{"id":"W4313408358","doi":"10.3390/math10244827","title":"Rolling Geodesics, Mechanical Systems and Elastic Curves","year":2022,"lang":"en","type":"article","venue":"Mathematics","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Geodesic; Affine transformation; Class (philosophy); Differentiable function; Quadratic equation; Mechanical system; Mathematics; Affine connection; Maximum principle; Pure mathematics; Optimal control; Mathematical analysis; Applied mathematics; Computer science; Mathematical optimization; Geometry; Artificial intelligence","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002962441,0.000104802,0.0002303052,0.00002104433,0.0001913463,0.00004472322,0.0001099056,0.00001351095,0.0001887527],"category_scores_gemma":[0.000008498032,0.00009131702,0.00004867899,0.00007459544,0.00001659863,0.00003178744,0.0001297663,0.0001400771,0.00001646977],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001733133,"about_ca_system_score_gemma":0.00001367059,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007439758,"about_ca_topic_score_gemma":5.538955e-7,"domain_scores_codex":[0.9991539,0.00004762142,0.0002630884,0.0001447298,0.0002165239,0.0001741777],"domain_scores_gemma":[0.9995055,0.0001471904,0.0001028723,0.0001587299,0.00001713097,0.0000686264],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00000379136,0.0002575566,0.001043976,0.0006861436,0.00008212236,0.000003812511,0.0003735432,0.002223213,0.0003153451,0.9932157,0.001291915,0.0005029289],"study_design_scores_gemma":[0.0004369178,0.0001004945,0.00004013342,0.0002692669,0.0000812139,0.00001968371,0.00250721,0.9178108,0.00003192823,0.07474618,0.003610513,0.0003456752],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6332282,0.001896084,0.3532283,0.0003782061,0.001034845,0.001012921,0.000182911,0.0001615129,0.008877046],"genre_scores_gemma":[0.9988151,0.000004674488,0.0004725505,0.00002479699,0.0001100359,0.00007486353,0.00001412678,0.00001821815,0.000465668],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9184695,"threshold_uncertainty_score":0.37238,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01361614027428126,"score_gpt":0.2255500598637626,"score_spread":0.2119339195894814,"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."}}