{"id":"W2052105293","doi":"10.1007/s00209-013-1194-1","title":"The relative approximation degree in valued function fields","year":2013,"lang":"de","type":"article","venue":"Mathematische Zeitschrift","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Saskatchewan","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Uniformization (probability theory); Modulo; Degree (music); Rationality; Field (mathematics); Function (biology); Pure mathematics; Function field; Discrete mathematics; Epistemology","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":[0.00288234,0.0007411393,0.001301132,0.004554243,0.001693374,0.005188216,0.001616183,0.001444366,0.006048723],"category_scores_gemma":[0.007881299,0.000722457,0.0007761402,0.002997991,0.006525108,0.01596875,0.00339061,0.003768674,0.000610831],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001833295,"about_ca_system_score_gemma":0.0004346605,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006263055,"about_ca_topic_score_gemma":0.0004025555,"domain_scores_codex":[0.9985542,0.0004642226,0.00008183325,0.0003191511,0.000363535,0.0002171524],"domain_scores_gemma":[0.9941205,0.003523401,0.0005829853,0.0004499736,0.0004405824,0.0008824616],"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":[0.00004285536,0.00001000165,0.0002877786,0.00002365412,0.000006513636,0.00003094532,0.0002806277,0.0006009663,0.0005632455,0.9956878,0.0001870737,0.002278525],"study_design_scores_gemma":[0.00001446586,0.00002627931,0.0006003877,0.00001789781,0.00001511222,0.0001567426,0.000144683,0.004661572,0.0006973924,0.9919394,0.001709264,0.00001677414],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.758111,0.00260515,0.1672725,0.004610173,0.0004174183,0.00003470288,0.0003441008,0.0002378601,0.06636714],"genre_scores_gemma":[0.9838732,0.001071821,0.007277811,0.0001316705,0.000338054,0.00002220511,0.0001212614,0.00006166598,0.007102363],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006048723,"threshold_uncertainty_score":0.02023494,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03419317995262328,"score_gpt":0.2772806007072403,"score_spread":0.243087420754617,"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."}}