{"id":"W4210661217","doi":"10.1007/s00440-022-01108-1","title":"Maximizing expected powers of the angle between pairs of points in projective space","year":2022,"lang":"en","type":"article","venue":"Probability Theory and Related Fields","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Mathematics; Combinatorics; Conjecture; Exponent; Euclidean space; Uniqueness; Space (punctuation); Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001853784,0.00008013818,0.000218745,0.00005459752,0.00006951945,0.000003667937,0.0001214057,0.0001027661,0.0004430148],"category_scores_gemma":[0.001406411,0.00005292532,0.00007325913,0.000314136,0.0001333307,0.0000491731,0.0001137268,0.0003734943,3.497592e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003605656,"about_ca_system_score_gemma":0.00002855054,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001310541,"about_ca_topic_score_gemma":0.000005811654,"domain_scores_codex":[0.9984705,0.0007232761,0.0004111455,0.0001408878,0.0001617689,0.00009241795],"domain_scores_gemma":[0.99867,0.0008400042,0.0002015769,0.0002206426,0.00004969559,0.00001808765],"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":[0.00008970208,0.0002431244,0.002768428,0.000232859,0.00003369075,2.355186e-7,0.01761119,0.000007535584,0.0001441261,0.978486,0.00002987491,0.0003532354],"study_design_scores_gemma":[0.0002914536,0.00009663814,0.001195209,0.00005978221,0.00002176807,0.00000235022,0.003826713,0.000317958,0.003454042,0.9906645,0.00001030933,0.00005924014],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9873393,0.00002811435,0.00163858,0.0006813552,0.00004368846,0.0006790006,0.00001041207,0.0000214213,0.009558173],"genre_scores_gemma":[0.9976155,0.000001633301,0.002071073,0.00001494386,0.000002611938,0.00002910558,0.000002427412,0.000005940004,0.0002567566],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01378447,"threshold_uncertainty_score":0.4850702,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02772788550128599,"score_gpt":0.2697134295629081,"score_spread":0.2419855440616221,"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."}}