{"id":"W4399452446","doi":"10.2298/pim2429045d","title":"Arithmetic functions at factorial arguments","year":2024,"lang":"en","type":"article","venue":"Publications de l Institut Mathematique","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto; Université Laval","funders":"","keywords":"Arithmetic function; Mathematics; Combinatorics; Order (exchange); Asymptotic formula; Factorial; Variety (cybernetics); Value (mathematics); Arithmetic; Arithmetic progression; Discrete mathematics; Statistics; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0008614152,0.0002871577,0.0003084014,0.0004136996,0.0005045961,0.0002737389,0.0004332211,0.0002143889,0.002341922],"category_scores_gemma":[0.00144885,0.0002642426,0.0002100197,0.0005869445,0.0001778718,0.0005674789,0.000126075,0.0003616092,0.00212883],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006956984,"about_ca_system_score_gemma":0.0003137383,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004991205,"about_ca_topic_score_gemma":0.00003854921,"domain_scores_codex":[0.9981364,0.000112477,0.0005843075,0.0004129086,0.0003447322,0.0004091803],"domain_scores_gemma":[0.9977677,0.0009195835,0.0001327861,0.0008218833,0.0001405809,0.0002174113],"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":[0.000004626653,0.0002708707,0.00001919921,0.0004607711,0.0001022775,0.000008851825,0.0025953,0.000004726233,0.0004576342,0.9355618,0.05999098,0.000522992],"study_design_scores_gemma":[0.0001313396,0.0000170195,0.00001046876,0.0001238872,0.00008652022,0.0002114535,0.0000723115,0.001031385,0.0004392856,0.5786412,0.4190115,0.0002236244],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05907493,0.0003363639,0.5865738,0.002912353,0.002093797,0.001212883,0.0001546902,0.002712982,0.3449282],"genre_scores_gemma":[0.7070829,0.00006284721,0.08948109,0.0002393645,0.001151409,0.001777932,0.0001525557,0.0002149217,0.199837],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6480079,"threshold_uncertainty_score":0.999981,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0570123056415484,"score_gpt":0.3187504740968033,"score_spread":0.2617381684552549,"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."}}