{"id":"W1965527979","doi":"10.4153/cmb-2002-012-1","title":"The Distribution of Totatives","year":2002,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Coprime integers; Conjecture; Integer (computer science); Distribution (mathematics); Combinatorics; Discrete mathematics; Pure mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001824746,0.0003191677,0.000740417,0.003342378,0.00150217,0.003264658,0.0007894724,0.0005838436,0.005897199],"category_scores_gemma":[0.0128665,0.0003326617,0.0002759563,0.001200092,0.005213575,0.004099939,0.00153397,0.001533159,0.000715897],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002208048,"about_ca_system_score_gemma":0.0006547546,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00142338,"about_ca_topic_score_gemma":0.0006997688,"domain_scores_codex":[0.9989958,0.0002381616,0.00004316933,0.000219988,0.0003191382,0.0001837163],"domain_scores_gemma":[0.9943687,0.002664632,0.0006384679,0.0005109882,0.001098073,0.0007191431],"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":[0.00005997942,0.000009767821,0.001035077,0.0000258309,0.00000560514,0.00007269189,0.0001981488,0.001530521,0.001091925,0.9894483,0.001496909,0.005025187],"study_design_scores_gemma":[0.00001805149,0.00003429552,0.001395594,0.000037679,0.000005632897,0.0002019117,0.0001551949,0.007073879,0.001206072,0.9831517,0.00669493,0.00002503623],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8444223,0.003300535,0.06525915,0.004081831,0.0004199502,0.00003734956,0.0008246759,0.0002705441,0.08138364],"genre_scores_gemma":[0.9885217,0.0008527738,0.002270973,0.0001812401,0.0003461353,0.00002660478,0.0002095944,0.0000594364,0.007531512],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005897199,"threshold_uncertainty_score":0.01972806,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05101437734579777,"score_gpt":0.2984812977922299,"score_spread":0.2474669204464321,"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."}}