{"id":"W4378378023","doi":"10.4153/s0008439523000425","title":"From the Ideal Theorem to the class number","year":2023,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Ideal (ethics); Class (philosophy); Constant (computer programming); Upper and lower bounds; Combinatorics; Ideal class group; Discrete mathematics; Pure mathematics; Mathematical analysis; Algebraic number field; Law","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003280846,0.000726954,0.001008002,0.00303601,0.001865345,0.00292836,0.002442589,0.0009358053,0.01742969],"category_scores_gemma":[0.01525396,0.0003340253,0.000639547,0.00108911,0.006384275,0.008262454,0.004288863,0.006024315,0.002496273],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003435941,"about_ca_system_score_gemma":0.001106458,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002552879,"about_ca_topic_score_gemma":0.001765638,"domain_scores_codex":[0.9977603,0.0004856714,0.00006305854,0.0004179435,0.0008860888,0.0003869171],"domain_scores_gemma":[0.992559,0.004583245,0.0003585671,0.0008055882,0.0009824533,0.0007112509],"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":[0.00001818523,0.000007267361,0.0001093662,0.00004303571,0.000003124008,0.00001994841,0.00003869033,0.0009213026,0.0003082367,0.9897285,0.003301922,0.005500421],"study_design_scores_gemma":[0.00000938807,0.00001097465,0.0002288265,0.00004081731,0.000006696598,0.00006531252,0.00003035664,0.01184369,0.0008511188,0.9737332,0.01316539,0.00001420349],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06322989,0.009653987,0.4626063,0.0181472,0.004039112,0.00005631896,0.0004596544,0.001017887,0.4407897],"genre_scores_gemma":[0.8945059,0.004635902,0.04528347,0.002176549,0.005741118,0.0001069846,0.0002867782,0.0007414167,0.04652193],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01742969,"threshold_uncertainty_score":0.05830806,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04826690352330532,"score_gpt":0.3249942816114428,"score_spread":0.2767273780881375,"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."}}