{"id":"W2963269671","doi":"10.1512/iumj.2008.57.3285","title":"On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution","year":2008,"lang":"en","type":"article","venue":"Indiana University Mathematics Journal","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":85,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Homomorphism; Multiplicative function; Semigroup; Pure mathematics; Convolution (computer science); Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003467737,0.0001679725,0.0003667422,0.0003463251,0.000436081,0.00001791127,0.0005160403,0.00007649539,0.00009401334],"category_scores_gemma":[0.0002911784,0.0001430017,0.000115492,0.0005663605,0.0001323433,0.0001370339,0.00007437546,0.0002793268,0.00003137257],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000197281,"about_ca_system_score_gemma":0.0001184187,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002515757,"about_ca_topic_score_gemma":0.00003311885,"domain_scores_codex":[0.998781,0.00005719128,0.0003101887,0.0001813661,0.0004310136,0.0002392996],"domain_scores_gemma":[0.9978484,0.000636921,0.0004960014,0.0005365852,0.0002739862,0.0002080917],"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":[0.001146867,0.002265584,0.0006436624,0.0003103616,0.0005672252,0.00062385,0.02205525,0.0005380795,0.002057522,0.8912072,0.07834688,0.0002375188],"study_design_scores_gemma":[0.02634646,0.003819997,0.004443284,0.002142709,0.001039654,0.00612068,0.02142252,0.003063218,0.01206355,0.901208,0.01609076,0.002239127],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8948797,0.00001708967,0.08725276,0.0004407353,0.00002309741,0.0005871042,0.00006344778,0.00005130294,0.01668477],"genre_scores_gemma":[0.8333617,0.00007106581,0.1640181,0.00003947223,0.00005403962,0.000003008347,0.000002723995,0.00003212315,0.002417777],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07676535,"threshold_uncertainty_score":0.5831439,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03403075408774042,"score_gpt":0.2474128436754331,"score_spread":0.2133820895876927,"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."}}