{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002518631,0.0003539754,0.0002954705,0.0008720472,0.0007852868,0.001110028,0.000382943,0.0008106526,0.002470281],"category_scores_gemma":[0.0006578658,0.0001647547,0.0002129076,0.0006351634,0.002797131,0.001855857,0.0008858298,0.0007874877,0.0001993336],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007144483,"about_ca_system_score_gemma":0.0002720724,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00136952,"about_ca_topic_score_gemma":0.00096878,"domain_scores_codex":[0.9997922,0.00005548338,0.000007940365,0.000046477,0.00006949611,0.00002845716],"domain_scores_gemma":[0.999824,0.00004796128,0.00004664357,0.0000241818,0.00002508359,0.00003229175],"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":[0.00000828337,0.000007892914,0.0002472395,0.00002191546,0.0000037633,0.0000498692,0.0001017207,0.006597448,0.001547848,0.9856266,0.0004988668,0.005288569],"study_design_scores_gemma":[0.00000432421,0.00001572531,0.0008770417,0.000008069479,0.000001459068,0.0001017655,0.0001040407,0.01658899,0.000363318,0.9761004,0.005827243,0.000007540471],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6356087,0.008767028,0.2079931,0.004076368,0.0001639383,0.00005354009,0.0002021451,0.0002157558,0.1429194],"genre_scores_gemma":[0.9744157,0.001250946,0.01499266,0.0001096445,0.00011772,0.00002104012,0.0001062034,0.00003274221,0.008953417],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002470281,"threshold_uncertainty_score":0.008263946,"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."}}