{"id":"W4386705567","doi":"10.4310/mrl.2023.v30.n2.a7","title":"On the distribution of multiplicatively dependent vectors","year":2023,"lang":"en","type":"article","venue":"Mathematical Research Letters","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs; Basic and Applied Basic Research Foundation of Guangdong Province; Macquarie University","keywords":"Mathematics; Distribution (mathematics); Pure mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":["metaresearch","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00449808,0.0001613838,0.000277606,0.0001711602,0.0002252902,0.00006196943,0.0004726574,0.00007778756,0.0007013311],"category_scores_gemma":[0.01966091,0.00009166941,0.0001318535,0.0009565388,0.0003879511,0.00007230377,0.0001391834,0.0004822738,0.001591492],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001059102,"about_ca_system_score_gemma":0.00002689552,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003653858,"about_ca_topic_score_gemma":0.000001024484,"domain_scores_codex":[0.9966634,0.0004750861,0.0005477067,0.0002653427,0.00157563,0.0004728391],"domain_scores_gemma":[0.9869938,0.01193406,0.0001172652,0.0006062771,0.0002369163,0.0001117206],"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":[0.00002028896,0.0001969949,0.000004195051,0.0002114262,0.00002308119,0.000002260254,0.0005776615,0.000004385833,0.005123034,0.9509249,0.04261896,0.0002928394],"study_design_scores_gemma":[0.0001842138,0.0000765643,0.0001267826,0.0001799708,0.00000803592,0.000001808964,0.000476704,0.01818536,0.01804668,0.9623802,0.0002293026,0.0001043371],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8988317,0.000002194891,0.0729805,0.01955585,0.00003514691,0.001191041,0.00003590299,0.0001974091,0.007170251],"genre_scores_gemma":[0.9964684,0.00000410973,0.002049359,0.0002123868,0.00004019468,0.0003676903,0.00002512973,0.0000316632,0.0008011112],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09763665,"threshold_uncertainty_score":0.9991859,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2288146839171075,"score_gpt":0.4320053537581006,"score_spread":0.2031906698409931,"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."}}