{"id":"W2905704646","doi":"10.4007/annals.2020.191.2.6","title":"Singularity of random Bernoulli matrices","year":2020,"lang":"en","type":"preprint","venue":"Annals of Mathematics","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Alberta","keywords":"Bernoulli's principle; Singularity; Mathematics; Random matrix; Combinatorics; Matrix (chemical analysis); Pure mathematics; Discrete mathematics; Physics; Mathematical analysis; Quantum mechanics; Materials science","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0009503865,0.000388261,0.001652172,0.000156206,0.00005464068,0.00004216988,0.00085741,0.0003576577,0.0001056233],"category_scores_gemma":[0.001116269,0.0003424673,0.0006950999,0.0002922739,0.0001430574,0.00005288213,0.00063063,0.0004421287,0.00001942776],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000008782622,"about_ca_system_score_gemma":0.0001205709,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005446962,"about_ca_topic_score_gemma":0.00000370165,"domain_scores_codex":[0.9969949,0.0000744712,0.001647118,0.000366163,0.0006539336,0.0002634842],"domain_scores_gemma":[0.9944239,0.001471486,0.002370994,0.001092893,0.0005176748,0.0001230045],"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":[0.0003061315,0.005123814,0.0001893179,0.07354057,0.002287123,0.00001630955,0.01696084,0.0002576854,0.001921475,0.8446075,0.05177868,0.003010586],"study_design_scores_gemma":[0.0009283321,0.00005490968,0.00002147058,0.0008522763,0.0004528695,0.000004058501,0.000333354,0.001948527,0.01006086,0.9833008,0.001706774,0.0003357408],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6834311,0.007952008,0.254171,0.01430203,0.0005844021,0.00641713,0.001948267,0.0006030684,0.03059101],"genre_scores_gemma":[0.5186183,0.00379028,0.4760881,0.0002054739,0.000404429,0.0001794799,0.00008957456,0.0001912936,0.000433085],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2219171,"threshold_uncertainty_score":0.9999027,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2048155364411196,"score_gpt":0.4048277762635193,"score_spread":0.2000122398223997,"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."}}