{"id":"W4402687120","doi":"10.1017/s096354832400021x","title":"The full rank condition for sparse random matrices","year":2024,"lang":"en","type":"article","venue":"Combinatorics Probability Computing","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Nederlandse Organisatie voor Wetenschappelijk Onderzoek; Deutsche Forschungsgemeinschaft","keywords":"Rank (graph theory); Mathematics; Statistics; Combinatorics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003401702,0.0008396655,0.001324055,0.002002913,0.0009552995,0.001989663,0.001039363,0.001649778,0.01471395],"category_scores_gemma":[0.03839704,0.0007287581,0.0007220543,0.001193096,0.003179212,0.004681203,0.002197045,0.002625938,0.002980046],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008298224,"about_ca_system_score_gemma":0.001758581,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009888748,"about_ca_topic_score_gemma":0.0009413644,"domain_scores_codex":[0.9952054,0.001539035,0.0003285419,0.000719637,0.001340815,0.0008666273],"domain_scores_gemma":[0.9626445,0.02206185,0.003142601,0.003779923,0.006537999,0.001833167],"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":[0.0004232524,0.0001315687,0.001878242,0.0003543019,0.00005597446,0.0007945723,0.000275055,0.03566646,0.01657424,0.9164274,0.01268226,0.01473674],"study_design_scores_gemma":[0.000161181,0.0001886317,0.001350687,0.0001109037,0.0000234669,0.0007121798,0.0001965539,0.2020929,0.009752269,0.7798948,0.005426148,0.00009025634],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1888628,0.0008169552,0.7563683,0.004282873,0.0003929741,0.0002107036,0.00361406,0.001106528,0.04434491],"genre_scores_gemma":[0.951517,0.0005101525,0.03892355,0.0008787135,0.0006907146,0.00026696,0.001721876,0.0002048789,0.005286184],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01471395,"threshold_uncertainty_score":0.04922307,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04308626993844079,"score_gpt":0.3308651380438634,"score_spread":0.2877788681054226,"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."}}