{"id":"W2283169748","doi":"10.4064/cm7048-9-2016","title":"Bertrand’s postulate for number fields","year":2016,"lang":"en","type":"preprint","venue":"Colloquium Mathematicum","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada; Queen's University","keywords":"Algebraic number field; Mathematics; Ideal (ethics); Combinatorics; Algebraic number; Generalization; Prime number theorem; Prime (order theory); Field (mathematics); Prime number; Discrete mathematics; Number theory; Norm (philosophy); Interval (graph theory); Upper and lower bounds; Pure mathematics; 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":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.00205234,0.0007720517,0.001506721,0.0001813362,0.0002323595,0.0002195992,0.001352278,0.0009296373,0.003158577],"category_scores_gemma":[0.002088612,0.0005822383,0.0008907492,0.0001686752,0.000232943,0.0001172922,0.001241705,0.0007285907,0.001133871],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002534282,"about_ca_system_score_gemma":0.000390836,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008663827,"about_ca_topic_score_gemma":0.00001880138,"domain_scores_codex":[0.995703,0.0002022674,0.001210865,0.000963307,0.0008622287,0.00105829],"domain_scores_gemma":[0.9927559,0.003639502,0.0006146575,0.002112108,0.0005584029,0.0003193752],"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":[0.0003722408,0.0006867871,0.0001455837,0.01042557,0.001363076,0.00005142847,0.002066713,0.000003909545,0.0003552282,0.6457085,0.3382759,0.0005450014],"study_design_scores_gemma":[0.001268167,0.00005944975,0.000006931703,0.00127046,0.0003915929,0.00004469853,0.0001216038,0.0009178943,0.001198044,0.9897659,0.004202982,0.000752323],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09688143,0.0002429216,0.6096067,0.009124318,0.003392554,0.01241153,0.001101109,0.001284412,0.265955],"genre_scores_gemma":[0.5829485,0.00007186401,0.08322635,0.0004371852,0.002080338,0.003925525,0.0001082874,0.0007889275,0.326413],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5263804,"threshold_uncertainty_score":0.9996629,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07858747563899673,"score_gpt":0.38773246865133,"score_spread":0.3091449930123332,"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."}}