{"id":"W2165720266","doi":"10.1016/j.jalgebra.2009.11.023","title":"Towers of complements to valuation rings and truncation closed embeddings of valued fields","year":2009,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Mathematics; Residue field; Algebraically closed field; Pure mathematics; Embedding; Discrete valuation ring; Valuation (finance); Linear subspace; Truncation (statistics); Field (mathematics); Discrete mathematics; Combinatorics","routes":{"ca_aff":true,"ca_fund":false,"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":[],"consensus_categories":[],"category_scores_codex":[0.0008029559,0.0001035199,0.0003463468,0.0002041438,0.00003344938,0.00001707647,0.0001464005,0.00005605596,0.00005021946],"category_scores_gemma":[0.0004042239,0.00009100729,0.00009619968,0.0001363281,0.00002439122,0.0001989949,0.00002132083,0.0001094335,0.000001048899],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003380917,"about_ca_system_score_gemma":0.00004089314,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007530531,"about_ca_topic_score_gemma":0.000001753006,"domain_scores_codex":[0.9985511,0.00004262755,0.0007513153,0.00009528699,0.0004358987,0.0001237603],"domain_scores_gemma":[0.9985515,0.0001146739,0.0007966239,0.000137612,0.0003192193,0.00008031259],"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":[0.001684908,0.002518801,0.02055595,0.001223055,0.001013672,0.00002444642,0.06071489,0.0003622694,0.2340901,0.4366724,0.02665488,0.2144846],"study_design_scores_gemma":[0.003604393,0.002631843,0.1319619,0.0007286391,0.0003177614,0.00004363461,0.001264072,0.0006952588,0.1134442,0.7445248,0.0004526402,0.0003309053],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9901929,0.00006292082,0.00849176,0.0006135815,0.0001077712,0.0001522821,0.000001950971,0.000006276762,0.0003705437],"genre_scores_gemma":[0.9789761,0.00002581892,0.02068763,0.0001641562,0.00008367606,5.957223e-7,0.00000102864,0.000008377711,0.00005259249],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3078524,"threshold_uncertainty_score":0.371117,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04860923672729769,"score_gpt":0.3321262438214173,"score_spread":0.2835170070941196,"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."}}