{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001254529,0.0003912581,0.0003844789,0.00110345,0.001055976,0.001801393,0.0003950845,0.0003199955,0.002421467],"category_scores_gemma":[0.002798768,0.0002560196,0.0005053621,0.0005215245,0.002711473,0.003191289,0.001170273,0.001182908,0.0002024259],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006762195,"about_ca_system_score_gemma":0.0005165784,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006248135,"about_ca_topic_score_gemma":0.000429489,"domain_scores_codex":[0.9989371,0.000272609,0.000062329,0.0001668822,0.0003656796,0.0001954198],"domain_scores_gemma":[0.9982074,0.0006694974,0.0002768694,0.0001589982,0.000390259,0.0002968271],"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":[0.00003683326,0.00001833368,0.0007424501,0.00002984564,0.00001284068,0.0001526937,0.0003286136,0.001439001,0.003920557,0.9899307,0.0001771134,0.00321104],"study_design_scores_gemma":[0.00002858932,0.00013419,0.002080992,0.00001434913,0.00002176683,0.0005839377,0.0003082627,0.0196593,0.008653198,0.964817,0.003653202,0.00004527999],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8642043,0.0005832786,0.1059769,0.0004054298,0.00005827457,0.00002633159,0.0001092856,0.00007720354,0.02855888],"genre_scores_gemma":[0.9942998,0.00010769,0.003322586,0.00002221305,0.00004967316,0.000009043118,0.00004655582,0.000009604066,0.002132899],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002421467,"threshold_uncertainty_score":0.008100629,"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."}}