{"id":"W3197583273","doi":"10.1090/tran/8653","title":"Curvature-free linear length bounds on geodesics in closed Riemannian surfaces","year":2022,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Mathematics and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Geodesic; Sectional curvature; Curvature; Scalar curvature; Mathematical analysis; Negative curvature; Geometry","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":[0.000832524,0.0002477715,0.0005767239,0.00005021862,0.0005237288,0.00002141426,0.00104716,0.000051101,0.0004105656],"category_scores_gemma":[0.0001574365,0.0001900296,0.0005681393,0.001038171,0.0005068151,0.0000518202,0.0001028261,0.000738229,0.000009913197],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001536639,"about_ca_system_score_gemma":0.00008159914,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005548603,"about_ca_topic_score_gemma":0.00001921088,"domain_scores_codex":[0.9977998,0.0001705172,0.0006595256,0.0002972095,0.000721649,0.0003513337],"domain_scores_gemma":[0.9969396,0.001153982,0.0004521216,0.001320052,0.00005381399,0.00008040516],"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":[0.000357603,0.0232459,0.0006374252,0.002984105,0.001751733,0.000006802933,0.04347493,0.02576009,0.006580673,0.7794248,0.1088652,0.006910688],"study_design_scores_gemma":[0.001354179,0.0004104028,0.0005547914,0.000139983,0.0003200576,0.00002071805,0.007259725,0.05805956,0.001618086,0.92159,0.008009112,0.0006633511],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8709579,0.00003913909,0.1127719,0.008209496,0.0001660671,0.001663074,0.0003882986,0.0002280078,0.005576127],"genre_scores_gemma":[0.900802,0.0000218558,0.09692062,0.0003681971,0.00002683226,0.0002971879,0.000003297121,0.00006465714,0.001495358],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1421652,"threshold_uncertainty_score":0.7749184,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03119079191546963,"score_gpt":0.3047747489883195,"score_spread":0.2735839570728499,"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."}}