{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006156078,0.002994782,0.002157097,0.008260899,0.003796812,0.006696729,0.004979937,0.002426404,0.01213109],"category_scores_gemma":[0.03921099,0.0009320812,0.001911084,0.004740628,0.008776196,0.01187213,0.004547962,0.007531564,0.005217037],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004561077,"about_ca_system_score_gemma":0.001580748,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008153139,"about_ca_topic_score_gemma":0.0006741562,"domain_scores_codex":[0.9962218,0.0009868041,0.0001833328,0.0007580947,0.001102242,0.0007477286],"domain_scores_gemma":[0.9654123,0.02539306,0.001590446,0.002347608,0.003240387,0.00201628],"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":[0.0001993011,0.00008323984,0.001253588,0.0002056654,0.00002927114,0.0001131297,0.0002546733,0.008288737,0.002976979,0.9608216,0.004949296,0.02082444],"study_design_scores_gemma":[0.000015523,0.0000614631,0.0009623694,0.0002074833,0.00005489221,0.0003172787,0.0001015883,0.07566237,0.004488346,0.9086727,0.009369396,0.00008670572],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1273131,0.01122581,0.6398056,0.007670413,0.001047477,0.0001422212,0.0009773427,0.0012041,0.210614],"genre_scores_gemma":[0.7760555,0.008831523,0.1689567,0.001494807,0.003170633,0.001170896,0.001646858,0.001047347,0.0376257],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01213109,"threshold_uncertainty_score":0.04058254,"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."}}