{"id":"W4289024158","doi":"","title":"Multiplicatively dependent vectors with coordinates algebraic numbers In memory of Professor Alan Baker","year":2019,"lang":"en","type":"preprint","venue":"HAL (Le Centre pour la Communication Scientifique Directe)","topic":"Aerospace Engineering and Control Systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Algebraic number; Algebra over a field; Mathematics; Arithmetic; Pure mathematics; 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"],"consensus_categories":[],"category_scores_codex":[0.001792066,0.000393613,0.0006034431,0.0001947744,0.00004969732,0.00007544429,0.0007450529,0.000295842,0.00002459236],"category_scores_gemma":[0.0002241353,0.0003877662,0.0001216792,0.0002905498,0.00009617105,0.00008652701,0.000302455,0.0007193863,0.00002431736],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001853691,"about_ca_system_score_gemma":0.0001133171,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001262817,"about_ca_topic_score_gemma":0.002281799,"domain_scores_codex":[0.9972922,0.0009844468,0.0005101588,0.0005098634,0.0003396854,0.0003636576],"domain_scores_gemma":[0.9969987,0.0006527752,0.0002759655,0.001407068,0.0005548827,0.0001105614],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000208045,0.001940401,0.1963426,0.01005343,0.002280229,0.00004709675,0.0978099,0.5690176,0.07074541,0.02201264,0.002680557,0.02686203],"study_design_scores_gemma":[0.006958295,0.000004740379,0.1217245,0.02022067,0.0002424903,0.00003250011,0.002672799,0.5941097,0.2472554,0.0005716498,0.002802836,0.003404415],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9184219,0.001699884,0.062123,0.0008341708,0.0003981584,0.001246711,0.00007091914,0.0004935114,0.01471172],"genre_scores_gemma":[0.992505,0.0001023525,0.003191293,0.000006168678,0.00001363009,0.000214429,0.000111413,0.00009607959,0.003759616],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.17651,"threshold_uncertainty_score":0.9998574,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005763319766121116,"score_gpt":0.1878421098078129,"score_spread":0.1820787900416917,"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."}}