{"id":"W1971713457","doi":"10.1007/s10711-004-3734-7","title":"The Length of a Shortest Closed Geodesic on a Two-Dimensional Sphere and Coverings by Metric Balls","year":2005,"lang":"en","type":"article","venue":"Geometriae Dedicata","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Geodesic; Ball (mathematics); Combinatorics; Mathematics; Bounded function; RADIUS; Hyperbolic geometry; Differential geometry; Metric (unit); Mathematical analysis; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005772318,0.0007315323,0.00067409,0.003409817,0.001071827,0.00234005,0.0009607488,0.001312846,0.002050783],"category_scores_gemma":[0.004677347,0.0004984458,0.0005646987,0.001959423,0.002153964,0.003319907,0.001454906,0.0008138892,0.0002600057],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001139475,"about_ca_system_score_gemma":0.0003483815,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001815188,"about_ca_topic_score_gemma":0.0009959731,"domain_scores_codex":[0.9996131,0.00008660446,0.00003495291,0.00007776326,0.0001268052,0.00006088314],"domain_scores_gemma":[0.9976374,0.0008443691,0.0005908486,0.0001361689,0.0002730448,0.0005181509],"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":[0.0004776923,0.00006243097,0.009096375,0.0002782854,0.00009631745,0.0007037511,0.001708364,0.03531064,0.02021426,0.9102385,0.001926568,0.01988682],"study_design_scores_gemma":[0.00004452998,0.0002112531,0.01331142,0.00006796931,0.00005617217,0.001010381,0.000854205,0.1258364,0.004686024,0.8462437,0.007551336,0.0001265669],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9712436,0.001390004,0.01764503,0.0004035386,0.00008144629,0.00001102111,0.0001905293,0.00004554406,0.008989372],"genre_scores_gemma":[0.9866613,0.0009848144,0.007661378,0.00004234024,0.0001675443,0.00002256245,0.0003142059,0.00004859376,0.004097277],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003409817,"threshold_uncertainty_score":0.008267522,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01924072249659508,"score_gpt":0.2893313198383622,"score_spread":0.2700905973417672,"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."}}