{"id":"W1972907494","doi":"10.7169/facm/1229624653","title":"Two exceptional classes of real numbers","year":2008,"lang":"en","type":"article","venue":"Functiones et Approximatio Commentarii Mathematici","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Queen's University","keywords":"Class (philosophy); Transcendental number; Mathematics; Assertion; Conjecture; Real number; Modulo; Natural number; Perspective (graphical); Algebraic number; Rational point; Set (abstract data type); Point (geometry); Frame (networking); Distribution (mathematics); Discrete mathematics; Combinatorics; Pure mathematics; Computer science; Artificial intelligence; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001218045,0.0003290153,0.0006395311,0.0002328632,0.0002918553,0.00003267269,0.0003989513,0.0000977698,0.003547349],"category_scores_gemma":[0.0003837342,0.0002945699,0.0002409321,0.0004314207,0.0003768837,0.0003939641,0.0002026944,0.0003151653,0.0002517612],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000190248,"about_ca_system_score_gemma":0.0001516163,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002367561,"about_ca_topic_score_gemma":0.0001007253,"domain_scores_codex":[0.9969255,0.0002979747,0.0009768843,0.0003532475,0.001034453,0.0004118879],"domain_scores_gemma":[0.9965402,0.001803594,0.0004928877,0.0007366564,0.000285106,0.0001415793],"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":[0.0001366394,0.001390629,0.004705733,0.0006433523,0.0003850332,0.00001059697,0.005275507,0.00003768529,0.0008337682,0.9391573,0.04723607,0.0001876865],"study_design_scores_gemma":[0.002803021,0.0002085166,0.001183362,0.0002169635,0.0002083666,0.0003683305,0.0047455,0.00419717,0.00246776,0.9815187,0.00147879,0.0006034927],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7288848,0.00002257413,0.1156409,0.001707765,0.0002694824,0.001182861,0.00005160475,0.0003545471,0.1518855],"genre_scores_gemma":[0.8610718,0.00005658938,0.1300712,0.0003557214,0.0001775635,0.0002448018,0.0001254951,0.0001102059,0.00778663],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1440989,"threshold_uncertainty_score":0.9999506,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1257733802989782,"score_gpt":0.375540840539007,"score_spread":0.2497674602400288,"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."}}