{"id":"W2887237514","doi":"10.1007/s00013-019-01299-5","title":"Hermite’s theorem via Galois cohomology","year":2019,"lang":"en","type":"preprint","venue":"Archiv der Mathematik","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Galois cohomology; Generic polynomial; Cohomology; Hermite polynomials; Pure mathematics; Extension (predicate logic); Fundamental theorem of Galois theory; Galois module; Galois extension; Galois group; Discrete mathematics; Degree (music); Element (criminal law); Polynomial; Field (mathematics); Algebra over a field; Mathematical analysis; Physics; Computer science","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":[0.001478031,0.0008745517,0.001479258,0.0003593896,0.0001576994,0.00009129234,0.001430496,0.0006678505,0.002676474],"category_scores_gemma":[0.0006066175,0.0007652193,0.0006369164,0.000188849,0.0003573868,0.00009661614,0.002041099,0.001644125,0.002958645],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000911619,"about_ca_system_score_gemma":0.0001767277,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001991142,"about_ca_topic_score_gemma":0.000007496204,"domain_scores_codex":[0.9958515,0.0005687459,0.001042863,0.001083181,0.0005932859,0.0008603958],"domain_scores_gemma":[0.9932726,0.002994274,0.0007661335,0.00263951,0.0001108426,0.0002166255],"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":[0.0001030533,0.0006681738,0.0003487153,0.004116505,0.001070598,0.000111444,0.008276325,0.00004211519,0.0002561053,0.9678173,0.01342497,0.003764708],"study_design_scores_gemma":[0.0004893498,0.00005453256,0.0002160556,0.0004587033,0.0002820795,0.0003355985,0.0002308974,0.0005157536,0.001202196,0.9944258,0.0009685277,0.0008204683],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4999724,0.0007393369,0.1894343,0.0008428594,0.002411735,0.002765503,0.0001479881,0.001053616,0.3026322],"genre_scores_gemma":[0.9532864,0.00005689623,0.03085716,0.0005370172,0.0004789129,0.0001942059,0.0001246435,0.0002870141,0.01417771],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.453314,"threshold_uncertainty_score":0.9994799,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03300249616697188,"score_gpt":0.2953566632361272,"score_spread":0.2623541670691553,"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."}}