{"id":"W2550265542","doi":"10.1007/s00365-017-9412-4","title":"The Stolarsky Principle and Energy Optimization on the Sphere","year":2018,"lang":"en","type":"article","venue":"Constructive Approximation","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":27,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Geodesic; Mathematics; Euclidean geometry; Point (geometry); Pairwise comparison; Finite set; Discrete geometry; Set (abstract data type); Energy (signal processing); Euclidean distance; Combinatorics; Mathematical analysis; Pure mathematics; Geometry; Computer science","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":[0.0005606267,0.0001600124,0.0001362592,0.00003528476,0.0007304783,0.0001782053,0.0001596419,0.00007948998,0.000256605],"category_scores_gemma":[0.001237863,0.00008362091,0.00004093179,0.0001974999,0.0005378154,0.0001971392,0.0000506403,0.0001249089,0.0000246394],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005203883,"about_ca_system_score_gemma":0.00003267961,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003047146,"about_ca_topic_score_gemma":0.00001480596,"domain_scores_codex":[0.9988167,0.0001812442,0.0003277025,0.0002179996,0.0002870328,0.000169302],"domain_scores_gemma":[0.9981478,0.0009149911,0.0002397216,0.0003440868,0.0003085509,0.00004477761],"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":[0.00002318841,0.00002599316,0.00001214207,0.00001308747,0.00001816366,7.407389e-8,0.0003600716,0.000004008341,0.00007626238,0.9850623,0.0006249381,0.01377974],"study_design_scores_gemma":[0.0002485345,0.0001003829,0.00006218545,0.0000501561,0.00002174932,0.00001458445,0.00103347,0.2323181,0.005184641,0.7566723,0.004151489,0.0001424399],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09098142,0.00002955293,0.8292493,0.002261678,0.0002189199,0.0006043225,0.000006888721,0.000143956,0.07650395],"genre_scores_gemma":[0.8334695,0.00004441777,0.162559,0.0006990792,0.0003961925,0.0003575342,0.00002245018,0.00005784611,0.002393923],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.7424881,"threshold_uncertainty_score":0.5618322,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03215655093242278,"score_gpt":0.2896524401664572,"score_spread":0.2574958892340344,"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."}}