{"id":"W3013350763","doi":"","title":"A simplified proof of the reduction point crossing sign formula for Verma modules","year":2020,"lang":"en","type":"article","venue":"Algebra and Discrete Mathematics","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Windsor","funders":"","keywords":"Mathematics; Hermitian matrix; Invariant (physics); Unitary state; Verma module; Pure mathematics; Sign (mathematics); (g,K)-module; Algebra over a field; Mathematical analysis; Lie algebra; Mathematical physics; Affine Lie algebra","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":[0.002691959,0.001936365,0.001544953,0.003286703,0.001770521,0.003013329,0.002492239,0.001931458,0.03214615],"category_scores_gemma":[0.007692552,0.0008417631,0.002733356,0.002529078,0.003974251,0.007807632,0.004929565,0.008233796,0.009372678],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002135747,"about_ca_system_score_gemma":0.001319888,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002557276,"about_ca_topic_score_gemma":0.00231865,"domain_scores_codex":[0.9977842,0.0003588436,0.0001419011,0.0003493951,0.001148482,0.0002171133],"domain_scores_gemma":[0.9976959,0.0007888291,0.000138339,0.0004180665,0.0008252668,0.0001336226],"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":[0.00003395817,0.0000422811,0.000210807,0.0002228934,0.00002426666,0.0003563265,0.0003174138,0.001196834,0.002529891,0.9600096,0.01590851,0.01914722],"study_design_scores_gemma":[0.00001912612,0.00002866629,0.000478983,0.00006716446,0.00003230608,0.0003054322,0.00006469667,0.00532059,0.001574985,0.9603239,0.03174414,0.00004003461],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02322419,0.003941739,0.6955554,0.01416748,0.005798467,0.0003592297,0.002275191,0.001670591,0.2530078],"genre_scores_gemma":[0.5547845,0.006622724,0.3152327,0.01030306,0.005959386,0.0008950414,0.002630737,0.002243929,0.101328],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.03214615,"threshold_uncertainty_score":0.1075396,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0392782227896963,"score_gpt":0.2974086147531312,"score_spread":0.2581303919634349,"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."}}