{"id":"W3027799413","doi":"10.1080/00029890.2020.1736468","title":"On Certain Probabilistic Properties of Polynomials over the Ring of <i>p</i>-adic Integers","year":2020,"lang":"en","type":"article","venue":"American Mathematical Monthly","topic":"advanced mathematical theories","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"","keywords":"Ring (chemistry); Coprime integers; Ring of integers; Monic polynomial; Gaussian integer; Eisenstein integer; Quadratic integer; Difference polynomials; Orthogonal polynomials","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":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.0005355689,0.0003629722,0.001206851,0.00006178799,0.00007168544,0.00002058894,0.0006322818,0.00006113725,0.000152181],"category_scores_gemma":[0.01387454,0.0002140112,0.0002715191,0.0004999193,0.001939612,0.000099251,0.0001958561,0.0003066718,0.00003689118],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005066412,"about_ca_system_score_gemma":0.00006028426,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001630047,"about_ca_topic_score_gemma":0.000002025166,"domain_scores_codex":[0.9972181,0.0002186816,0.00115641,0.0003555625,0.0006409897,0.0004102769],"domain_scores_gemma":[0.9942253,0.003980793,0.0007507022,0.0007346245,0.0001223961,0.0001861425],"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":[0.0002252826,0.0003496567,0.0000108865,0.001490353,0.000116266,0.000003067643,0.004598342,0.0001786478,0.006164394,0.9861879,0.0002854236,0.0003898193],"study_design_scores_gemma":[0.0003309216,0.000562421,0.00001875786,0.0006021155,0.0001257561,0.00000233294,0.002267847,0.003716726,0.02187739,0.9701995,0.00004009685,0.000256181],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9272609,0.0001225237,0.02432104,0.002555473,0.000059588,0.001990829,0.0000514515,0.0002472558,0.04339099],"genre_scores_gemma":[0.9811714,0.000003219648,0.01814057,0.0004122314,0.00004890317,0.00009212048,6.58208e-7,0.00007310729,0.00005775527],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05391058,"threshold_uncertainty_score":0.994432,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0458663386240355,"score_gpt":0.2912183905391045,"score_spread":0.245352051915069,"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."}}