{"id":"W3198589245","doi":"10.1093/imrn/rnac183","title":"Rank of Matrices with Entries from a Multiplicative Group","year":2022,"lang":"en","type":"article","venue":"International Mathematics Research Notices","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Multiplicative function; Rank (graph theory); Combinatorics; Group (periodic table); Diagonal; Multiplicative group; Geometry; 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":[0.001270425,0.0006949655,0.0006262533,0.001875751,0.0008156589,0.002475535,0.0007492301,0.0006287259,0.005748409],"category_scores_gemma":[0.008880395,0.0003143744,0.0003643463,0.000708884,0.002186783,0.002630992,0.001948335,0.001182614,0.00105496],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004364203,"about_ca_system_score_gemma":0.0003648858,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002857761,"about_ca_topic_score_gemma":0.0002729797,"domain_scores_codex":[0.9983171,0.0003884626,0.00009096326,0.0003010114,0.0006579002,0.000244658],"domain_scores_gemma":[0.9902638,0.005066427,0.001433306,0.001025278,0.001147768,0.001063379],"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":[0.0005090592,0.0001565193,0.004250263,0.0002366057,0.00005383271,0.0003283602,0.0007132808,0.0220383,0.02536574,0.921257,0.002847641,0.02224333],"study_design_scores_gemma":[0.00006195781,0.0003356862,0.002316105,0.00005658365,0.00003585244,0.0006106002,0.000317639,0.0678841,0.02026123,0.9015145,0.006523048,0.0000825939],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8087239,0.0006341214,0.1573645,0.0007989939,0.0001164704,0.00004890313,0.0005151458,0.0003534796,0.03144457],"genre_scores_gemma":[0.9841141,0.000233866,0.01074613,0.0001064315,0.0001741457,0.0000423185,0.0002575251,0.00004029162,0.004285292],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005748409,"threshold_uncertainty_score":0.01923037,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09204157074507788,"score_gpt":0.399452728671909,"score_spread":0.3074111579268312,"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."}}