{"id":"W3095213287","doi":"10.1142/s0219025721500193","title":"On operator-valued infinitesimal Boolean and monotone independence","year":2021,"lang":"en","type":"article","venue":"Infinite Dimensional Analysis Quantum Probability and Related Topics","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University; University of Waterloo","funders":"Consejo Nacional de Ciencia y Tecnología","keywords":"Mathematics; Infinitesimal; Stone's representation theorem for Boolean algebras; Complete Boolean algebra; Two-element Boolean algebra; Monotone polygon; Discrete mathematics; Independence (probability theory); Parity function; Logical matrix; Pure mathematics; Boolean function; Algebra over a field; Boolean expression; Group (periodic table); Mathematical analysis; Algebra representation; Statistics","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":[0.0006273435,0.0002344805,0.0005176993,0.0001676474,0.0003259558,0.00009225491,0.0001005988,0.0002612859,0.0001975409],"category_scores_gemma":[0.000636614,0.0001897393,0.0001880174,0.0009980719,0.0001800971,0.0001118728,0.0001453025,0.0004441858,0.00001495676],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002585018,"about_ca_system_score_gemma":0.00008179748,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003690285,"about_ca_topic_score_gemma":0.0000367182,"domain_scores_codex":[0.9979544,0.0002111904,0.0006324003,0.0005834865,0.0003866655,0.0002318586],"domain_scores_gemma":[0.9980946,0.0008236991,0.0001666587,0.0004667236,0.0002850822,0.0001632297],"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":[0.00008536353,0.0005052734,0.005860913,0.00009540705,0.0009551368,0.00004131615,0.0004124177,0.001404227,0.00023597,0.9893968,0.000107706,0.0008995416],"study_design_scores_gemma":[0.001332168,0.0001049314,0.01111872,0.00005556589,0.001209634,0.00004123262,0.0001047382,0.04743982,0.0003362564,0.9371253,0.0007390155,0.0003926049],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9961321,0.000447018,0.0003549978,0.001619368,0.00004345696,0.0002326323,0.00002684703,0.0000625903,0.001080925],"genre_scores_gemma":[0.9955207,0.0001588211,0.00317131,0.0003148233,0.00002654614,0.0000251368,0.00005027757,0.00001374938,0.0007186553],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05227142,"threshold_uncertainty_score":0.7737343,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02659049761500897,"score_gpt":0.286536710726381,"score_spread":0.259946213111372,"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."}}