{"id":"W2074364431","doi":"10.1090/s0002-9947-2011-05507-8","title":"Representation of unity by binary forms","year":2011,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Diophantine equation; Binary number; Discriminant; Degree (music); Logarithm; Pure mathematics; Root of unity; Mathematical analysis; Combinatorics; Discrete mathematics; Arithmetic","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009668349,0.0008806222,0.0005817658,0.00179741,0.001675739,0.004212419,0.0009131238,0.0007107869,0.02198655],"category_scores_gemma":[0.003222026,0.0003851569,0.0008921368,0.00161361,0.002853421,0.005310412,0.003710489,0.002059503,0.00874956],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00154073,"about_ca_system_score_gemma":0.0007534627,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001656397,"about_ca_topic_score_gemma":0.001273368,"domain_scores_codex":[0.9984824,0.0003276577,0.0001086506,0.0003320409,0.0005051362,0.0002440571],"domain_scores_gemma":[0.99937,0.0001550596,0.00007847563,0.00014665,0.0001763899,0.00007330495],"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":[0.00002285558,0.000006816777,0.00004919237,0.00003212253,0.000002022851,0.00004798446,0.0003088385,0.0002649502,0.0004729012,0.9822122,0.002781277,0.01379883],"study_design_scores_gemma":[0.00001613505,0.00002901197,0.0001059672,0.00004443992,0.000008760743,0.0001955995,0.000170677,0.005029941,0.001870068,0.9199241,0.0725814,0.00002376684],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04758451,0.002039459,0.5148146,0.001655231,0.001926182,0.0001425526,0.000628383,0.002222339,0.4289868],"genre_scores_gemma":[0.7122961,0.002178309,0.1580985,0.0008857303,0.001279843,0.0001993202,0.001039434,0.001326117,0.1226965],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02198655,"threshold_uncertainty_score":0.07355231,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04170913787954517,"score_gpt":0.2984584682056036,"score_spread":0.2567493303260584,"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."}}