{"id":"W4387353088","doi":"10.1016/j.aim.2023.109322","title":"Projective freeness and Hermiteness of complex function algebras","year":2023,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Pure mathematics; Nest algebra; Holomorphic function; Commutative property; Non-associative algebra; Algebra over a field; Algebra representation","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":[0.0006391074,0.00019858,0.000462899,0.0002993273,0.00007212019,0.0000179182,0.0002219901,0.0000825091,0.00005008176],"category_scores_gemma":[0.0008586214,0.0001756224,0.00004396099,0.001092255,0.0002177646,0.0004506187,0.0001846475,0.0001827392,0.00002054239],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005209989,"about_ca_system_score_gemma":0.00003886476,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003676403,"about_ca_topic_score_gemma":0.00006126806,"domain_scores_codex":[0.9983293,0.00008079764,0.000520057,0.0002962631,0.000426234,0.0003472984],"domain_scores_gemma":[0.9979875,0.001217442,0.0001855134,0.0003926721,0.0001605051,0.00005637117],"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":[0.0001398002,0.0006584183,0.01245676,0.006238764,0.00009332518,0.00004830528,0.005724561,0.0007228284,0.006913821,0.9137262,0.0002038018,0.0530735],"study_design_scores_gemma":[0.0006677376,0.0001073156,0.004694963,0.0002508515,0.00001974964,0.00001076261,0.003248574,0.006594084,0.001743728,0.9819657,0.0004615773,0.0002349098],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.965013,0.0005739966,0.02791578,0.00008210258,0.0001522814,0.00115497,0.00002887433,0.0002568516,0.004822148],"genre_scores_gemma":[0.9229485,0.000781672,0.07531257,0.00002182033,0.00005756873,0.0002139373,0.00001418504,0.0000930295,0.0005567466],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06823962,"threshold_uncertainty_score":0.7161674,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0751853730765323,"score_gpt":0.3956485198754606,"score_spread":0.3204631467989283,"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."}}