{"id":"W4416242263","doi":"10.48550/arxiv.2508.07447","title":"Brauer classes not split by genus one curves","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Genus; Field (mathematics); Class (philosophy); Conjecture; Simple (philosophy)","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":[0.0005802778,0.0008715268,0.0008804838,0.001895334,0.002715436,0.003741538,0.0007281548,0.001111816,0.008394886],"category_scores_gemma":[0.003089586,0.0004175086,0.0006237056,0.0009292995,0.003136732,0.008215888,0.00227001,0.002255226,0.0009782386],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001175054,"about_ca_system_score_gemma":0.0004039491,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006533982,"about_ca_topic_score_gemma":0.000777146,"domain_scores_codex":[0.9993119,0.0000522058,0.00002316203,0.0001642648,0.0001410071,0.0003074359],"domain_scores_gemma":[0.9984712,0.0005562591,0.0003021932,0.0002372351,0.0001121323,0.0003209779],"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":[0.0002558413,0.0001166026,0.006073617,0.0001193295,0.00002225743,0.0006766476,0.001115582,0.001585798,0.007858338,0.9547792,0.002408808,0.02498808],"study_design_scores_gemma":[0.00007752042,0.0001262737,0.005572917,0.0001113014,0.00005539099,0.001475373,0.001123795,0.007992649,0.009142792,0.9544875,0.01977051,0.00006405191],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.915889,0.0008357243,0.01281385,0.001053127,0.0001588703,0.00001637079,0.0001077909,0.0001845452,0.06894072],"genre_scores_gemma":[0.9904113,0.0003732041,0.002073206,0.0001150377,0.00007882206,0.00001393366,0.0001290551,0.00006380612,0.006741636],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008394886,"threshold_uncertainty_score":0.02808374,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08432577853550909,"score_gpt":0.3217841102393049,"score_spread":0.2374583317037958,"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."}}