{"id":"W2884556464","doi":"10.4064/aa171204-9-4","title":"Sets generated by finite sets of algebraic numbers","year":2018,"lang":"en","type":"article","venue":"Acta Arithmetica","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Algebraic number; Distribution (mathematics); Finite set; Set (abstract data type); Discrete mathematics; Combinatorics; Pure mathematics; Algebra over a field; Mathematical analysis; Computer science","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":[0.002408101,0.0005974341,0.0007014705,0.00348264,0.00123938,0.004322137,0.001801802,0.0006404739,0.004569225],"category_scores_gemma":[0.01594887,0.0004153453,0.0006169654,0.002038104,0.003506698,0.004600161,0.001746918,0.001332139,0.0004535209],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001603031,"about_ca_system_score_gemma":0.0006199713,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005927735,"about_ca_topic_score_gemma":0.0003141878,"domain_scores_codex":[0.9979784,0.0006453914,0.00008315375,0.0003305573,0.0007245979,0.0002379138],"domain_scores_gemma":[0.9885921,0.008274633,0.001250885,0.000620143,0.000664009,0.0005983189],"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":[0.00004030368,0.00002170566,0.001065411,0.00003721013,0.00001604095,0.00009857781,0.0002683134,0.004639412,0.001110483,0.9885132,0.0003329503,0.00385636],"study_design_scores_gemma":[0.0000383368,0.00007444707,0.001517374,0.00005165885,0.00002384997,0.0004540253,0.0003357797,0.08498012,0.003440116,0.9058081,0.003238633,0.00003755864],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.699101,0.001108894,0.2679519,0.00127333,0.0001185745,0.00006860971,0.0004438032,0.000201674,0.02973211],"genre_scores_gemma":[0.9800273,0.0006275485,0.01313366,0.0001138046,0.0002744525,0.0001168498,0.0002728887,0.00004940205,0.005384095],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004569225,"threshold_uncertainty_score":0.01528561,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04531828308548306,"score_gpt":0.3484034039037707,"score_spread":0.3030851208182876,"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."}}