{"id":"W143048750","doi":"10.1007/978-3-0348-8223-1_18","title":"The Lehmer Problem on the Euler Totient: A Pendora’s Box of Unsolvable Problems","year":2002,"lang":"en","type":"book-chapter","venue":"Birkhäuser Basel eBooks","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Euler's totient function; Euler's formula; Computer science; Mathematics; Arithmetic; Mathematical analysis","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","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001794837,0.0008316193,0.0008948197,0.0001722102,0.0007303887,0.0000881651,0.001173423,0.0004661235,0.001803237],"category_scores_gemma":[0.0003160903,0.0004757554,0.0005835624,0.00003552993,0.0007420793,0.00005382969,0.0002082894,0.001008158,0.0007397659],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001740181,"about_ca_system_score_gemma":0.0001827588,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009225992,"about_ca_topic_score_gemma":0.000043553,"domain_scores_codex":[0.9963583,0.0001927542,0.001228446,0.0005799981,0.001027834,0.0006126192],"domain_scores_gemma":[0.9932644,0.003003788,0.001181855,0.00207948,0.000327378,0.0001431082],"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":[0.00005263435,0.0001227256,3.318079e-7,0.0006336538,0.0002659679,0.00001234,0.002266388,0.000005417978,0.00002029098,0.9301498,0.0651217,0.001348779],"study_design_scores_gemma":[0.0002646899,0.0001253295,1.027102e-7,0.0008144848,0.0001767846,0.00001254274,0.00005729025,0.00003270119,0.000238805,0.5084579,0.4894685,0.0003508475],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.0001243053,0.0003887264,0.0002170844,0.0004016828,0.0003905118,0.002247023,0.00008639047,0.0001786827,0.9959656],"genre_scores_gemma":[0.003419725,0.00008113177,0.001088434,0.0002463918,0.0002131855,0.0002255576,0.000007033112,0.0003145318,0.994404],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.4243468,"threshold_uncertainty_score":0.9997694,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07384623848894113,"score_gpt":0.2430294545794192,"score_spread":0.169183216090478,"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."}}