{"id":"W4226320327","doi":"10.4064/cm8893-5-2023","title":"Sharp estimates for the hypergeometric functions related to root systems of type $A$ and of rank $1$","year":2023,"lang":"en","type":"article","venue":"Colloquium Mathematicum","topic":"Hermeneutics and Narrative Identity","field":"Arts and Humanities","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Laurentian University","funders":"Centre National de la Recherche Scientifique; Agence Nationale de la Recherche; Centre Henri Lebesgue","keywords":"Conjecture; Mathematics; Hypergeometric function; Rank (graph theory); Invariant (physics); Pure mathematics; Basic hypergeometric series; Hypergeometric distribution; Type (biology); Combinatorics; Mathematical physics; Geology","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":[0.0004280673,0.00008639166,0.000249728,0.0002212843,0.0002182502,0.00006997099,0.0001114296,0.00002851896,0.0002787072],"category_scores_gemma":[0.0005327238,0.0000570446,0.00005096611,0.0004960271,0.0001044092,0.00006395741,0.00005380395,0.00003619964,0.00006310052],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001020651,"about_ca_system_score_gemma":0.00002627655,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009551484,"about_ca_topic_score_gemma":0.0002202181,"domain_scores_codex":[0.9992809,0.00001588299,0.0003255335,0.000109606,0.0001351408,0.0001329529],"domain_scores_gemma":[0.9987267,0.0005852724,0.00009859209,0.0001808967,0.0003729916,0.00003556566],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0001225685,0.0003404439,0.003078172,0.003611424,0.0009084304,0.000002387899,0.02553337,0.001204177,0.006969888,0.7672274,0.1903402,0.0006616162],"study_design_scores_gemma":[0.007127334,0.005187807,0.05508499,0.00287385,0.003463897,0.00003820876,0.07859711,0.3283149,0.007234751,0.1106832,0.3988947,0.002499248],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9899285,0.0006514894,0.0001303289,0.0003507352,0.001213643,0.001189907,0.0001968456,0.00006479419,0.0062737],"genre_scores_gemma":[0.9787688,0.00001343582,0.00002837227,0.000006846129,0.00003920122,0.00008866264,0.000007903837,0.00001510938,0.02103172],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6565441,"threshold_uncertainty_score":0.3051649,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04949629569349306,"score_gpt":0.2746968053041815,"score_spread":0.2252005096106884,"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."}}