{"id":"W2615582274","doi":"10.1515/ms-2016-0280","title":"Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials","year":2017,"lang":"en","type":"article","venue":"Mathematica Slovaca","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Antisymmetric relation; Exponential function; Symmetric function; Fourier transform; Lattice (music); Pure mathematics; Mathematical analysis; Mathematical physics; Physics","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":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.001096157,0.0004240162,0.0008685633,0.0004903296,0.001397417,0.0006988172,0.0004169299,0.0002496955,0.0007726651],"category_scores_gemma":[0.004103042,0.0003530349,0.0001401239,0.0003628147,0.0003356505,0.0004288263,0.0005063714,0.0002909806,0.0001415033],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000331502,"about_ca_system_score_gemma":0.00006042146,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005016595,"about_ca_topic_score_gemma":0.0000253999,"domain_scores_codex":[0.9975354,0.00006256743,0.0008270939,0.0005852149,0.0004373238,0.0005523707],"domain_scores_gemma":[0.9959678,0.001752617,0.0005175003,0.00130379,0.0001147032,0.0003435817],"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":[0.00004073902,0.0003813567,0.001121862,0.0008121232,0.0002287723,0.00001159095,0.0001768655,2.005342e-7,0.001089056,0.9735624,0.0141278,0.008447255],"study_design_scores_gemma":[0.001844527,0.0001900698,0.005503484,0.0003342637,0.0006385128,0.0003272517,0.0002536293,0.002658593,0.000517079,0.978951,0.007900424,0.0008811771],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7910522,0.001114612,0.1077748,0.001182537,0.000879501,0.001431265,0.0001207344,0.0003309054,0.09611344],"genre_scores_gemma":[0.9020163,0.0001367988,0.09013999,0.00009675688,0.0005826963,0.0001661991,0.000009971704,0.0001227338,0.006728608],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.110964,"threshold_uncertainty_score":0.9999026,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05521825993349409,"score_gpt":0.3038164119455011,"score_spread":0.2485981520120071,"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."}}