{"id":"W4297234428","doi":"10.48550/arxiv.1111.5604","title":"Shirshov's theorem and division rings that are left algebraic over a\\n subfield","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Subring; Mathematics; Division ring; Ring (chemistry); Discrete mathematics; Algebraic number; Combinatorics; Bounded function; Division (mathematics); Pure mathematics; Arithmetic","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"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":[0.00149697,0.0002689591,0.0005911886,0.0007804132,0.001901903,0.001918885,0.0005603335,0.0005338925,0.003389194],"category_scores_gemma":[0.003815117,0.0002886062,0.0006523936,0.0009978128,0.004270245,0.005606553,0.001998722,0.001491416,0.0006283787],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001565506,"about_ca_system_score_gemma":0.001050721,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001353478,"about_ca_topic_score_gemma":0.001023128,"domain_scores_codex":[0.9991255,0.0001681376,0.00006698375,0.0002147158,0.0002002565,0.0002244091],"domain_scores_gemma":[0.9965492,0.00201761,0.0003844623,0.000466552,0.0002715124,0.0003106618],"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":[0.00009335261,0.00001628403,0.001045906,0.00005215017,0.00000738288,0.0001240811,0.0004583772,0.001178938,0.001363401,0.9821374,0.001462784,0.01205979],"study_design_scores_gemma":[0.00002823813,0.00003991857,0.0008762035,0.00002101011,0.00001117118,0.0002234186,0.0002191813,0.003774945,0.001974841,0.9837298,0.00908336,0.00001805201],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7853711,0.003471063,0.1236429,0.004523834,0.0003430671,0.00004709402,0.0004809884,0.0002768657,0.08184317],"genre_scores_gemma":[0.9685465,0.001212692,0.01718585,0.000519622,0.0003567081,0.0000476594,0.0003081173,0.00004706436,0.01177588],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003389194,"threshold_uncertainty_score":0.01135856,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06469745723471905,"score_gpt":0.1709160450110573,"score_spread":0.1062185877763383,"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."}}