{"id":"W2406959043","doi":"","title":"Some Identities Of Symmetry For Carlitz q-Bernoulli Polynomials Invariant Under S 4 .","year":2015,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Invariant (physics); Pure mathematics; Symmetry (geometry); Bernoulli's principle; Algebra over a field; Mathematical physics; Geometry; Physics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007700069,0.0002353899,0.0006394011,0.0001429361,0.00007347313,0.00006082217,0.0003811202,0.0001444636,0.00002687034],"category_scores_gemma":[0.002147776,0.0002262343,0.0001729888,0.0001589423,0.0001923224,0.0005126626,0.0001857761,0.0001237736,0.00003601469],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001566684,"about_ca_system_score_gemma":0.0001464348,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003964558,"about_ca_topic_score_gemma":0.000007098642,"domain_scores_codex":[0.9981405,0.00007501637,0.0006860383,0.000256669,0.0004667436,0.0003750859],"domain_scores_gemma":[0.9973378,0.001251016,0.0003378337,0.0005618567,0.0003389714,0.0001725194],"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":[0.00002696024,0.0001958125,0.00006148871,0.0003780397,0.00009674869,0.000002975372,0.000573835,0.000003757087,0.0004007853,0.9849671,0.01328197,0.0000105271],"study_design_scores_gemma":[0.001408864,0.0001367646,0.00002052964,0.00009877165,0.0001086519,0.0000074302,0.001640032,0.00004548929,0.01020424,0.9859346,0.0001538811,0.0002407918],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9780455,0.00166551,0.005772541,0.0005043779,0.005058238,0.001551547,0.000113404,0.0003276161,0.006961329],"genre_scores_gemma":[0.9750362,0.00003429908,0.01685889,0.00008572551,0.00007981608,0.0001239587,0.0000104598,0.0000980438,0.007672585],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01312809,"threshold_uncertainty_score":0.9225566,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07598120615535635,"score_gpt":0.3334851002544522,"score_spread":0.2575038940990958,"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."}}