{"id":"W2897059155","doi":"10.1007/s00526-023-02584-6","title":"On the existence of closed $$C^{1,1}$$ curves of constant curvature","year":2023,"lang":"en","type":"article","venue":"Calculus of Variations and Partial Differential Equations","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Constant (computer programming); Curvature; Mathematical analysis; Center of curvature; Mean curvature; Point (geometry); Geometry; Pure mathematics","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":[0.000379213,0.0001183669,0.0003591789,0.0001932321,0.0001270574,0.00001325881,0.0001595905,0.00008087393,0.0003073197],"category_scores_gemma":[0.002273469,0.00007851021,0.0001755382,0.001203342,0.0001632283,0.00005065404,0.00005328453,0.0001170557,0.000004170023],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000618893,"about_ca_system_score_gemma":0.00005848024,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004527106,"about_ca_topic_score_gemma":0.00002224705,"domain_scores_codex":[0.9986318,0.00013329,0.0005750915,0.0001517211,0.0003671583,0.0001409425],"domain_scores_gemma":[0.9968919,0.002026524,0.0004065741,0.0003393474,0.0002892468,0.00004646087],"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":[0.00001212403,0.000175498,0.00003617396,0.0001205227,0.0001501838,2.074183e-7,0.000348659,0.0000532485,0.00235686,0.9952759,0.001158008,0.0003126399],"study_design_scores_gemma":[0.002875251,0.0009120778,0.02211446,0.001860413,0.003738281,0.000002605213,0.001714332,0.7006565,0.01891515,0.2456233,0.0006754234,0.0009122139],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2267586,0.0004364307,0.7677562,0.001789688,0.0002718323,0.0006489031,0.0005116265,0.00004930386,0.001777413],"genre_scores_gemma":[0.9994451,0.0001166334,0.0001318614,0.00002541156,0.0000299239,0.00002582073,0.00005982342,0.000008261034,0.0001571504],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7726865,"threshold_uncertainty_score":0.3364936,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07276215899632729,"score_gpt":0.3139263619829898,"score_spread":0.2411642029866626,"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."}}