{"id":"W4206897161","doi":"10.1090/mbk/139/21","title":"The multiplicative structure of integers","year":2021,"lang":"en","type":"book-chapter","venue":"American Mathematical Society eBooks","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"","keywords":"Multiplicative function; Mathematics; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003533877,0.0005987376,0.0004175609,0.001400754,0.00150177,0.00402935,0.000485148,0.0005663316,0.01499979],"category_scores_gemma":[0.001414184,0.0003326125,0.0001929258,0.001556919,0.002988495,0.00420235,0.001039619,0.002555974,0.004793331],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002007915,"about_ca_system_score_gemma":0.0007313159,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001433233,"about_ca_topic_score_gemma":0.001618674,"domain_scores_codex":[0.9997395,0.00007503221,0.000008946894,0.0000378508,0.0001144281,0.00002430469],"domain_scores_gemma":[0.9997181,0.0001404833,0.00001745646,0.00004182965,0.00005984009,0.00002228231],"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":[0.000002859654,0.000003107194,0.00001747861,0.00001621714,7.148277e-7,0.000005770191,0.0001436536,0.0000471255,0.00009558303,0.9726629,0.01787202,0.009132417],"study_design_scores_gemma":[0.000002834162,0.00000537533,0.0001169073,0.00003159585,0.00000220218,0.00005657787,0.00007633115,0.0001754215,0.00009219209,0.6603242,0.339113,0.000003506441],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.002342908,0.01655606,0.005764865,0.003368578,0.001192964,0.00001111389,0.00008372377,0.00009834805,0.9705814],"genre_scores_gemma":[0.1608208,0.0245278,0.009150473,0.00232435,0.004499944,0.00009670459,0.0002362711,0.0001969491,0.7981468],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01499979,"threshold_uncertainty_score":0.05017924,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03487546126465951,"score_gpt":0.3251930031614893,"score_spread":0.2903175418968298,"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."}}