{"id":"W2973097972","doi":"10.1093/qmathj/haz026","title":"COUNTING INTEGERS WITH A SMOOTH TOTIENT","year":2019,"lang":"en","type":"article","venue":"The Quarterly Journal of Mathematics","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Australian Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Euler's totient function; Mathematics; Prime (order theory); Combinatorics; Euler's formula; Discrete mathematics; 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":[0.003080033,0.0002008782,0.0005133885,0.0001358238,0.0000825068,0.0001051503,0.000730866,0.00005427019,0.0003595374],"category_scores_gemma":[0.0002304971,0.0001020443,0.0001759053,0.0002415746,0.000145144,0.0002016163,0.00003150518,0.0005365256,0.0001599933],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000121447,"about_ca_system_score_gemma":0.0001698396,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000376092,"about_ca_topic_score_gemma":0.000005172499,"domain_scores_codex":[0.9975941,0.0001479887,0.0007691428,0.0001129813,0.001027264,0.0003484753],"domain_scores_gemma":[0.9962986,0.001563165,0.0008999709,0.0005775792,0.0005553562,0.0001053664],"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":[0.000753216,0.002434945,0.002320178,0.002654416,0.002321061,0.0002781436,0.13795,0.0002099433,0.001729992,0.8187433,0.01015255,0.02045229],"study_design_scores_gemma":[0.001957585,0.002957947,0.00004761045,0.001224051,0.0003626964,0.001563399,0.07891119,0.00414573,0.000366799,0.907053,0.001026632,0.0003833974],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9627306,0.00006904468,0.03024926,0.0006348449,0.0001381383,0.0003790172,0.000001543972,0.00002379197,0.005773719],"genre_scores_gemma":[0.9824677,0.000005540913,0.01563828,0.0000566497,0.0001224891,0.000003175326,2.013281e-7,0.00005521321,0.001650802],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08830966,"threshold_uncertainty_score":0.4161247,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02959364574912909,"score_gpt":0.3045827615024386,"score_spread":0.2749891157533095,"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."}}