{"id":"W3083017445","doi":"10.5817/am2020-3-141","title":"Bounds for the counting function of the Jordan-Pólya numbers","year":2020,"lang":"en","type":"article","venue":"Archivum Mathematicum","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Integer (computer science); Combinatorics; Function (biology); Upper and lower bounds; Product (mathematics); Computer science; 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":[0.001282442,0.0001971933,0.0003481972,0.00003187667,0.0003740108,0.00006571414,0.0008329182,0.00004774347,0.0002267095],"category_scores_gemma":[0.002593094,0.000106963,0.000335957,0.0003396183,0.0003313422,0.00009352776,0.0002782932,0.0002826974,0.00006158499],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002863932,"about_ca_system_score_gemma":0.00009360023,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001333816,"about_ca_topic_score_gemma":0.00001739766,"domain_scores_codex":[0.9980448,0.0001439184,0.0005508729,0.000247659,0.0006182047,0.0003945654],"domain_scores_gemma":[0.9943941,0.004340139,0.0003413745,0.0007149945,0.0001221396,0.00008723141],"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":[0.0001315832,0.0001195747,0.000301078,0.001311416,0.0003425273,7.884703e-7,0.006389655,0.00002098434,0.001918683,0.9666175,0.02163253,0.001213708],"study_design_scores_gemma":[0.0005436633,0.00008550526,0.0001575781,0.000124878,0.0002780253,0.000009195124,0.002430321,0.01968587,0.001691907,0.9688731,0.005955462,0.0001644689],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.378122,0.0001629127,0.5248258,0.02627021,0.0007384496,0.005192825,0.00009795107,0.0003166826,0.06427322],"genre_scores_gemma":[0.9890459,0.000004840527,0.007187584,0.000563763,0.0002486912,0.000131845,0.000002513828,0.00007269347,0.002742152],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6109239,"threshold_uncertainty_score":0.4361823,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0742623804083499,"score_gpt":0.3249738946327691,"score_spread":0.2507115142244192,"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."}}