{"id":"W4324279136","doi":"10.1017/fms.2023.7","title":"Albert algebras over and other rings","year":2023,"lang":"en","type":"article","venue":"Forum of Mathematics Sigma","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Generality; Affine transformation; Ring (chemistry); Context (archaeology); Mathematics; Commutative property; Simple (philosophy); Pure mathematics; Field (mathematics); Base (topology); Commutative ring; Type (biology); Algebra over a field; Commutative algebra; Mathematical analysis; Philosophy","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":[0.00115167,0.0002844995,0.0003944673,0.001307311,0.00146086,0.002841213,0.0004686865,0.0004921877,0.006111232],"category_scores_gemma":[0.0014188,0.0001864934,0.0004289837,0.0009753491,0.002413739,0.004499294,0.001305774,0.0007302141,0.0006538364],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009724318,"about_ca_system_score_gemma":0.0007994251,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008429808,"about_ca_topic_score_gemma":0.000701955,"domain_scores_codex":[0.9993338,0.0001954627,0.00004043966,0.00009032102,0.0002257717,0.0001142318],"domain_scores_gemma":[0.9990995,0.0002175472,0.0001946084,0.00008805625,0.0001760615,0.000224274],"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":[0.00001103911,0.000010234,0.0001465013,0.00001360406,0.000002482757,0.00004101114,0.0001422233,0.0002276206,0.0003675069,0.997566,0.0003265516,0.001145226],"study_design_scores_gemma":[0.00001253129,0.00002108424,0.000363198,0.0000137765,0.000006178105,0.0001695203,0.000207851,0.00197494,0.0006178583,0.9833004,0.01330132,0.00001122384],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5805902,0.004764284,0.05315478,0.00291613,0.0005718274,0.00006940051,0.0003029033,0.0002700895,0.3573604],"genre_scores_gemma":[0.963632,0.001074759,0.006694275,0.0002806128,0.0005200241,0.00003016644,0.0001150712,0.0000257828,0.02762723],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006111232,"threshold_uncertainty_score":0.0204441,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.037205865578959,"score_gpt":0.3181625061205572,"score_spread":0.2809566405415982,"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."}}