{"id":"W3201541924","doi":"10.4153/s0008439521000825","title":"On nonmonogenic number fields defined by","year":2021,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Trinomial; Mathematics; Algebraic number; Algebraic number field; Prime (order theory); Integer (computer science); Combinatorics; Class number; Prime number; Field (mathematics); Class (philosophy); Finite field; Root (linguistics); Discrete mathematics; Pure mathematics; Quadratic equation; Mathematical analysis; Geometry","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":[0.001192137,0.0003564485,0.0004456114,0.001607702,0.001533369,0.00159339,0.0004259364,0.0004096063,0.003661892],"category_scores_gemma":[0.002377528,0.0001867174,0.0003084913,0.0008071339,0.002659352,0.002169268,0.001718885,0.001059685,0.0004036704],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002008763,"about_ca_system_score_gemma":0.0007280303,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007591965,"about_ca_topic_score_gemma":0.0008937091,"domain_scores_codex":[0.9990512,0.0001915932,0.0000649407,0.00018478,0.0002450378,0.0002625808],"domain_scores_gemma":[0.9987043,0.0003397616,0.0003260493,0.000114924,0.00018597,0.0003288987],"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":[0.00009795848,0.00003704143,0.001676116,0.00002608366,0.000003112054,0.000428639,0.0003574807,0.0006339171,0.001806536,0.9894775,0.0003826776,0.005073018],"study_design_scores_gemma":[0.00009220459,0.0001472596,0.004707315,0.00008768387,0.0000173895,0.001254076,0.000944311,0.007466147,0.0044585,0.9667329,0.01404692,0.00004528259],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.93312,0.0003906874,0.01851032,0.0005437649,0.0001002804,0.00004287914,0.0001252672,0.00007966066,0.04708711],"genre_scores_gemma":[0.9935448,0.0001266317,0.002646431,0.0000471672,0.00006534294,0.00002395941,0.0001202969,0.00001053048,0.003414768],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003661892,"threshold_uncertainty_score":0.01457471,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01598192236584116,"score_gpt":0.2486296665850976,"score_spread":0.2326477442192564,"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."}}