{"id":"W2521563500","doi":"10.1007/s00009-017-0948-0","title":"A Laplace-Type Representation of the Generalized Spherical Functions Associated with the Root Systems of Type A","year":2017,"lang":"en","type":"preprint","venue":"Mediterranean Journal of Mathematics","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"Laurentian University","funders":"","keywords":"Type (biology); Laplace transform; Mathematics; Representation (politics); Trigonometry; Expression (computer science); Operator (biology); Trigonometric functions; Pure mathematics; Mathematical analysis; Root (linguistics); Computer science; Geometry","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":[0.001484388,0.0003116792,0.001240268,0.0001135447,0.0001591808,0.00006054958,0.001068052,0.0002548301,0.00006426832],"category_scores_gemma":[0.0054983,0.0001533182,0.0003720399,0.0003743562,0.0003223928,0.00009430318,0.0002776379,0.0009364799,0.000001688023],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008321191,"about_ca_system_score_gemma":0.0003049491,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000805566,"about_ca_topic_score_gemma":0.0000382071,"domain_scores_codex":[0.9966553,0.0003815072,0.001359745,0.0001728292,0.001214662,0.0002159126],"domain_scores_gemma":[0.989418,0.001454848,0.006381405,0.001205199,0.001458539,0.00008201952],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.007745126,0.01956898,0.03486444,0.05443453,0.05053405,0.0007259652,0.2119576,0.1649428,0.0199881,0.05040609,0.3770871,0.00774514],"study_design_scores_gemma":[0.02068938,0.006539125,0.009308979,0.06616185,0.02380172,0.003263012,0.0447132,0.05733612,0.01123479,0.749381,0.003646351,0.003924493],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9721929,0.0007198108,0.0226578,0.0004761801,0.002719732,0.0006886644,0.00003986017,0.00001846946,0.0004865378],"genre_scores_gemma":[0.9910293,0.00005804902,0.006659352,0.00001239954,0.0005424321,0.000009169619,0.00001066502,0.00007170578,0.001606986],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6989749,"threshold_uncertainty_score":0.6582376,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09325782678734927,"score_gpt":0.3372785421108512,"score_spread":0.2440207153235019,"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."}}