{"id":"W2404913692","doi":"10.4169/amer.math.monthly.120.01.048","title":"Transcendence of Generalized Euler Constants","year":2012,"lang":"en","type":"article","venue":"American Mathematical Monthly","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Transcendence (philosophy); Euler's formula; Mathematics; Euler number (physics); Pure mathematics; Mathematical analysis; Philosophy; Euler equations; Backward Euler method; Semi-implicit Euler method; Epistemology","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001050045,0.0002255455,0.0007436462,0.00009643412,0.00005175349,0.00001355424,0.0003842565,0.00005696971,0.001656139],"category_scores_gemma":[0.001367681,0.0001788128,0.0001979005,0.0004232103,0.001101415,0.0001510951,0.00007240038,0.0002034523,0.0002585169],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004767365,"about_ca_system_score_gemma":0.00004862972,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003329054,"about_ca_topic_score_gemma":0.000002765157,"domain_scores_codex":[0.9975399,0.000239795,0.0006265175,0.0002131677,0.0006926876,0.0006878786],"domain_scores_gemma":[0.9966823,0.001997556,0.0002467583,0.0006137982,0.0001130031,0.0003465349],"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":[0.00007017105,0.0006734343,0.002073736,0.0002090496,0.0001439567,0.000005691393,0.001566499,0.000001072152,0.001855719,0.9912909,0.001256233,0.0008535566],"study_design_scores_gemma":[0.0006271389,0.0001362007,0.0006659139,0.0001239022,0.0001544931,0.0000229282,0.001512201,0.0009260144,0.004974794,0.9900487,0.0004447889,0.0003629338],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6576147,0.0001806204,0.04744168,0.000422234,0.0001022894,0.0006436672,0.00005429613,0.0001873262,0.2933532],"genre_scores_gemma":[0.9423099,0.000007745231,0.05676952,0.00006891559,0.00006615416,0.00002926175,0.000001480098,0.00004625132,0.0007008045],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2926524,"threshold_uncertainty_score":0.9992565,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06492344431355893,"score_gpt":0.3629818898759438,"score_spread":0.2980584455623849,"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."}}