{"id":"W3209632476","doi":"10.2478/udt-2021-0002","title":"Extreme Values of Euler-Kronecker Constants","year":2021,"lang":"en","type":"article","venue":"Uniform distribution theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Kronecker delta; Mathematics; Discriminant; Combinatorics; Euler's formula; Euler number (physics); Log-log plot; Binary logarithm; Zero (linguistics); Field (mathematics); Constant (computer programming); Mathematical analysis; Physics; Pure mathematics; Backward Euler method; Euler equations; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001713541,0.0001592217,0.0003203063,0.00004903055,0.0001090729,0.00002347402,0.0002275474,0.0001098814,0.004659304],"category_scores_gemma":[0.00279303,0.0001437537,0.0001577157,0.0003710441,0.0003967973,0.0001557265,0.0001513113,0.000194073,0.0001618837],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001403431,"about_ca_system_score_gemma":0.0002291516,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001931315,"about_ca_topic_score_gemma":0.000003381138,"domain_scores_codex":[0.9981263,0.0003546384,0.0004548704,0.0002433991,0.0004653537,0.0003554515],"domain_scores_gemma":[0.99744,0.001171725,0.0001685818,0.0005859149,0.0005133786,0.0001203503],"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":[0.00008501177,0.0002073137,0.0005889854,0.00007665603,0.00008647369,0.0000271519,0.0001517393,0.000001236187,0.001038027,0.9938492,0.001756225,0.002131996],"study_design_scores_gemma":[0.0005296404,0.0000294453,0.0002270336,0.00008885081,0.00006862365,0.00003971791,0.001957903,0.0001462321,0.03711359,0.9567683,0.002866485,0.0001642325],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4586186,0.0007742232,0.3922038,0.0002626085,0.0003369035,0.0004130664,0.00153181,0.000174088,0.145685],"genre_scores_gemma":[0.992693,0.00006585576,0.00111262,0.00002091293,0.00004713495,0.000005799127,0.0002677606,0.000021717,0.00576522],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5340744,"threshold_uncertainty_score":0.9962506,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06726412899835386,"score_gpt":0.3297811285375025,"score_spread":0.2625169995391486,"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."}}