{"id":"W2964119244","doi":"10.1134/s0081543816010053","title":"On the size of the genus of a division algebra","year":2016,"lang":"en","type":"article","venue":"Proceedings of the Steklov Institute of Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Division (mathematics); Division algebra; Mathematics; Genus; Degree (music); Prime (order theory); Division ring; Brauer group; Field (mathematics); Combinatorics; Pure mathematics; Set (abstract data type); Finite field; Algebra over a field; Discrete mathematics; Arithmetic; Algebra representation; Physics; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002595498,0.0005808622,0.001304532,0.004051405,0.00171773,0.004390101,0.001609592,0.001210699,0.001752905],"category_scores_gemma":[0.01525432,0.0007927835,0.0007357229,0.001492595,0.008079923,0.006483833,0.003341333,0.001778937,0.0001992238],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001525892,"about_ca_system_score_gemma":0.0004309338,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007236241,"about_ca_topic_score_gemma":0.0004041754,"domain_scores_codex":[0.9984354,0.0004418761,0.00007931439,0.0003920942,0.0003172579,0.0003340506],"domain_scores_gemma":[0.9798217,0.01585312,0.001405727,0.001057983,0.0004757738,0.001385805],"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":[0.0008574453,0.0001055577,0.02516441,0.0003425736,0.0001408621,0.0006834136,0.001860631,0.021492,0.01026398,0.9122469,0.002144165,0.02469801],"study_design_scores_gemma":[0.000047419,0.0001085429,0.01019167,0.0001796603,0.0001162502,0.0009766227,0.0005496553,0.06746469,0.00578485,0.9119349,0.002546954,0.00009883977],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9557132,0.002097628,0.02400475,0.001610597,0.0001127767,0.00002002011,0.0002869474,0.0001651316,0.01598906],"genre_scores_gemma":[0.9958027,0.0005141252,0.002685045,0.0000495774,0.0001590085,0.0000210753,0.0001195979,0.00003509103,0.0006137885],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004390101,"threshold_uncertainty_score":0.01372647,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02425726956708338,"score_gpt":0.2487971700399396,"score_spread":0.2245399004728563,"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."}}