{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001703296,0.001310111,0.001233391,0.001174617,0.00144864,0.002746489,0.001053553,0.0007262788,0.008941318],"category_scores_gemma":[0.006934027,0.0005516154,0.0004506742,0.002226468,0.002308779,0.004862646,0.002643474,0.003748594,0.004077851],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001560339,"about_ca_system_score_gemma":0.0007071786,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005705375,"about_ca_topic_score_gemma":0.0004347521,"domain_scores_codex":[0.9986118,0.0004980883,0.00007008349,0.0003702495,0.0003520776,0.00009753318],"domain_scores_gemma":[0.997665,0.0009416937,0.0002203349,0.0003301089,0.0006274472,0.0002153298],"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":[0.0001131575,0.00002943345,0.0003223321,0.0002467883,0.00003069565,0.0001260218,0.0007273519,0.001325933,0.001901557,0.8582488,0.1057687,0.03115916],"study_design_scores_gemma":[0.00004887843,0.0001163661,0.0006870174,0.0001338788,0.00005411659,0.0005224455,0.0002143072,0.003134655,0.005547453,0.5365554,0.4528864,0.0000991113],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09859961,0.06864054,0.2783579,0.2143456,0.1130197,0.00009759248,0.001403845,0.001528585,0.2240066],"genre_scores_gemma":[0.63933,0.02774545,0.03101698,0.009473699,0.06636517,0.0001415958,0.001283456,0.001125473,0.2235182],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008941318,"threshold_uncertainty_score":0.0299117,"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."}}