invariant (physics); Lie conformal algebra; Algebra over a field; Loop algebra; Mathematical analysis; Geometry; Mathematical physics; Current algebra","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000552664,0.0003448267,0.0003280838,0.000907053,0.0008055864,0.001221121,0.0005345843,0.0007664114,0.003267592],"category_scores_gemma":[0.001339333,0.0001250574,0.0002701755,0.0007195933,0.002860341,0.002631461,0.001202445,0.0009503876,0.0003467956],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009987464,"about_ca_system_score_gemma":0.0005380472,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001547887,"about_ca_topic_score_gemma":0.0008248169,"domain_scores_codex":[0.9996744,0.0001084081,0.0000115208,0.00004348958,0.0001195273,0.0000426026],"domain_scores_gemma":[0.9996235,0.0001021015,0.00008896551,0.0000372322,0.00006261899,0.00008552205],"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":[0.000002319518,0.000004451147,0.00006157177,0.00001116077,0.000001708459,0.00002425556,0.0001061297,0.001516474,0.0002375659,0.9961668,0.0003803737,0.001487296],"study_design_scores_gemma":[0.000001951089,0.000003874155,0.0001010783,0.000005450181,7.607465e-7,0.0000233054,0.00006565291,0.004520167,0.00005704541,0.9933075,0.001909988,0.000003128573],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5063112,0.01890352,0.222829,0.01666186,0.0005568945,0.00005866197,0.0002559236,0.0003281463,0.2340948],"genre_scores_gemma":[0.9793284,0.002707267,0.007121019,0.0003131621,0.0003665156,0.00002208103,0.0000819283,0.00002750362,0.01003218],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003267592,"threshold_uncertainty_score":0.01093119,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03913677045455675,"score_gpt":0.2678639650604078,"score_spread":0.228727194605851,"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."}}