{"id":"W2232628145","doi":"10.1093/imrn/rny074","title":"The Average of the Smallest Prime in a Conjugacy Class","year":2018,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; National Research Foundation of Korea; Ulsan National Institute of Science and Technology","keywords":"Conjugacy class; Mathematics; Combinatorics; Conjecture; Prime (order theory); Automorphism; Class (philosophy); Field (mathematics); Finite field; Prime number; Discrete mathematics; Pure mathematics; Computer science","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":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.00825204,0.0002983596,0.0004595015,0.0003450594,0.0002834192,0.0002949886,0.004078989,0.000311375,0.000509434],"category_scores_gemma":[0.01220024,0.0001747672,0.0002637777,0.0003809457,0.001217325,0.00008456929,0.003879258,0.001782654,0.0001052104],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002482276,"about_ca_system_score_gemma":0.0004026722,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008400601,"about_ca_topic_score_gemma":0.0002673936,"domain_scores_codex":[0.9948849,0.0007230886,0.001101082,0.0004292609,0.002336038,0.0005256076],"domain_scores_gemma":[0.9856946,0.01087869,0.0007802314,0.001460769,0.001109692,0.00007605409],"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":[0.0001384626,0.0008908845,0.001141578,0.001293475,0.0005715583,0.00001752997,0.006199362,0.0001555511,0.0001783249,0.9853146,0.003608135,0.0004905572],"study_design_scores_gemma":[0.0003272348,0.00003629977,0.0008269222,0.001371736,0.00002280748,0.000007803936,0.001061942,0.00680352,0.002469862,0.9852504,0.001632023,0.0001894941],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9034286,0.0002265286,0.0006152902,0.003517521,0.001807014,0.001503497,0.00008396382,0.00003907699,0.08877854],"genre_scores_gemma":[0.9907508,0.0001022289,0.002771508,0.00002937693,0.0003681685,0.0001395549,0.000007122471,0.00004950539,0.005781721],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08732225,"threshold_uncertainty_score":0.9961204,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1411208745817185,"score_gpt":0.4268022637388484,"score_spread":0.2856813891571298,"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."}}