{"id":"W2028322679","doi":"10.1093/qmath/ham056","title":"MULTIPLICATIVE STRUCTURES FOR KOSZUL ALGEBRAS","year":2007,"lang":"en","type":"article","venue":"The Quarterly Journal of Mathematics","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":48,"is_retracted":false,"has_abstract":true,"ca_institutions":"The Scarborough Hospital; University of Toronto","funders":"","keywords":"Multiplicative function; Library science; Mathematics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001893433,0.0002390031,0.0004997121,0.0001014452,0.000185858,0.00006162711,0.0007236226,0.0001201851,0.00003556788],"category_scores_gemma":[0.0004422359,0.000136227,0.000333838,0.0001366031,0.0001179831,0.0001250867,0.00002289158,0.0003071693,0.000003484139],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005661073,"about_ca_system_score_gemma":0.00005750995,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001952586,"about_ca_topic_score_gemma":0.000004704877,"domain_scores_codex":[0.9979358,0.00005021232,0.001044614,0.0001222484,0.0004971057,0.0003500233],"domain_scores_gemma":[0.9950922,0.002686863,0.001198856,0.0004532555,0.0004489827,0.0001198832],"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":[0.00009477758,0.000129377,0.000008477748,0.0001116214,0.0002042378,0.000004766669,0.01517237,0.000004489221,0.0004148769,0.9748212,0.001461285,0.007572587],"study_design_scores_gemma":[0.0009615733,0.0006288028,0.00006461543,0.00006057361,0.0001650639,0.0001984953,0.007607244,0.0001375901,0.00202096,0.9875766,0.0004175361,0.0001609176],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7369888,0.0002608944,0.2608203,0.0003076588,0.0007614122,0.0005293422,0.00000504063,0.00002930529,0.0002972888],"genre_scores_gemma":[0.9199172,0.000006344925,0.07913998,0.00007980412,0.0007130505,0.000006425916,4.800631e-7,0.00004637235,0.00009034996],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1829284,"threshold_uncertainty_score":0.5555174,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03822447967039452,"score_gpt":0.3292165441872883,"score_spread":0.2909920645168937,"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."}}